Appendix A
Second Quantization
The most remarkable fact about a system of fermions is that no more than one fermion can occupy a quantum particle state (Pauli’s exclusion principle). For bosons no such restriction applies. That is, any number of bosons can occupy the same state. We shall discuss the second quantization formalism in which creation and annihilation operators associated with each quantum state are used. This formalism is extremely useful in treating of many-boson and/or many-fermion system.
A.1 Boson Creation and Annihilation Oper- ators
The quantum state for a system of bosons (or fermions) can most conve- niently be represented by a set of occupation numbers where are the numbers of bosons (or fermions) occupying the quantum particle-states This representation is called the occupation number representation or simply the number representation. For bosons, the possible values for are zero, one, two, or any positive integers:
The many-boson state can best be represented by the distribution of particles (balls) in the states (boxes) as shown in Fig. A.1. Let us introduce operators (without prime) whose eigenvalues are given by 0, 1, 2, ... . Since Eq. (A.1) is meant for each and every state indepen-
333 334 APPENDIX A. SECOND QUANTIZATION
dently, we assume that
It is convenient to introduce complex dynamic variables and instead of directly dealing with the number operators We attach labels to the dynamic variables and associated with the states and assume that and satisfy the following Bose commutation rules:
Let us set which is Hermitean. Clearly, satisfy Eqs. (A.2). We shall show that has as eigenvalues all non-negative integers. Let be an eigenvalue of (dropping the suffix a) and an eigenket belonging to it. By definition
Now is the squared length of the ket and hence A.1. BOSON CREATION AND ANNIHILATION OPERATORS 335
Also by definition hence from Eqs. (A.5) and (A.6), we obtain
the case of equality occurring only if
Consider now We may use the following identities:
and obtain
Hence
Now if then is, according to Eq. (A.11), an eigenket of belonging to the eigenvalue Hence for non-zero is another eigenvalue. We can repeat the argument and deduce that, if is another eigenvalue of Continuing in this way, we obtain a series of eigenvalues which can terminate only with the value 0 because of inequality (A.7). By a similar process, we can show from the Hermitean conjugate of Eq. (A.10): that the eigenvalue of has no upper limit [Problem A.1.1]. Hence, the eigenvalues of are non- negative integers: 0,1,2,... . (q.e.d) Let be a normalized eigenket of belonging to the eigenvalue 0 so that
By multiplying all these kets together, we construct a normalized eigen- ket:
which is a simultaneous eigenket of all belonging to the eigenvalues zero. This ket is called the vacuum ket. It has the following property: 336 APPENDIX A. SECOND QUANTIZATION
Using the commutation rules (A.3) we obtain a relation (dropping suffix a) which may be proved by induction (Problem A.1.2). Multiply Eq. (A.15) by from the left and operate the result to Using Eq. (A.14) we obtain
indicating that is an eigenket belonging to the eigenvalue The square length of is
We see from Eq. (A.11) that is an eigenket of belonging to the eigenvalue Similarly, we can show from that is an eigenket of belonging to the eigenvalue Thus operator acting on the number eigenket, annihilates a particle while operator creates a particle. Therefore, and are called annihilation and creation operators, respectively. From Eqs. (A.16) and (A.17) we infer that if are any non-negative integers,
is a normalized simultaneous eigenket of all the belonging to the eigenvalues Various kets obtained by taking different form a complete set of kets all orthogonal to each other. Following Dirac [1], we postulate that the quantum states for N bosons can be represented by a symmetric ket
where S is the symmetrizing operator:
and P are permutation operators for the particle-indices (1,2,..., N). The ket in Eq. (A.19) is not normalized but A.2. OBSERVABLES 337 is a normalized ket representing the same state. Comparing Eqs. (A.21) and (A.18), we obtain
That is, unnormalized symmetric kets for the system can be constructed by applying N creation operators to the vacuum ket So far we have tacitly assumed that the total number of bosons is fixed at N' . If this number is not fixed but is variable, we can easily extend the theory to this case. Let us introduce a Hermitean operator N defined by
the summation extending over the whole set of boson states. Clearly, the operator N has eigenvalues 0,1,2,..., and the ket is an eigenket of N belonging to the eigenvalue N'. We may arrange kets in the order of N', i.e., zero-particle state, one-particle states, two-particle states, ... :
These kets are all orthogonal to each other, two kets referring to the same number of bosons are orthogonal as before, and two referring to different numbers of bosons are orthogonal because they have different eigenvalues N'. By normalizing the kets, we get a set of kets like (A.21) with no restriction on These kets form the basic kets in a representation where are diagonal.
Problem A.1.1. (a) Show (twice) that by taking the Hermitian-conjugation of Eq. (A.10) and also by using Eqs. (A.9). (b) Use this relation and obtain a series of eigenvalues where is an eigenvalue of Problem A.1.2. Prove Eq. (A.15) by mathematical induction. Hint: use Eqs. (A.9).
A. 2 Observables We wish to express observable physical quantities (observables) for the system of identical bosons in terms of and These observables are by postulate symmetric functions of the boson variables. 338 APPENDIX A. SECOND QUANTIZATION
An observable may be written in the form:
where is a function of the dynamic variables of the boson, that of the dynamic variables of the and bosons, and so on. We take Since acts only on the ket of the boson, we have
The matrix element does not depend on the particle index Summing Eq. (A.26) over all and applying operator S to the result, we obtain
Since Y is symmetric, we can replace SY by YS for the lhs. After straight- forward calculations, we obtain, from Eq. (A.27),
Using the commutation rules and the property (A.14) we can show that A.3. FERMIONS CREATION AND ANNIHILATION OPERATORS 339
(Problem A.2.1). Using this relation, we obtain from Eq. (A.28)
Since the kets form a complete set, we obtain
In a similar manner Z in Eq. (A.25) can be expressed by [Problem A.2.2]
Problem A.2.1. Prove Eq. (A.29). Hint: Start with cases of one- and two- particle-state kets. Problem A.2.2. Prove Eq. (A.32) by following those steps similar to (A.27)- (A.31).
A.3 Fermions Creation and Annihilation Op- erators
In this section we treat a system of identical fermions in a parallel manner. The quantum states for fermions, by postulate, are represented by anti- symmetric kets:
where is the antisymmetrizing operator, with being +1 or – 1 according to whether P is even or odd. Each antisymmetric ket in Eq. (A.34) is charac- terized such that it changes its sign if an odd permutation of particle indices 340 APPENDIX A. SECOND QUANTIZATION
is applied to it, and the fermion states are all different. Just as for a boson system, we can introduce observables each with eigenvalues 0 or 1, representing the number of fermions in the states respectively. The many-fermion occupation-number can be represented as in Fig. A.2. We can also introduce a set of linear operators one pair for each state satisfying the Fermi anticommutation rules:
The number of fermions in the state is again represented by
Using Eqs. (A.36), we obtain
If an eigenket of belonging to the eigenvalue is denoted by Eq. (A.38) yields
Since we obtain meaning that the eigenvalues are either 0 or 1 as required: A.4. HEISENBERG EQUATION OF MOTION 341
Similarly to the case of bosons, we can show that
which is normalized to unity. Observables describing the system of fermions can be expressed in terms of operators and and the results have the same form Eqs. (A.31) and (A.32) as for the case of bosons. In summary both states and observables for a system of identical particles can be expressed in terms of creation and annihilation operators. This formal- ism, called the second quantization formalism, has some notable advantages over the usual Schrödinger formalism. First, the permutation-symmetry property of the quantum particles is represented simply in the form of Bose commutation (or Fermi anticommutation) rules. Second, observables in sec- ond quantization are defined for an arbitrary number of particles so that the formalism may apply to systems in which the number of particles is not fixed, but variable. Third, and most importantly, all relevant quantities (states and observables) can be defined referring only to the single-particle states. This property allows one to describe the motion of the many-body system in the 3D space. This is a natural description since all particles in nature move in 3D. In fact, relativistic quantum field theory can be developed only in second quantization.
A.4 Heisenberg Equation of Motion
In the Schrödinger Picture (SP), the energy eigenvalue equation is where H is the Hamiltonian and E the eigenvalue. In the position represen- tation this equation is written as where is the wave function for the system. We consider a one-dimensional motion for conceptional and notational simplicity. [For a three-dimensional motion, should be replaced by If the num- ber of electrons N is large, the wave unction contains many electron vari- ables This complexity needed in dealing with many electron 342 APPENDIX A. SECOND QUANTIZATION
variables can be avoided if we use the second quantization formulation and the Heisenberg Picture (HP), which will be shown in this section. If the Hamiltonian H is the sum of single-particle Hamiltonians:
this Hamiltonian H can be represented by
where are annihilation (creation) operators associated with particle- state and satisfying the Fermi commutation rules. In the HP a variable changes in time, following the Heisenberg equa- tion of motion:
Setting we obtain
whose Hermitian conjugate is given by
By quantum postulate the physical observable is Hermitian: Variables and are not Hermitian, but both obey the same Heisenberg equation of motion. We introduce Eq. (A.45) into Eq. (A.47), and calculate the commutator In such a commutator calculation, identities (A.9) and the following identities:
are very useful. Note: The negative signs on the right-hand terms in Eqs. (A.49) occur when the cyclic order is destroyed. We obtain from Eqs. (A.47) and (A.48) A.4. HEISENBERG EQUATION OF MOTION 343
Equation (A.50) means that the change of the one-body operator is de- termined by the one-body Hamiltonian This is the main advantage of working in the HP. Equations (A.50)-(A.51) are valid for any single-particle states In the field operator language Eq. (A.51) reads
which is formally identical to the Schrödinger equation of motion for a par- ticle. If the system Hamiltonian H contains an interparticle interaction
the evolution equation for is nonlinear (Problem A.4.2):
In quantum field theory the basic dynamical variables are particle-field oper- ators. The quantum statistics of the particles are given by the Bose commu- tation or the Fermi commutation rules satisfied by the field operators. The evolution equations of the field operators are intrinsically nonlinear when the interparticle interaction is present.
Problem A.4.1. Verify that the equation of motion Eq. (A.50) holds for bosons. Problem A.4.2. Use Eq. (A.46) to verify Eq. (A.54). REFERENCES
Chapter 1
1. H. Kamerlingh Onnes, Akad. V. Wetenschappen (Amsterdam) 14, 113 (1911). 2. W. Meissner and R. Ochsenfeld, Naturwiss, 21, 787 (1933). 3. J. File and R. G. Mills, Phys. Rev. Lett. 10, 93 (1963). 4. B. S. Deaver and W. M. Fairbank, Phys. Rev. Lett. 7, 43 (1961). 5. R. Doll and M. Näbauer, Phys. Rev. Lett. 7, 51 (1961). 6. B. D. Josepson, Phys. Lett. 1, 251 (1962). 7. P. W. Anderson and J. M. Rowell, Phys. Rev. Lett. 10, 486 (1963). 8. R. C. Jaklevic, J. Lambe, J. E. Marcereau and A. H. Silver, Phys. Rev. A 140, 1628 (1965). 9. R. E. Glover III and M. Tinkham, Phys. Rev. 108, 243 (1957); M. A. Biondi and M. Garfunkelm, Phys. Rev. 116, 853 (1959). 10. I. Giaever, Phys. Rev. Lett. 5, 147, 464 (1960). 11. N. E. Phillips, Phys. Rev. 114, 676 (1959). 12. I. Giaever and K. Megerle, Phys. Rev. 122, 1101 (1961). 13. C. A. Reynolds et al., Phys. Rev. 78, 487 (1950); E. Maxwell, Phys. Rev. 78, 477 (1950). 14. J. G. Bednorz and K. A. Müller, Z. Phys. B 64, 189 (1986). 15. M. K. Wu et al., Phys. Rev. Lett. 58, 908 (1987). 16. P. A.. M. Dirac, Principles of Quantum Mechanics. 4th Ed., (Oxford University Press, London, 1958). 17. P. Ehrenfest and J. R. Oppenheimer, Phys. Rev. 37, 333 (1931); H. A. Bethe and R. F. Bacher, Rev. Mod. Phys. 8, 193 (1936). 18. F. London, Nature, 141, 643 (1938); Superfluids, I and II, (Dover, New York 1964). 19. A. Einstein, Sits. Ber. Berl. Akad. 3 (1925). 20. L. D. Landau, J. Exptl. Theoret. Physics. (USSR) 30, 1058 (1956); ibid, 32, 59 (1957). 21. A. Haug, Theoretical Solid State Physics, Vol. I, (Pergamon,Oxford 1972,); C. Kittel, Introduction to Solid State Physics. 6-th ed., (Wiley, New York 1986); N. W. Ashcroft and N. D. Mermin, Solid State Physics, (Saunders, Philadelphia, 1976); W. Harrison, Solid State Theory, (Dover, New York, 1980).
Chapter 2
1. K. Huang, Statistical Mechanics, 2nd ed. (Wiley, New York, 1987). 2. C. J. Gorter and H. B. G. Casimir, Physica, 1, 306 (1934). 3. V. L. Ginzburg and L. D. Landau, J. Exp. Theor. Phys. (USSR) 20, 1064 (1950). 4. B. S. Deaver and W. M. Fairbank, Phys. Rev. Lett. 7, 43 (1961); R. Doll and M. Näbauer, Phys. Rev. Lett. 7, 51(1961). 5. R. C. Jaklevic, J. Lambe, J. E. Marcereau and A. H. Silver, Phys. Rev. A 140, 1628 (1965). 6. P. Ehrenfest and J. R. Oppenheimer, Phys. Rev. 37, 333 (1931); H. A. Bethe and R. F. Bacher, Rev. Mod Phys. 8, 193 (1936). 7. S. Fujita and D. L. Morabito, Mod. Phys. Lett. 12, 753 (1998). 8. A. Einstein, Sits. Ber. Berl. Akad. 3 (1925). 9. M. H. Anderson et al., Science 269, 198 (1995). 10. K. B. Davis et al., Phys. Rev. Lett. 75, 3969 (1995). 11. L. N. Cooper, Phys. Rev. 104, 1189 (1956); J. R.Schrieffer, Theory of Superconductivity (Addison-Wesley, Redwood City, CA, 1964), pp. 38-39. 12. S. Fujita, J. Supercond. 4, 297 (1991). 346 REFERENCES
13. J. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957). 14. I. Giaever, Phys. Rev. Lett. 5, 147, 464 (1960). 15. J. G. Bednorz and K .A. Müller, Z. Phys. B, 64, 189 (1986). 16. T. Ishiguro and K. Yamaji, Organic Superconductors (Springer, New York, 1990). 17. S. Fujita, T. Kimura and Y. Zheng, Found. Phys. 21, 1117(1991). 18. P. C. Hohenberg, Phys. Rev. 158, 383 (1967).
Chapter 3
1. F. Bloch, Z. Phys. 52, 555 (1928). 2. L. D. Landau, J. Exptl. Theoret. Phys. (U.S.S.R.) 30, 1058 (1956). 3. W. A. Harrison, Phys. Rev. 118, 1190 (1960). 4. W. A. Harrison, Solid State Theory (Dover, New York, 1979). 5. T. L. Loucks and P. H. Cutler, Phys. Rev. 133, A 819 (1964). 6. D. Schönberg and A.V. Gold, D. "Physics of Metals - 1" in Electrons, ed. J. M. Ziman, (Cambridge University Press, Cambridge, UK, 1969), p. 112. 7. C. Kittel, Introduction to Solid State Physics, 6h ed. (Wiley, New York 1986). 8. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, Philadelphia 1976). 9. S. Fujita, S. Godoy and D. Nguyen, Found. Phys. 25, 1209 (1995). 10. P. A.. M. Dirac, Principles of Quantum Mechanics. 4h ed. (Oxford University Press, London, 1958). 11. e.g. see L. P. Eisenhart, Introduction to Differential Geometry, (Princeton University Press, Princeton, 1940). 12. T. W. B. Kibble, Classical Mechanics, (McGraw-Hill, Maidenhead, England, 1966), pp. 166-171.
Chapter 4
1. T. W. B. Kibble, Classical Mechanics, (McGraw-Hill, Maidenhead, England, 1966), pp. 166-171. 2. C. B. Walker, Phys. Rev. 103, 547 (1956). 3. L. Van Hove, Phys. Rev. 89, 1189 (1953). 4. H. Fröhlich, Phys, Rev. 79, 845 (1950); Proc. R. Soc. London A 215, 291 (1950). 5. R. P. Feynman, Statistical Mechanics (Addison-Wesley, Reading, MA. 1972); Quantum Electrodynamics (Addison-Wesley, Reading, MA. 1961). 6. S. Fujita and S. Godoy, Quantum Statistical Theory of Superconductivity, (Plenum, New York, 1996), pp. 150-153. 7. L. N. Cooper, Phys. Rev. 104, 1189 (1956).
Chapter 5
1. L. N. Cooper, Phys. Rev. 104, 1189 (1956). 2. J. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957). 3. D. Douglas Jr. and R. W. Schmitt, Rev. Mod Phys. 36, 1-331 (1964); R. D. Park, ed., Superconductivity (Marcel Dekker, NewYork, 1969).
Chapter 6
1. L. N. Cooper, Phys. Rev. 104, 1189 (1956). REFERENCES 347
Chapter 7
1. J. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957). 2. S. Fujita, J. Supercond. 4, 297 (1991); ibid 5, 83 (1992); S. Fujita and S. Watanabe, J. Supercond. 5, 219 (1992); ibid 6, 75 (1993); S. Fujita and S. Godoy, J. Supercond. 6, 373 (1993). 3. L. D. Landau, Sov. Phys. JETP 3, 920 (1957); ibid 5, 101 (1957); ibid 8, 70 (1959). 4. L. N. Cooper, Phys. Rev. 104, 1189 (1956). 5. J. R. Schrieffer, Theory of Superconductivity, (Benjamin, NewYork, 1964). 6. C. J. Gorter and H. G. B. Casimir, Phys. Z. 35, 963 (1934); Z. Tech. Phys. 15, 539 (1934). 7. Y. Onuki, H. Suematsu and S. Tamura, J. Phys. Chem. Solids 38, 419 and 431 (1977) (experiment); S. Watanabe and S. Fujita, J. Phys. Chem. Solids 52, 985 (1991) (theory).
Chapter 8
1. P. A. M. Dirac, Principles of Quantum Mechanics, 4th ed. (Oxford University Press, London, 1958), p. 211, pp. 136-138, p. 37, pp. 253-257. 2. W. Pauli, Phys. Rev. 58, 716 (1940). 3. P. Ehrenfest and J. R. Oppenheimer, Phys. Rev. 37, 331 (1931). 4. H. A. Bethe and R. Jackiw, Intermediate Quantum Mechanics, 2d. ed. (Benjamin, New York, 1968), p. 23. 5. L. N. Cooper, Phys, Rev. 104, 1189 (1956). 6. R. P. Feynman, R. B. Leighton and M. Sands, Feynman Lectures on Physics, vol. III (Addison-Wesley, Reading, MA. 1965), p. 21-7, p. 21-8. 7. S. Fujita and D. L. Morabito, Int. J. Mod. Phys. 12, 2139 (1998). 8. J. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957). 9. S. Fujita, Introduction to Non-Equilibrium Quantum Statistical Mechanics, (Krieger, Malabar, FL. 1983), pp. 9-11. 10. R. P. Feynman, Statistical Mechanics (Addison-Wesley, Redwood City, CA, 1972), p. 304. 11. B. D. Josephson, Phys. Lett. 1, 251 (1992); Rev. Mod. Phys. 36, 216 (1964). 12. S. Fujita and S. Godoy, Quantum Statistical Theory of Superconductivity, (Plenum, New York, 1996), pp. 122-124; S. Fujita, J. Supercond. 4, 297 (1991); 5, 83 (1992). 13. D. M. Dennison, Proc. Roy. Soc. London 115, 483 (1927); T. Hori, Zeits. f. Physik 44, 834 (1927). 14. E. Fermi and C. N. Yang, Phys. Rev. 76, 1739 (1949). 15. M. Gell-Mann and Y. Ne’eman, The Eightfold Way (Benjamin, Reading, MA, 1964).
Chapter 9
1. S. Fujita, T. Kimura and Y. Zheng, Found. Phys. 21, 1117 (1991). 2. P. C. Hohenberg, Phys. Rev. 158, 383 (1967). 3. J. Bardeen, L. N. Cooper and J .R. Schrieffer, Phys. Rev. 108, 1175 (1957). 4. A. B. Pippard, Proc. Roy. Soc. (London) A 216, 547 (1953).
Chapter 10
1. J. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957).
Chapter 11
1. S. Fujita and S. Watanabe, J. Supercond. 5, 219 (1992). 348 REFERENCES
2. J. Bardeen, L. N. Cooper and J. R. Schriefer, Phys. Rev. 108, 1175 (1957).
Chapter 12
1. I. Giaever and K. Megerle, Phys. Rev. 122, 1101 (1961). 2. I. Giaever, Phys. Rev. Lett. 5, 147 (1960); 5, 464 (1960). 3. I. Giaever, H. R. Hart and K. Megerle, Phys. Rev. 126, 941 (1961). 4. J. Bardeen, Phys. Rev. Lett. 6, 57 (1961). 5. R. E. Glover III and M. Tinkham, Phys. Rev. Lett. 108, 243 (1957); M. A. Biondi and M. Garfunkel, Phys. Rev. 116, 853 (1959). 6. B. N. Taylor and E. Burstein, Phys. Rev. Lett. 10, 14 (1963); C. J. Adkins, Phil, Mag. 8, 1051 (1963); P. Townsend and J. Sutton, Proc. Phys. Soc. (London) 78, 309 (1961).
Chapter 13
1. J. File and R. G. Mills, Phys. Rev. Lett. 10, 93 (1963). 2. J. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957). 3. B. S. Deaver and W. M. Fairbank, Phys. Rev. Lett. 7, 43 (1961); R. Doll and M. Näbauer, Phys. Rev. Lett. 7, 51 (1961). 4. L. Onsager, Phyl. Mag. 43, 1006 (1952). 5. L. Onsager, Phys. Rev. Lett. 7, 50 (1961); N. Byers and C. N. Yang, Phys. Rev. Lett. 7, 46 (1961). 6. F. London and H. London, Proc. Roy. Soc. (London) A 149, 71 (1935); Physica 2, 341 (1935); F. London, Superfluids, Vol I, (Wiley, New York 1950).
Chapter 14
1. V. L. Ginzburg and L. D. Landau, J. Exp. Theor. Phys. (USSR) 20, 1064 (1950). 2. L. D. Landau and E. M. Lifshitz, Statistical Physics, part I, 3d ed., (Pergamon Press, Oxford, England, 1980) pp. 171-174. 3. F. and H. London, Proc. Roy. Soc. (London) A, 149, 71 (1935); Physica 2, 341 (1935). 4. P. G. de Gennes, Superconductivity of Metals and Alloys, (Addison-Wesley, Redwood City, CA, 1989), pp. 176-209. 5. A.. A. Abrikosov, Sov. Phys. JETP 5, 1174 (1957). 6. H. Träuble and U. Essmann, J. Appl. Phys. 39, 4052 (1968). 7. B. S. Deaver and W. M. Fairbank, Phys. Rev. Lett. 7, 43 (1961); R. Doll and M. Näbauer, Phys. Rev. Lett. 7, 51 (1961) (experiment). 8. L. Onsager, Phys. Rev. Lett. 7, 50 (1961); N. Byers and C. N. Yang. Phys. Rev. Lett. 7, 46 (1961) (theory). 9. L. N. Cooper, Phys. Rev. 104, 1189 (1956). 10. J. Bardeen, L. Cooper and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957). 11. S. Fujita and S. Godoy, Int. J. Mod. Phys. B 12, 99 (1998); J. Supercond. 6, 373 (1993). 12. I. Giaever, Phys. Rev. Lett. 5, 147 (1960); 5, 464 (1960); I. Giaever and K. Megerle, Phys, Rev. 122, 1101 (1961). 13. P. A. M. Dirac, Proc. Roy. Soc. (London) A, 114, 243 (1927). 14. P. Jordan and E. Wigner, Zeits. f. Phys. 47, 631 (1928); P. Jordan and O. Klein, Zeitz. f. Phys. 45, 751 (1927). 15. L. P. Gorkov, Sov. Phys. JETP 7, 505 (1958); ibid 9, 1364 (1959); 10, 998 (1960). 16. N. R. Werthamer, Phys. Rev. 132, 663 (1963); Rev. Mod. Phys. 36, 292 (1964); T. Tewardt, Phys. Rev. 132, 595 (1963); B. B. Goodman, Rev. Mod. Phys. 36, 12 (1964). 17. S. Fujita and S. Watanabe, J. Supercond. 5, 219 (1992). REFERENCES 349
18. R. E. Glover, III and Tinkham, Phys. Rev. 108, 243 (1957); M. A. Biondi and M. Garfunkel, Phys, Rev. 116, 853 (1959). 19. J. R. Schrieffer, Theory of Superconductivity, (Addison- Wesley, Redwood City, CA, 1964), p. 33, p. 44.
Chapter 15
1. D. Josephson, Phys. Lett. 1, 251 (1962); Rev. Mod. Phys. 36, 216 (1964). 2. P. W. Anderson and J. M. Rowell: Phys. Rev. Lett. 10, 486 (1963). 3. R. C. Jaklevic, J. Lambe, J. E. Marcereau and A. H. Silver, Phys. Rev. A 140, 1628 (1965). 4. E. A. Ueling and G. E. Uhlenbeck, Phys. Rev. 43, 552 (1933). 5. S. Tomonaga, Zeits. f. Physik, 110, 573 (1938). 6. R. P. Feynman, R. B. Leighton and M. Sands, Feynman Lectures on Physics, vol. III, (Addison-Wesley, Reading, MA, 1965), p. 21-8. 7. R. P. Feynman, Statistical Mechanics, (Addison-Wesley, Redwood City, CA., 1972). 8. S. Shapiro, Phys. Rev. Lett. 11, 80 (1963). 9. A. Hartland, Precis. Meas. Fundam. Constants, 2, 543 (1981). 10. D. H. Menzel; Fundamental Formulas of Physics, (Dover, New York., 1960), p. 59. 11. A. A. Abrikosov, J. Exptl. Theor. Phys. (USSR) 32, 1442 (1957).
Chapter 16
1. B. T. Matthias, Progress in Low Temperature Physics, ed. C. J. Gorter, Vol. 2 (North-Holland, Amsterdam, 1957), p. 138; B. T. Matthias et al., Rev. Mod. Phys. 36, 155 (1964). 2. D. Saint-James, E. D. Thomas and G. Sarma, Type II Superconductivity, (Pergamon, Oxford, 1969). 3. A. A. Abrikosov, J. Exp. Theor. Phys. (USSR), 5, 1174 (1957). 4. V. L. Ginzburg and L. D. Landau, J. Exp. Theor. Phys. (USSR), 20, 1064 (1950). 5. U. Essmann and H. Träuble, Phys. Lett. A 24, 526 (1967). 6. T. McConville and B. Serin, Rev. Mod. Phys. 36, 112 (1964). 7. A. D. B. Woods et al., Phys. Rev. 131, 1025 (1963). 8. H. Yukawa, Proc. Math. Soc. Japan, 17, 48 (1935).
Chapter 17
1. J. G. Bednorz and K. A. Müller, Z. Phys. B. Cond. Matt. 64, 189 (1986). 2. J. W. Halley, ed., Theory of High-Temperature Superconductivity (Addison-Wesley, Redwood City, CA. 1988). 3. S. Lundquist et al., eds., Towards the Theoretical Understanding of High-T Superconductivity, (World Scientific, Singapore 1988). 4. D. M. Ginsberg, ed., Physical Properties of High-Temperature Superconductors (World Scientific, Singapore 1989). 5. S. A. Wolf and W. Z. Kresin, Novel Superconductivity (Plenum, New York, 1989); K. Kitazawa and T. Ishiguro, eds. Advances in Superconductivity, (Springer, Tokyo, 1989). 6. M. K. Wu et al., Phys. Rev. Lett. 58, 908 (1987). 7. See, e.g. Ginsberg’s overview, Ref. 4, pp. 1-38. 8. 8. D. E. Farrell et al.,Phys. Rev. B 42, 6758 (1990). 9. S. Godoy and S. Fujita, J. Eng. Sci. 29, 1201 (1991). 10. J. H. Kang, R. T. Kampwirth and K. E. Gray, Appl. Phys. Lett, 52, 2080 (1988); M. J. Naughton et al., Phys. Rev. B 38, 9280(1988). 11. L. Onsager, Phil. Mag. 43, 1006 (1952). 350 REFERENCES
12. J. Wosnitza et al., Phys. Rev. Lett. 67, 263, (1991). 13. Y. Maeno, H, Hashimoto, K. Yoshida, S. Nishizaki, T. Fujita, J. G. Bednorz and F. Lichtenberg, Nature 372, 532 (1994).
Chapter 18
1. J. G. Bednorz and K. A. Müller, Z. Phys. B. Cond. Matt. 64, 189 (1986). 2. J. W. Halley, ed., Theory of High-Temperature Superconductivity (Addison-Wesley, Redwood City, CA. 1988); S. Lundquist et al., eds., Towards the Theoretical Understanding of Superconductivity, (World Scientific, Singapore 1988);. S. A. Wolf and D. M. Ginsberg, ed., Physical Properties of High- Temperature Superconductors (World Scientific, Singapore, 1989)-(series); W. Z. Kresin, Novel Superconductivity (Plenum, New York, 1989); K. Kitazawa and T. Ishiguro, eds. Advances in Superconductivity, (Springer, Tokyo, 1989). 3. P. W. Anderson, Theory of Superconductivity in Cuprates, (Princeton University Press, Princeton, NJ, 1997); J. R. Waldram Superconductivity of Metals and Cuprates, (Intitute of Physics Publishing, Bristol, UK, 1996). 4. S. Fujita and D. L. Morabito, Mod. Phys. Lett. B 12, 1061 (1998). 5. S. Fujita and S. Watanabe, J. Supercond. 5, 219 (1992). 6. S. Fujita and D. L. Morabito, Int. J. Mod. Phys. B 21, 2139 (1998). 7. J. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957). 8. R. A. Fisher, J. E. Gordon, and N. E. Phillips, J. Supercond. 1, 231(1988). 9. J. W. Loram, K. A. Mirza, J. R. Cooper and W. Y. Liang, J. Supercond. 7, 347 (1994). 10. T. Ekino et al., Physica C 218, 387 (1993); P. J. M. van Bentum et al., Phys. Rev, B 36, 843 (1987); F. Frangi et al., Sol. State Commun. 81, 599 (1992).
Chapter 19
1. J. G. Bednorz and K. A. Müller, Z. Phys. B 64 189 (1986). 2. J. B. Torrance et al., Phys. Rev. Lett. 61, 1127 (1988); M. W. Shafer, T. Penney and B. L. Olsen, Phys. Rev. B 36, 4047 (1987); R. B. van Dover et al., Phys. Rev. B 35, 5737 (1987). 3. H. Takagi, S. Uchida and Y. Tokura, Phys. Rev. Lett. 62, 1197 (1989); H. Takagi, Kotai Butsuri 25, 736 (1990). 4. J. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957). 5. R. P. Feynman, R. B. Leighton and M. Sands, Feynman Lectures on Physics, Vol. III (Addison-Wesley, Reading. MA. 1965) p. 21-7, p. 21-8. 6. B. D. Josephson, Phys. Lett. 1, 251 (1962); Rev. Mod. Phys. 36, 216 (1964). 7. (experiment); B. S. Deaver and W. M. Fairbank, Phys. Rev. Lett. 7, 43 (1961); R. Doll and M. Näbauer, Phys. Rev. Lett. 7, 51 (1961); (theory) L. Onsager, Phys. Rev. Lett. 7, 50 (1961); N. Byers and C. N. Yang, Phys. Rev. Lett. 7, 46(1961). 8. R. C. Jaklevic, J. Lambe, J. E. Marcereau and A. H. Silver, Phys. Rev. A 140, 1628 (1965). 9. J. R. Schrieffer, Theory of Superconductivity (Addison-Wesley, Redwood City, CA, 1964), p. 33, pp. 49-50. 10. P. C. Hohenberg, Phys. Rev. 158, 383 (1967). 11. R. A. Ogg Jr., Phys. Rev. 69, 243 (1946). 12. F. London, Superfluids, vols. 1 and 2 (Dover, New York, 1964). 13. M. R. Schafroth, S. T. Butler and J. M. Blatt. Helv. Phys. Acta, 30, 93 (1957). 14. A. J. Leggett, in Modern Trends in Theory of Condensed Matter, eds. by A. Pekalski and Przystawa (Springer, 1980), pp. 14-17. 15. P. Nozieres and S. Schmit-Rink, J. Low Temp. Phys. 59, 195 (1985). 16. H. Takagi et al., Phys. Rev. B 40, 2254 (1989). REFERENCES 351
Chapter 20
1. Y. Iye, in Physical Properties of High Temperature Superconductors III, D. M. Ginzberg, ed. (Word Sc., 1992). 2. J. G. Bednorz and K. A. Müller Z. Phys. B 64, 189 (1996). 3. H. Takagi, Kotai Butsuri, 25, 736 (1990). 4. J. B. Torrance et al., Phys. Rev. Lett. 61, 1127 (1998); H. Takagi, S. Uchida and Y. Tokura, Phys. Rev. Lett. 62, 1197 (1989); T. Tokura, H. Takagi and S. Uchida, Nature 337, 345 (1989). 5. H. Nakano, Prog. Theoret. Phys. 15, 77 (1956); R. Kubo, J. Phys. Soc. Japan 12, 570 (1957). 6. S. Fujita, Y-G. Kim and Y. Okamura, Mod. Phys. Lett. B 14, 495 (2000). 7. S. Fujita, Y-G. Kim, Mod. Phys. Lett. B 14, 505 (2000). 8. e.g. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, Philadelphia, 1976), pp. 239-240, 133- 141. 9. T. R. Chien et al., Phys. Rev. Lett. 67, 2088 (1991).
Chapter 21
1. I. Terasaki et al., Phys. Rev. B 52, 16246 (1995); I. Terasaki, Y. Sato and S. Tajima, Phys. Rev. B 55, 15300 (1997); I. Terasaki, Y. Sato and S. Tajima, J. Kor. Phys. Soc. 31, 23 (1997). 2. T. Kimura et al., Physica C 192, 247 (1992). 3. S. Fujita, Y. Tamura and Suzuki, Mod. Phys. Lett. B, (submitted) 4. S. Godoy and S. Fujita, J. Eng. Sci. 29, 1201 (1991). 5. S. Fujita, Physica 51, 601 (1971). 6. J. G. Bednorz and K. A. Müller, Z. Phys. B 64, 189 (1996). 7. Y. Maeno, H, Hashimoto, K. Yoshida, S. Nishizaki, T. Fujita, J. G. Bednorz and F. Lichtenberg, Nature 372, 532 (1994).
Chapter 22
1. e.g. P. L. Rossiter and J. Bass, Metals and Alloys, in Encyclopedia of Applied Physics 10, VCH Publ., 163-197 (1994). 2. I. Terasaki, Y. Sato, S. Tajima, S. Miyamoto and S. Tanaka, Physica C 235, 1413 (1994); I. Terasaki, Y. Sato, S. Tajima, S. Miyamoto and S. Tanaka, Phys. Rev. B 52, 16246 (1995). 3. S. Fujita, T. Obata, T. Shane and D. Morabito, Phys. Rev. B 63, 54402 (2001). 4. N. W. Ashcroft and N. D. Mermin, Solid State Physics, (Saunders, Philadelphia, 1976), pp. 256-258, pp. 290- 293. 5. S. Fujita, H-C. Ho and D. L. Morabito, Int. J. Mod. Phys. B 14, 2223 (2000). 6. I. Tersasaki, Y, Sato and S. Tajima, J. Kor. Phys. Soc. 31, 23 (1997). 7. S. Fujita, H-C. Ho and S. Godoy, Mod. Phys. Lett. B 13, 689, (1999).
Chapter 23
1. H. Takagi, T. Ido, S. Ishibashi, M. Uota, S. Uchida and Y. Tokura, Phys. Rev. B 40, 2254 (1989). 2. J. B. Torrance, A. Bezinge, A. I. Nazzal, T. C. Huang, S. S. P. Parkin, D. T. Keane, S. J. La Placa, P. M. Horn, and G. A. Held, Phys. Rev. B 40, 8872 (1989). 3. I. Terasaki, M. Hase, A. Maeda, K. Uchinokura, T. Kimura, K. Kishio, I. Tanaka and H. Kojima, Physics C 193, 365 (1992). 4. W. Pauli, Zeits. f. Phys. 41, 81 (1927). 352 REFERENCES
5. e.g. L. D. Landau and E. M. Lifshitz, Statistical Physics, part I, 3d ed., (Pergamon Press, Oxford, England, 1980), pp. 171-174. 6. S. Fujita, T. Obata, T. F. Shane and D. L. Morabito, Phys. Rev. B 63, 54402 (2001). 7. L. Onsager, Phil. Mag. 43, 1006 (1952).
Chapter 24
1. J. Cerne, D. C. Schmadel, M. Grayson, G. S. Jenkins, J. R. Simpson and H. D. Drew, Phys. Rev. B 61, 8133 (2000). 2. J. Cerne, M. Grayson, D. C. Schmadel, G. S. Jenkins, H. D. Drew, H. Hughes, J. S. Preston and P. J. Kung. Phys. Rev. Lett. 84, 3418 (2000). 3. S. Fujita, Y-G. Kim and Y. Okamura, Mod. Phys. Lett. B 14, 495 (2000). 4. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, Philadelpia, 1976), pp. 225 and 240. 5. S. Fujita and Y-G. Kim, Mod. Phys. Lett. B 14, 505 (2000). 6. J. Cerne, private communication.
Chapter 25
1. D. A. Wollman et al., Phys. Rev. Lett. 71, 2134 (1993); C. C. Tsuei et al., Nature 386, 481 (1997). 2. J. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957). 3. W. A. Harrison, Solid State Theory (Dover, New York, 1980), pp. 390-397. 4. D. S. Dessau et al., Phys. Rev. Lett. 71, 2781 (1993); Z-X. Shen et al., Phys. Rev. Lett. 70, 1553 (1993).
Chapter 26
1. H. Kamerlingh Onnes, Akad. V. Wetenschappen (Amsterdam) 14, 113 (1911). 2. B. J. Gorter and H. B. G. Casimir, Physica 1, 306 (1934). 3. F. London, Nature (London) 141, 643 (1938); Superfluids, I and II (Dover, New York, 1964). 4. W. Meissner and R. Ochsenfeld, Naturwiss. 21, 787 (1933). 5. F. London and H. London, Proc. Roy. Soc. (London) A 149, 71 (1935); Physica 2, 341 (1935). 6. S. Fujita and S. Godoy, I. J. Mod. Phys. B 12, 49 (1998). 7. V. L. Ginzburg and L. D. Landau, J. Exp. Theor. Phys. (USSR) 20, 1064 (1950). 8. A. A. Abrikosov, Sov. Phys. JETP 5, 1174 (1957). 9. H. Träuble and U. Essmann, J. Appl. Phys. 39, 4052 (1968). 10. H. Fröhlich, Phys, Rev. 79, 845 (1950); Proc. Roy. Soc. London A 215, 291 (1950). 11. A. A. Reynolds, B. Serin, W. H. Wright and N. B. Nesbitt, Phys. Rev. 78, 487 (1950); E. Maxwell, Phys. Rev. 78, 477 (1950). 12. H. Yukawa, Proc. Phys. Math. Soc. Japan, 17, 48 (1935). 13. S. Fujita and D. L. Morabito, Mod. Phys. Lett. B 12, 1061, (1998). 14. L. N. Cooper, Phys. Rev. 104, 1189 (1956). 15. J. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957). 16. A. S. Deaver and W. M. Fairbank, Phys. Rev. Lett. 7, 43 (1961); R. Doll and M. Näbauer, Phys. Rev. Lett. 7, 51 (1961) (experiment). 17. L. Onsager, Phys. Rev. Lett. 7, 50 (1961); N. Byers and C. N. Yang. Phys. Rev. Lett. 7, 46 (1961) (theory). 18. R. E. Glover III and M. Tinkham: Phys. Rev. Lett. 108, 243 (1957); M. A. Biondi and M. Garfunkel, Phys. Rev. 116, 853 (1959). 19. I. Giaever, Phys. Rev. Lett. 5, 147 (1960); 5, 464 (1960); I. Giaever, H. R. Hart and K. Megerle, Phys. Rev. 126, 941 (1961). 20. R. Doll and M. Näbauer, Phys. Rev. Lett. 7, 51 (1961). REFERENCES 353
21. A. Einstein, Sits. Ber. Berl. Akad. 3 (1925). 22. M. R. Schafroth, S. T. Butler and J. M. Blatt. Helv. Phys. Acta, 30, 93 (1957); A. J. Leggett, in Modern Trends in Theory of Condensed Matter, eds. by A. Pekalski and Przystawa (Springer, 1980), pp. 14-17; P. Nozieres and S. Schmit-Rink, J. Low Temp. Phys. 59, 195 (1985). 23. S. Fujita, T. Kimura and Y. Zheng, Found. Phys. 21, 1117 (1991). 24. P. C. Hohenberg, Phys. Rev. 158, 383 (1967). 25. B. D. Josephson, Phys. Lett. 1, 251 (1962); Rev. Mod. Phys. 36, 216 (1964). 26. P. W. Anderson and J. M. Rowell, Phys. Rev. Lett. 10, 486 (1963). 27. R. C. Jaklevic, J. Lambe, J. E. Marcereau and A. H. Silver, Phys. Rev. A 140, 1628 (1965). 28. S. Shapiro, Phys. Rev. Lett. 11, 80 (1963). 29. R. P. Feynman, R. B. Leighton and M. Sands, 1965, Feynman Lectures on Physics, vol. III, p. 21-8; R. P. Feynman, 1972, Statistical Mechanics, Addison-Wesley, Redwood City, CA. 30. J. G. Bednorz and K. A. Müller, Z. Phys. B. Cond. Matt. 64, 189 (1986). 31. M. K. Wu et al., Phys. Rev. Lett. 58, 908 (1987). 32. W. L. McMillan, Phys. Rev. 167, 331 (1968); P. B. Allen and R. C. Dynes, Phys. Rev. 12, 905 (1975). 33. J. W. Halley, ed., Theory of High-Temperature Superconductivity (Addison-Wesley, Redwood City, CA. 1988); S. Lundquist et al., eds., Towards the Theoretical Understanding of High-T Superconductivity, Vol. 14, (World Scientific, Singapore 1988). 34. C. M. Ginsberg, ed., Physical Properties of High-Temperature Superconductors (World Scientific, Singapore 1989)-(series). 35. S. A. Wolf and D. M. Ginsberg, ed., Physical Properties of High-Temperature Superconductors (World Scientific, Singapore 1989)-(series); W. Z. Kresin, Novel Superconductivity (Plenum, New York, 1989); K. Kitazawa and T. Ishiguro, eds. Advances in Superconductivity, (Springer, Tokyo, 1989). 36. A. S. Alexandrov and N. F. Mott, Int. J. Mod. Phys. B 8, 2075 (1994); A. S. Alexandrov, Phys. Rev. B 38, 925 (1988); N. F. Mott, Phys. Rev. Lett. 71, 1075 (1993). 37. R. Friedberg and T. D. Lee, Phys. Rev. B 40, 1745 (1986). 38. P. W. Anderson, Science, 235, 1196 (1987). 39. V. J. Emery, Phys. Rev. Lett, 58, 2794 (1987); H. Kamimura, S. Matsuno, Y. Suva and H. Ushio, Phys. Rev. Lett. 77, 723 (1996); A. Sano, M. Eto and H. Kamimura, Int. J. Mod. Phys. B 11, 3733 (1997). 40. J. E. Hirsch, Phys. Rev. B 31, 4403 (1985); Phys. Rev. Lett. 25, 1317 (1985). 41. F. C. Zhang and T. M. Rice, Phys. Rev. B, 37, 3759 (1989). 42. L. Onsager, Phys. Rev. 65, 117 (1944). 43. R. Willett, J. P. Eisenstein, H. L. Störmer, D. C. Tsui, A. C. Gossard and J. H. English, Phys. Rev. Lett. 59, 1776 (1987); H. L. Störmer, D. C. Tsui and A. C. Gossard, ibid, 48, 1559 (1982). 44. K. von Klitzing, G. Dorda and M. Pepper, Phys. Rev. Lett. 45, 494 (1980). 45. R. E. Prange and S. M. Girvin, eds., Quantum Hall Effect, (Springer-Verlag, Berlin, 1988). 46. R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983). 47. S. C. Zhang, T. H. Hansson and S. Kivelson, Phys. Rev. Lett. 62, 82 (1989); R. B. Laughlin, ibid, 60, 2677 (1989); S. Kivelson, D. H. Lee and S-C Zhang, Sci. Amer. 274, 86 (1996). 48. S. M. Girvin and A. H. MacDonald, Phys. Rev. Lett. 58, 1252 (1987); N. Read, ibid, 62, 86 (1989); R. Shankar and G. Murthy, ibid, 79, 4437 (1997). 49. J. K. Jain, Phys. Rev. Lett. 63, 199 (1989); Phys. Rev. B 40, 8079, (1989); ibid, B 41, 7653 (1990). 50. S. Fujita, Y. Tamura and A. Suzuki, Mod. Phys. Lett. B 15, (2001). 51. P. A. M. Dirac, Principles of Quantum Mechanics, 4th ed. (Oxford University Press, 1958), p. 267. 52. R. G. Clark et al., Phys. Rev. Lett. 62, 1536 (1989); J. P. Eisenstein, H. L. Stormer, L. Pfeiffer and K. W. West, ibid, 62, 1540 (1989).
Chapter 27
1. F. B. Silsbee, J. Wash. Acad. Sci. 6, 597 (1916). 354 REFERENCES
Appendix
1. P. A.. M. Dirac, Proc. Roy. Soc. (London) 117, 610 (1928). 2. P. Ehrenfest and J. R. Oppenheimer Phys. Rev. 37, 333 (1931); H. A. Bethe and R. Jackiw, Intermediate Quantum Mechanics, 2nd. ed., (Benjamin, New York, 1968), pp. 23. 3. W. Pauli, Phys. Rev. 58, 716 (1940). Bibliography
SUPERCONDUCTIVITY
Introductory and Elementary Books
Lynton, E. A.: Superconductivity, (Methuen, London, 1962). Vidali, G.: Superconductivity, (Cambridge University Press, Cambridge, England, 1993).
General Textbooks at about the same level as the present text.
Feynman, R. P., Leighton R. B. and Sands, M.: Feynman Lectures on Physics. Vol 3, (Addison-Wesley, Reading, MA, 1965) pp. 1-19. Feynman, R. P.: Statistical Mechanics, (Addison-Wesley, Reading, MA, 1972), pp. 265-311. Rose-Innes, A. C. and Rhoderick, E. H.: Introduction to Superconductivity, 2d ed., (Pergamon, Oxford, England, 1978).
More Advanced Texts and Monographs
Abrikosov, A. A.: Fundamentals of the Theory of Metals, A. Beknazarov, trans. (North Holland-Elsevier, Amsterdam, 1988). Gennes, P.: Superconductivity of Metals and Alloys, (Benjamin, Menlo Park, CA. 1966). Rickayzen, G.: Theory of Superconductivity, (Interscience, New York, 1965). Saint-James, D., Thomas, E. J. and Sarma, G.: Type II Superconductivity, (Pergamon, Oxford, England, 1969). Schafroth, M. R.: Solid State Physics, Vol. 10, eds. F. Seitz and D. Turnbull, (Academic, New York, 1960) p. 488. Schrieffer, J. R.: Theory of Superconductivity, (Benjamin, New York, 1964). Tilley, D. R. and Tilley, J.: Superfluidity and Superconductivity, 3d ed., (Adam Hilger, Bristol, England, 1990). Tinkham, M.: Introduction to Superconductivity, (McGraw-Hill, New York, 1975).
High-Temperature Superconductivity
Anderson, P. W.: Theory of Superconductivity in Cuprates, (Princeton University Press, Princeton, NJ, 1997) Burns, G.: High-Temperature Superconductivity, an Introduction, (Academic, New York, 1992). Ginsberg D. M., ed., Physical Properties of High-Temperature Superconductors (World Scientific, Singapore 1989)-(series). Halley, J. W.: ed., Theory of High-Temperature Superconductivity (Addison-Wesley, Redwood City, CA. 1988). Kresin, V. Z. and Wolf S. A.: Fundamentals of Superconductivity, (Plenum, New York, 1990). Kresin, W. Z.: Novel Superconductivity (Plenum, New York, 1989). Lindquist, S.: et al., eds., Towards the Theoretical Understanding of Superconductivity, Vol. 14, (World Scientific, Singapore 1988). 356 BIBLIOGRAPHY
Lynn, J. W., ed., High Temperature Superconductivity (Springer-Verlag, New York, 1990). Owens, F. J. and Poole, C. P.: New Superconductors, (Plenum, New York, 1996). Phillips, J. C.: Physics of Superconductors, (academic Press, san Diego, CA, 1989). Poole, C. P., Farach, H. A. and Creswick, R. J.: Superconductivity, (Academic, New York, 1995). Sheahen, T. P.: Introduction to High-Temperature Superconductivity, (Plenum, New York, 1994). Waldram J. R.: Superconductivity of Metals and Cuprates, (Intitute of Physics Publishing, Bristol, UK, 1996).
BACKGROUND
Solid State Physics
Ashcroft, N. W. and Mermin, N. D.: Solid State Physics, (Saunders, Philadelphia, 1976). Harrison, W. A. : Solid State Theory, (Dover, New York, 1979). Haug, A.: Theoretical Solid State Physics, I, (Pergamon, Oxford, England, 1972). Kittel, C.: Introduction to Solid State Physics, 6th ed. (Wiley, New York, 1986).
Mechanics
Goldstein, H.: Classical Mechanics, (Addison Wesley, Reading, MA, 1950). Kibble, T. W. B.: Classical Mechanics, (McGraw-Hill, London, 1966). Marion, J. B.: Classical Dynamics, (Academic, New York, 1965). Symon, K. R.: Mechanics, 3d ed. (Addison-Wesley, Reading, MA, 1971).
Quantum Mechanics
Alonso, M. and Finn, E. J.: Fundamental University Physics, III Quantum and Statistical Physics, (Addison-Wesley, Reading, MA, 1989). Dirac, P. A. M.: Principles of Quantum Mechanics, 4th ed. (Oxford University Press, London, 1958). Gasiorowitz, S.: 1974, Quantum Physics, (Wiley, New York, 1974). Liboff, R. L.: Introduction to Quantum Mechanics, (Addison-Wesley, Reading, MA, 1992). McGervey, J. D.: Modern Physics, (Academic Press, New York, 1971). Pauling, L. and Wilson, E. B.: Introduction to Quantum Mechanics, (McGraw-Hill, New York, 1935). Powell, J. L. and Crasemann, B.: Quantum Mechanics, (Addison-Wesley, Reading, MA, 1961).
Electricity and Magnetism
Griffiths, D. J.: Introduction to Electrodynamics, 2d ed. (Prentice-Hall, Englewood Cliffs, NJ, 1989). Lorrain, P. and Corson, D. R.: Electromagnetism, (Freeman, San Francisco, 1978). Wangsness, R. K.: Electromagnetic Fields, (Wiley, New York, 1979).
Thermodynamics
Andrews, F. C.: Thermodynamics: Principles and Applications, (Wiley, New York, 1971). Bauman, R. P.: Modern Thermodynamics with Statistical Mecanics, (Macmillan, New York, 1992). Callen, H. B.: Thermodynamics, (Wiley, New York, 1960). Fermi, E.: Thermodynamics, (Dover, New York, 1957). Pippard, A. B.: Thermodynamics: Applications, (Cambridge University Press, Cambridge, England, 1957). BIBLIOGRAPHY 357
Statistical Physics (undergraduate)
Baierlein, R.: Thermal Physics, (Cambridge U. P., Cambridge, UK, 1999). Carter, A. H.: Classical and Statistical Thermodynamics, (Prentice-Hall, Upper Saddle River, NJ, 2001). Fujita, S.: Statistical and Thermal Physics, I and II, (Krieger, Malabar, FL, 1986). Kittel, C. and Kroemer, H.: Thermal Physics, (Freeman, San Francisco, CA, 1980). Mandl, F.: Statistical Physics, (Wiley, London, 1971). Morse, P. M.: Thermal Physics, 2d ed. (Benjamin, New York, 1969). Reif, F.: Fundamentals of Statistical and Thermal Physics, (McGraw-Hill, New York, 1965). Rosser, W. G. V.: Introduction to Statistical Physics, (Horwood, Chichester, England, 1982). Terletskii, Ya. P.: Statistical Physics, N. Froman, trans. (North-Holland, Amsterdam, 1971). Zemansky, M. W.: Heat and Thermodynamics, 5th ed. (McGraw-Hill, New York, 1957).
Statistical Physics (graduate)
Davidson, N.: Statistical Mechanics, (McGraw-Hill, New York, 1969). Feynman, R. P.: Statistical Mechanics, (Benjamin, New York, 1972). Finkelstein, R. J.: Thermodynamics and Statistical Physics, (Freeman, San Francisco, CA, 1969). Goodstein, D. L.: States of Matter, (Prentice-Hall, Englewood Cliffs, NJ). Heer, C. V.: Statistical Mechanics, Kinetic Theory, and Stochastic Processes, (Academic Press, New York, 1972). Huang, K.: Statistical Mechanics, 2d ed. (Wiley, New York, 1972). Isihara, A.: Statistical Physics, (Academic, New York, 1971). Kestin, J. and Dorfman, J. R.: Course in Statistical Thermodynamics, (Academic, New York, 1971). Landau, L. D. and Lifshitz, E. M.: Statistical Physics, 3d ed. Part 1, (Pergamon, Oxford, England, 1980). Lifshitz, E. M. and Pitaevskii, L. P.: Statistical Physics, Part 2, (Pergamon, Oxford, England, 1980). McQuarrie, D. A.: Statistical Mechanics, (Harper and Row, New York, 1976). Pathria, R. K.: Statistical Mechanics, (Pergamon, Oxford, England, 1972). Robertson, H. S.: Statistical Thermodynamics, (Prentice Hall, Englewood Cliffs, NJ.). Wannier, G. H.: Statistical Physics, (Wiley, New York, 1966). INDEX
Abrikosov, A. A., 182, 189, 207 energy gap equation, 62, 87, 123-132 vortex structure, 182, 188, 208-213, 313 finite temperature theory, 143 Ac Josephson effect, 200-204 formula, 124, 130 Acoustic -like Hamiltonian, 230 phonon, 213-216, 227, 252 picture of a superconductor, 88 phonon scattering rates, 279 superconductor, 143 Affinity between electron and phonon, 49 theory, 61-62, 88 148, 150 zero temperature coherence length, 24, 116 Analogy between laser and supercurrent, 152, 204 zero temperature pairon size, 244 Anderson-Rowell, 193 Bednorz and Müller, 10, 217, 241, 249 Angle-resolved photo-emission spectroscopy, 310 223 Annihilation operator, 14, 80, 127, 336 Binding energy per pairon, 88-89, 233, 237 Antiparticle, 103 Blackbody radiation, 113, 151 Anticommutation rules = Fermi anticommutation rules, Bloch 183 electron, 13, 24, 27-44 Antiferromagnetic, 221 electron dynamics, 39 insulator, 245 state, 39 state, 258 theorem, 27, 29-30, 219 Antisymmetric ket, 99 wave packet, 24, 40, 229 for fermions, 103, 339 wave function, 29, 39 Antisymmetrizing operator, 339 Blurred (fuzzy) Fermi surface, 93, 148 Antisymmetric I-V curve, 151 Bohr, N., 166 Applied magnetic field, 208 Bohr-Sommerfeld quantization rule, 22, 166 Ashcroft and Mermin, 275 Boltzmann principle = Boltzmann factor argument, 138, Asymmetric I-V curve, 237-238 149 (Average) time between scatterings, 15 Bose commutation rules (relations), 52-53, 183 distribution function, 12, 107, 139, 281 Balanced force equation, 301 Bose-Einstein (B-E) Bare lattice potential, 30 condensation, 107-111, 114-115, 138-141, 235 Basic properties of a superconductor, 1 statistics, 107, 138 Bose Boson, 95 distribution function, 264 composite, 101 commutation rules, 334 creation and annihilation operators, 333-337 Bose-Einstein (B-E) field operator, 183 condensation, 13, 20, 23, 107-121, 138-141, 235, enhancement effect, 197 243 nature of pairons, 115, 139, 159 integral, 140 Bound Cooper pair = Cooper pair = pairon, 61, 65-76, Bose Einstein condensation (BEC) 133-146 of massive bosons, 13, 244 Bound state = negative-energy state, 65 of massless bosons in 2D, 21, 69, 107-111, 235 Bra (vector), 11 of massless bosons in 3D, 21, 69, 111-114, 233 Bravais lattice vector, 29 Bosonically condensed pairons, 69, 114-115, 138-141, Brillouin boundary, 29, 32-35, 92, 228 244, 302 Brillouin zone B-L-C-O = Ba-La-Cu-O, 223 first zone,49, 32 Bardeen, J., 60, 153 second zone, 34, BCS Buckled plane = copper plane, 219 = Bardeen-Cooper-Schrieffer, 60-61, 105 Bulk limit, 47, 108 coherence length, 210 360 INDEX
Coulomb Cause of electron pairing, 227 interaction among electrons, 58 Cause of superconductivity, 45 repulsion (force), 58, 81 Center of mass (CM) motion, 95, 107, 248 Coupling constant, 104 Cerne, J., 295 Creation operator, 14, 80, 216, 336 Changing potential field, 49 Criterion for superconductivity, 59-61, 121 Charge Critical current density, 15 current in type II superconductors, 207-216 -spin carriers, 293 current, 166, 178 Chemical potential, 107, 139, 281 magnetic field, 89, 166, 178, 188 Chu, M. K., 320 temperature of a superconductor, 8-9, 23-24, 108, Circular 115-119, 130, 142 Fermi surface, 234 temperature, 8-9, 108, 115-119, 130, 138, 142, 234 dichroism, 295 Crystal = lattice, 28 Closely-packed circular disks, 211 body-centered cubic (bcc), 36 Coherence Cuprate length, 81, 116, 189, 234, 236, 256-257, 313 superconductor = high temperature superconductor, of a wave, 167 10, 217, 233 range, 167 lattice structures, 217-225 Commutation relations (rules), 183 Current density = electric current density, 15 Commutator-generating operator = quantum Liouville Current-carrying state, 164 operator, 56, 176 single-particle, 164 Complex Curvature, 42 dynamical variable, 334 inversion of the Cu Fermi surface, 246-248, 257-258, Faraday angle, 296 274, 285 order parameter = G-L wave function, 181, 313 sign, 42 Composite particle, 12, 95 Cusp, 161 Compound superconductor, 8-9, 207-216 Cyclic permutation = cycle, 342 Condensate density, 186 Cyclotron resonance, 219, Condensation temperature = critical temperature, 8-9, 23, 108, 130, 142 Condensation energy, 185-188 DC Josephson effect = Josephson tunneling, 147-161, Condensed pairon state, 131, 184 194, 204 Condensed pairon, 138-141 Deaver-Fairbank (experiment), 4, 166 Condensed phase, 20 Debye, P., 48 Conduction electron, 10 Debye Conductivity, 276 frequency, 65, 77 Conservation of kinetic energy potential = screened Coulomb potential Constriction, 195 screening Cooper temperature, 115, 121 equation, 70-76, 136 theory of heat capacity, 48 Hamiltonian, 74 Deformation potential, 51 pair (pairon) size, 65, 138 Density pair = bound Cooper pair = pairon, 65-75, 133 condition, 185, 313 plane = plane, 219, 228-229 matrix (operator), 56-58 Schrieffer relation = linear energy-momentum of condensed pairons, 138-141 relation, 23, 65-68, 114, 243 of pairons, 131, 138-141, 144 system, (problem), 65-67 of states at the Fermi energy, 37-38, 153 Copper of states in energy, 37-39, 153 critical temperature, 217 of states in frequency, 49 planes, 217-219, 229 of states in momentum, 108 Correlation length, 216 of states, 37, 47, 153, 262, 287 Cosine law formula, 219 wave mode, 50, 213 INDEX 361
Diamagnetic current, 196, 208-213 Electrical conductivity, 14-15, 252 Diamagnetic, 208 Electromagnetic stress tensor (magnetic pressure), Diffusion coefficient, 274 density of states, 65, Dirac, P.A.M., 10 effective mass, 43 Dirac’s formulation of quantum mechanics, 10, 103, “Electron”, 13-14, 16, 228-230 183 Electron Dispersion relation, 22, 39, 80, 118, 215, 243 flux quantum, 209 Distinguishable particles, 99 gas system, 55-58 Doll-Näbauer, 166 heat capacity, 37, 235, 271 Dome-shaped concentration dependence, 241 -phonon interaction strength, 45-58, 308 Doping phonon system, 54 dependence on 241-248 transport model, 149 in 246 Elemental superconductors, 8, 231 in 247 Elementary excitations in a superconductor, 144 Double-inverted caps, 93 Elementary particle, 103 Down-spin electron, 126 Elements, 8 D-p model, 320 Elipsoidal Fermi surface, 38, 42-44 Drift velocity, 17, 252 Ellipsoid, 42 Drude theory, 300 Elliptic polarization, 296 Dulong-Petit's Law, 46 Energy D-wave Cooper pairs, 230 -(k-q) representation, 136 Dynamic continuum, 153 conductivity, 303-304 eigenstate, 297 conductivity tensor, 300 eigenvalue equation (problem) for a quasiparticle, equilibrium, 11 70-73 Hall angle, 297 eigenvalue, 53, 66, 70 Hall coefficient, 303 gap equations at finite temperatures, 123, 128-132, inverse Hall angle, 303 135,138 momentum relation, = dispersion relation, 65, 215 of zero point motion, 47 Electron separation, 147 -positron pair creation, 156 Energy gap, 6, 85, 89, 133, 186 -electron collision, 257 between excited and ground pairons, = pairon energy -phonon interaction, 314 gap, 6, 85-89, 133-148, 151 “Electron”, 13, 18, 63, 230 equations at 0 K, 89-90, 126-129, 132 pairon, 77-93 equations below 132 -like, 287-288 for pairons, 137 Effective for quasi-electrons, 85-89, 123-126, 137, 147, 187, lattice potential, 30 236 mass approximation, 43 in superconductors, 233 mass, 38, 41, 43, 77, 165, 219 Energy-state phonon-exchange interaction, 54-55, 58, 314 annihilation (creation) operator, 127, 80, 336 Ehrenfest-Oppenheimer-Bethe´s (EOB's) rule, 12, 23, Equation-of-motion for a Bloch electron, 39 95-96, 103 Even permutation, 305-306 Eigenket (vector), 335 Evolution operator, 139 Eigenvalue equation, 70, 335 Exchange and permutation, 305-306 Eigenvalue, 52, 70 Excited pairons, 135, 148, 237 Eigenvector, 52, 70 Excited particles = moving particles, 67 Einstein, A., Extremum condition, 84 relation, 276-277 temperature theory of heat capacity Faraday rotation angle, 295-296 Electric current (density), 164, 299 Fermi 362 INDEX
anticommutation rules, 61, 183, 340 Gauge-invariant, 171 cylinder, 220 Generalized degeneracy, 287 BCS Hamiltonian, 77-82, 85, 134, 230-231, 241 distribution function, 12, 272 energy-gap equation, 85, 129-132, 135, 138, 232 golden rule, 153, 261 London penetration depth, 172, 180, 189 liquid model, 13, 30-31, 39 Ohm’s law, 151, 252, 300 momentum, 165 Giaever tunneling, 7, 25, 148-161, 193 sphere, 33 Giaever, I., 7, 24, 148 temperature, 121, 234 Ginzburg-Landau (G-L) velocity (speed), 50, 165, 234, 245 wave function = G-L complex order parameter, 181, Fermi surface, 32-33, 38, 65, 228 313 of Al, 35 equation, 182 of Be, 34 Gorkov L. P., 186 of Cu, 34, 229, 258 Gorter, C. J., 311 of Na, 33 Gorter-Casimir formula, 311 of Pb, 36 Grand canonical of W, 35 density operator, 125, 175 of YBCO, 229 ensemble, 75, 125, 127, 175, 185 Fermion, 95 ensemble average, 75, 125, 175 composite, 96 ensemble trace, 125, 175, 184-185 field operator, 183, 343 Ground pairon Fermion-boson composite, 100 = zero-momentum pairon, 77, 82-85, 107-114, 124- Ferromagnetic transition, 19, 313 131, 135-138, 151, 163, 231 Feynman diagram, 53-56, 79, 81 density, 144 Feynman, R. P., 53 Ground state for a quantum particle, 21, 82-88 Field operator, 181-183, 343 Ground state ket, 82, 231-232 Field, penetration depth, 180, 189-190, 209-210 Ground-state energy of a pairon, 82-88, 123-132, 151, Floating magnet, 3 231 Flux quantization, 3, 4, 60, 163-180, 209-210 wavefunction, 163 Flux quantum = magnetic flux unit, 4, 208 Ground-state energy of the BCS system, 123, 126-128, Fluxoid, 174 231 Formation of a supercondensate, 91, 128 Formula for quantum tunneling, 193, 236-238 Free Haas-van Alphen (dHvA) oscillations, 219 electron model for a metal, 33 Hall moving pairons, 234 angle, 253-255, 296, 299 Fröhlich Hamiltonian, 53 coefficients, 17, 249-250, 265, 269-283 Fröhlich, H., 53, 314 current, 17 Fugacity, 109 effect, 16-17, 253 Full Hamiltonian, 133-135 electric field, 253, 299 Fundamental magnetic flux unit = flux quantum, 208 Hamilton's equation of motion, 170 Fuzzy (blurred) Fermi surface, 93, 148 Harmonic approximation, 46-48 Heat capacity jump, 212 Gap, 7 of 2D bosons, 83, 109, 235 Ginzburg-Landau (GL) of 3D bosons, 111-113 coherence length, 182, 188, 209-212, 234 of a superconductor, 235-236 complex order parameter, 181 of a metal, 37-39 equation, 181 of a superconductor, 109-113, 145, theory, 181-191, 209 of solids, 37-39 wavefunction, 181, 212 of type I and II superconductors, 212 Gas-liquid transition, 19 of YBCO, 235-236 Gauge-choice, 171 Heavy-fermions, 258 INDEX 363
Heisenberg’s junction, 4-5, 193-195 uncertainty principle, 11 supercurrent tunneling, 193 equation of motion, 183, 341-343 tunneling = dc Josephson effect, 4-5, 147-161, 193- picture = HP, 341 206 Hermitean conjugate, 51 Josephson-Feynman equations, 199, 205, 241 Hermitean operator, 51, 335 Hexagonal closed pack (hcp), 210 223-225 K-q representation, 97 223-225 Kaon, 106 High critical temperature, 9, 217, 233-234 Kamerlingh Onnes, H., 1, 311 cuprate superconductor, 25, 217-225, 233-234 Ket (vector), 11 below 227-239 Kinetic theory, 14-18, 250-255 hamiltonian, 227-231 Hohenberg's theorem, 25, 110 “Hole”, 13-14, 16, 18, 63, 230 241, 246, 249-250, 257, 286, 294 pairon, 77-93, 230 Lagrangian, 46 -phonon scattering rate, 305 Landau, L.D., 13, -like, 287 Landau theory of second-order phase transition, 181 Hubard model, 320 Lattice Hyperboloid, 42 constant, 216 Hyperboloidal Fermi surfaces, 92 defects (imperfections) of one sheet, 42 dependent anisotropy, 307 of two sheets, 42 dynamics, 45-48 Hypothetical “superelectron”, 170, 182 potential, 28 structures of cuprates, 217-225, 229 vibration, 45-49, 215 I-V curve, 147-161, 193-194, 238 periodic, 28-29, 219 of 157 Law of corresponding states, 119, 234 Identical particles, 101 Layered organic superconductors, 217-225 Independent pairon picture (model), 116, 133-135, 147, Layered structure, 217-221 206, 293, 298 Lennard-Jones potential, 20 Indistinguishable quantum particles, 11, 95 Linear Inflexion point, 292 energy-momentum relation, 25, 114, 227, 243 Infrared Hall effect, 295-301 -T dependence, 37 Inhomogeneous pinning of vortex lines, 208 Linearly In-plane dependent heat capacity, 37 conduction, 280 polarized laser, 296 Hall coefficient, 271 Liouville operator algebras, 56, 71 resistivity, 260 Localized Bloch wave packets, 40, 229 Seebeck coefficient, 269-283, 279-280 London, F., 11, 13, 170 Internal energy (density), 109-113, 141 London's Interpairon distance, 116, 120, 138-141, 234 equation, 171-180, 182 lonization gap, 147 penetration depth, 172, 180 Isospin, 103 rigidity, 31, IR Hall effect, 301 London-London (theory), 170, 312 Longitudinal acoustic phonon, 50, 213-216, 227, 252, 309 Josephson, B. D., 60, 193 wave, 50, 213 Josephson Loram, J. W., 235 effect, 200 Lorentz electric force, 16, 165 equations, 197-200 Lower critical field, 9, 207-216 frequency = ac Josephson effect, 200 interference, 4, 60, 167, 206, 243 364 INDEX
Magnetic field, penetration depth, 180, 209-210 Moving supercondensate = supercondensate in motion, Magnetic field, flux quantization, 208-209 67, 91, 128-130, 133, 163, 176-178 Macrowavefunction, 312 Müller-Bednorz, 10, 217 Maeno, Y., 225 Multi-carrier metal, 269 Magnetic (field) moment, 291 flux lines, 2, 4 NaCl, 213 pressure, 179, 211 207 susceptibility, 285-294 222, 249-250, 294 Magnetization = magnetic moment per unit volume, “Neck”, 42, 91-93, 278 208, 288 at the Brillouin boundary, 269 Magneto-optical effect, 220 Néel temperature, 221, 258 Magnetotransport, 249 Negative ions 228 Major axis rotation, 296 Negative resistance, 157-158 Many Neutral supercondensate, 90-91, 165, 178 boson occupation number, 333 Newtonian equation of motion, 14, 41 boson state of motion, 164-165 Non-perovskite structure, 257-258, 266 boson state, 165 Normal fermion occupation numbers, 333 curvatures, 42 Markoffian approximation, 57 fluid, 311 Mass conservation law, 110 mode, 47 Massive Normalized ground state ket, 82, 231, 335 “atoms”, 103 Number pairs, 245 density operator = one-body density operator, 72, Mass tensor, 43 175 Massless bosons, 69, 107-114 density of vortex lines, 210 in 2D, 111, 230 Number of pairons, 138-141 Massless particles, 69 Number representation = occupation number Matthiessen's rule, 16, 255 representation, 333 Maximum heat capacity, 142 Maxwell's equations, 190 McConville and Serin, 211 Observable physical variable, 99 Mean free time, 15, 257, 299 Occupation number representation = number Megerle, K, 148 representation, 333 Mercereau, J. E., 319 Odd permutation, 336 Meissner O-Fermi surface, 246 effect, 1-2, 179 Ohm’s energy, 179, 210-211 law, 15, 147, 151, 201, 299 magnetic pressure, 179, 210 second law, 261 state, 173, 211 Ohmic conduction, 260-283, 279 Meissner, W., 173 One-body Meissner-Ochsenfeld effect, 2, 210-211, 312 average, 185 Minimum energy principle, 123, 131, 231 density matrix, 72, 175 Minimum excitation energy, 147 density operator, 72, 175 Mixed quantum Liouville equation, 175-177 representation, 191 trace (tr) = diagonal sum-over one-body states, 185 state of a type II superconductor, 9, 208 One-electron-picture approximation, 31 state, 9, 208 One-particle-state = single-particle state, 164 Monochromatic plane-wave, 167 Onsager, L., 166 Monovalent metals, 8, 27, 92 formula for magnetic oscillations, 220 Moving pairon = excited pairon, 67-69, 107-114, 128- hypothesis about flux quantization, 165-166, 291 130, 133-138, 237, 178 Optical branch (mode), 213-216 INDEX 365
ellipticity, 295 Permutation (operator), 103, 336 phonons, 47, 213-216, 228, 309 Perovskite, 221 -phonon exchange attraction, 45-58, 77, 228, 258 Perturbation (perturbing) Hamiltonian, 104 Order of phase transition, 19-20, 110 Phase diagram, 242 Organic superconductor, 220 Phase difference Ortho-hydrogen, 105 across a junction, 199 Orthorhombic (orc) lattice, 28 due to magnetic field, 22, 170 Out-of-plane due to particle motion, 22, 166-171 Hall coefficient, 271 Phase of a quasi-wavefunction, 22, 167-170 transport, 259-267 Phase transition resistivity, 259, 266, 280 of second order, 114-115, 211 Seebeck coefficient, 269-283, 280-282 of first order, 211 Ovservables, 337-339 of third order, 110, 114 Phonon, 45,49 exchange attraction, 45-58, 59, 77-82, 227, 230 Pair exchange-pairing Hamiltonian, 45, 54, 74, 77-78, annihilation operator, 127, 80 134, 227 creation operator, 80, 215 number density, 252 dissociation, 156 Photo-absorption, 148, 186 -annihilate, 80-81, 215 Photon, 22 -create, 80-81, 215 Physical vacuum (state), 52, 77, 79, 83, 335 Pairon, 22 Pinning of vortex lines, 210 annihilation operator, 134 Pion, 106 chemical potential, 281 Pippard-coherence length = BCS coherence length, 81, condensation energy, 185-188 116 density, 245, 290 Planck distribution function, 47, 151, 154 density operator, 175, 181, 204 Point contact, 195 density matrix, 175 Point-like repulsive interaction, 191 dynamics, 133, 144 Position density matrix, 184 energy, 22-24, 135 Positive ion 228 energy diagram, 24, 158 Predominant charge carriers, 115, 119, 154 energy gap, 90, 133, 147-148, 133-138, 186 Predominant pairon, 115, 119 energy-state annihilation operator, 127 Principal axes of curvature, 42 field operator, 181-183 Principal flux, 153 curvatures, 42-43 formation factor, 119-121, 234 mass, 42-43 heat capacity, 141-145 -axis transformation, 46 -phonon scattering rate, 304-305 repulsive interaction, 185 size, 23, 144, 186, 210 Quadratic dispersion relation, 228 statistics, 139 Quadrivalent, Ce, 246 transport model, 147, 149 Quantized flux, 209 Pairon = Cooper pair, 133 Quantum Para-hydrogen, 105 field operators, 183 Particle permutation symmetry, 104, 336 Hall effect, 311-323 Pauli’s jump, 261 exclusion principle, 11, 91, 98, Liouville equation, 56-58, 71, 176, 307 formula, 289, Liouville operator, 56 paramagnetism, 287, of lattice vibration = phonon, 45, 215 Penetration depth (magnetic-field), 3, 180, 190, 209- Seebeck coefficient, 271 210, 312, statistical factor, 154, 159, 196, 264 Periodic potential, 28 statistical postulate, 12, 95 Periodic table, 8 statistics, 59-63 366 INDEX
transition rate, 152 coefficient = thermopower, 269-283 tunneling circuits, 149 coefficients in metals, 277-279 tunneling experiments and energy gaps, 195, 235, currents, 269-283 237 semi-quantum, formula, 271 tunneling experiments, 147-161, 195 Self-focusing power, 196 tunneling in 156-161, 194 Shape of Fermi surface, 13, 31 zero-point motion, 11, 28, 47 Shapiro steps, 200-204 Quasi-electron Shapiro, S., 200 = unpaired electron, 62, 123-126, 147 Sharp Fermi surface, 13 energy gap, 62, 85, 123, 126-132, 147, 236 Shockley’s formula, 219 energy, 62, 124-126, 147 Sign change of the Hall coefficient, 241 transport model, 124 Similarity between supercurrent and laser, 178, 204 Quasi-wave function for a supercondensate, 71, 128, Single-particle Hamiltonian, 11, 104 167, 194 Single-particle state, 175 Quasi-wave function, 71, 167, 175-177, 194 Singlet pairs, 227 Small pockets, 228 Solid angle, 151 Random distribution, 219 Sommerfeld, A., 166 Rate of collision = collision rate = scattering rate, 16 Specific heat = heat capacity per gram, 109, 113, 141 Real Speed of sound, 80, 227 wave function, 21 Spherical Fermi surface = Fermi sphere, 37 order parameter, 181 Spin Reduced = spin angular momentum, 103 Hamiltonian, 77-78, 82, 87-88, 176, 231 dependent density of states, 290 supercondensate density, 141 statistics theorem (rule), 12, 102, 104 Repulsive interaction strength, 185 Spontaneous magnetization, 181, 313 Resistivity in the ab plane, 250 SQUID, 5-6, 199, 243 Resonant valence bond, 320 224 Revised 222 density condition, 183 Standard London equation, 312 model, 106 G-L wavefunction, 183 BCS model, 236 Right-left symmetry, 160 Static Ring supercurrent, 3, 163-169, 179, 184 equilibrium, 11 scattering rate, 299 Stationary pairon, 67, 124, 231 S-I-N, 238 Stephan-Boltzmann law, 113 S-I-S “sandwich” = S-I-S system, 147-156, 193 Supercondensate, 20, 91 system, 147, 156-161, 238 density, 129-132, 144 Scalar potential, 170 formation, 91 Scattering wavefunction, 128 rate, 16 Superconducting quantum interference device T- and 300 (SQUID), 5-6, 167, 243 Schafroth, Blatt and Butler (SBB), 244 Superconducting Schrödinger electron, 311 energy-eigenvalue equation, 70-72 temperature = critical temperature, 24, 130 equation of motion, 70-72, 177 transition, 19-25, 302 ket, 70 Superconductivity and band structures, 60 picture, 341 Superconductor (definition), 1, 77 Second quantization (operators, formalism), 14, 71-76, Supercurrent 163 314, 333-343 in 2D, 164, 217-225, 230 Seebeck in 3D, 233 classical formula, 271 density, 171, 178 INDEX 367
ring, 163, 169, 179 Type interference = Josephson interference, 6, 167, 193- I magnetic behavior, 9, 207-216 195, 206 I superconductor, 9, 186, 228 tunneling = Josephson tunneling, 147-161, 193-194, II magnetic behavior, 9, 207-216, 216-225 204 II superconductor, 9, 60, 208-213, 216-225 Superelectron, 182, 311 Superfluid transition, 13 Superfluid (helium) = liquid He II, 311 Ueling-Uhlenbeck, 197 Surface supercurrent, 179, 211 Uncertainty principle (Heisenberg's), 11 Symmetric ket, 336 Unit cell, 228 for bosons, 103, 337 Unpaired electron = quasi-electron, 62, 123-126 Symmetrizing operator, 336 Upper critical field, 9, 207-216 Symmetry of wave function, 95 Upper critical temperature, 9, 108, 130 Symmetry requirement, 336 Up-spin unpaired electron, 126 System-density operator, 56
V-I diagram, 202 Taylor-Burstein (experiments), 160 Vacuum ket (state) = zero-particle ket (state), 52, 77, Temperature-dependent energy gap, 123, 128-132 335 Temperature-dependent quasi-electron energy gaps, Van Hove singularity, 48 123, 128-132 Vapor-liquid transition, 19 Terasaki, I., 259, 271, 280 Variational calculation, 231 Tewardt, T., 186 Vector potential, 170 Thermal diffusion, 274-278 Virtual phonon exchange, 314 Thermodynamic critical field, 89, 166, 178-179, 188, Voltage standard, 151 211 Vortex line, 208-214 Thermopower, 269-283 Vortex structure, 182, 188-189, 208 of a semiconductor, 275 Threshold voltage, 148-150, 159, 238 Time-dependent perturbation method (theory), 57 Wave T-j model 320 function, 21 223-224 packet, 257 Tomonaga, S., 197 -particle duality, 40 Torque magnetometry, 219 Weak Torrance, J. B., 285 coupling approximation, 57 Transition link = Josephson junction, 195 probability, 152 Werthamer, N. R., 186 rate, 152 Transport above 249-267 Transverse oscillation, 215 Yang-Fermi, 106 Transverse wave, 215 217-225, 228, Trivalent Nd, 246 234-235, 255, 279-283, 298 Tunneling theory, 302-303 current, 153 Yukawa, H., 314 experiments, 7, 186, 195 junction = weak link, 195 Two Zero momentum boson = stationary boson, 77,107-114 charge carriers, 250 Zero point motion, 28, 47 -dimensional (2D) conduction, 217-219, 230 Zero resistance, 1, 207 energy gaps, 147, 217, 236-238 Zero-momentum Cooper pair = stationary pairon, 77- -fluid model, 90, 311 78, 124-127, 163-164, 231 electron composition aspect, 58 Zero-particle state = vacuum state, 52, 77, 335 pairon dissociation, 156 Zero-temperature coherence length, 81, 116 Fundamental Theories of Physics
Series Editor: Alwyn van der Merwe, University of Denver, USA
1. M. Sachs: General Relativity and Matter. A Spinor Field Theory from Fermis to Light Years. With a Foreword by C. Kilmister. 1982 ISBN 90 277 1381 2 2. G.H. Duffey: A Development of Quantum Mechanics. Based on Symmetry Considerations. 1985 ISBN 90 277 1587 4 3. S. Diner, D. Fargue, G. Lochak and F. Selleri (eds.): The Wave Particle Dualism. A Tribute to Louis de Broglie on his 90th Birthday. 1984 ISBN 90 277 1664 1 4. E. Prugovečki: Stochastic Quantum Mechanics and Quantum Spacetime. A Consistent Unific ation of Relativity and Quantum Theory based on Stochastic Spaces. 1984; 2nd printing 1986 ISBN 90 277 1617 X 5. D. Hestenes and G. Sobczyk: Clifford Algebra to Geometric Calculus. A Unified Language for Mathematics and Physics. 1984 ISBN 90 277 1673 0; Pb (1987) 90 277 2561 6 6. P. Exner: Open Quantum Systems and Feynman Integrals. 1985 ISBN 90 277 1678 1 7. L. Mayants: The Enigma of Probability and Physics. 1984 ISBN 90 277 1674 9 8. E. Tocaci: Relativistic Mechanics, Time and Inertia. Translated from Romanian. Edited and with a Foreword by C.W. Kilmister. 1985 ISBN 90 277 1769 9 9. B. Bertotti, F. de Felice and A. Pascolini (eds.): General Relativity and Gravitation. Proceedings of the 10th International Conference (Padova, Italy, 1983). 1984 ISBN 90 277 1819 9 10. G. Tarozzi and A. van der Merwe (eds.): Open Questions in Quantum Physics. 1985 ISBN 90 277 1853 9 11. J.V. Narlikar and T. Padmanabhan: Gravity, Gauge Theories and Quantum Cosmology. 1986 ISBN 90 277 1948 9 12. G.S. Asanov: Finsler Geometry, Relativity and Gauge Theories. 1985 ISBN 90 277 1960 8 13. K. Namsrai: Nonlocal Quantum Field Theory and Stochastic Quantum Mechanics. 1986 ISBN 90 277 2001 0 14. C. Ray Smith and W.T. Grandy, Jr. (eds.): Maximum Entropy and Bayesian Methods in Inverse Problems. Proceedings of the 1st and 2nd International Workshop (Laramie, Wyoming, USA). 1985 ISBN 90 277 2074 6 15. D. Hestenes: New Foundations for Classical Mechanics. 1986 ISBN 90 277 2090 8; Pb (1987) 90 277 2526 8 16. S. J. Prokhovnik: Light in Einstein’s Universe. The Role of Energy in Cosmology and Relativity. 1985 ISBN 90 277 2093 2 17. Y.S. Kim and M.E. Noz: Theory and Applications of the Poincaré Group. 1986 ISBN 90 277 2141 6 18. M. Sachs: Quantum Mechanics from General Relativity. An Approximation for a Theory of Inertia. 1986 ISBN 90 277 2247 1 19. W.T. Grandy, Jr.: Foundations of Statistical Mechanics. Vol. I: Equilibrium Theory. 1987 ISBN 90 277 2489 X 20. H. H von Borzeszkowski and H. J. Treder: The Meaning of Quantum Gravity. 1988 ISBN 90 277 2518 7 21. C. Ray Smith and G.J. Erickson (eds.): Maximum Entropy and Bayesian Spectral Analysis and Estimation Problems. Proceedings of the 3rd International Workshop (Laramie, Wyoming, USA, 1983). 1987 ISBN 90 277 2579 9 22. A.O. Barut and A. van der Merwe (eds.): Selected Scientific Papers of Alfred Landé. [1888 1975]. 1988 ISBN 90 277 2594 2 Fundamental Theories of Physics
23. W.T. Grandy, Jr.: Foundations of Statistical Mechanics. Vol. II: Nonequilibrium Phenomena. 1988 ISBN 90-277-2649-3 24. E.I. Bitsakis and C.A. Nicolaides (eds.): The Concept of Probability. Proceedings of the Delphi Conference (Delphi, Greece, 1987). 1989 ISBN 90-277-2679-5 25. A. van der Merwe, F. Selleri and G. Tarozzi (eds.): Microphysical Reality and Quantum Formalism, Vol. 1. Proceedings of the International Conference (Urbino, Italy, 1985). 1988 ISBN 90-277-2683-3 26. A. van der Merwe, F. Selleri and G. Tarozzi (eds.): Microphysical Reality and Quantum Formalism, Vol. 2. Proceedings of the International Conference (Urbino, Italy, 1985). 1988 ISBN 90-277-2684-1 27. I.D. Novikov and V.P. Frolov: Physics of Black Holes. 1989 ISBN 90-277-2685-X 28. G. Tarozzi and A. van der Merwe (eds.): The Nature of Quantum Paradoxes. Italian Studies in the Foundations and Philosophy of Modern Physics. 1988 ISBN 90-277-2703-1 29. B.R. Iyer, N. Mukunda and C.V. Vishveshwara (eds.): Gravitation, Gauge Theories and the Early Universe. 1989 ISBN 90-277-2710-4 30. H. Mark and L. Wood (eds.): Energy in Physics, War and Peace. A Festschrift celebrating Edward Teller’s 80th Birthday. 1988 ISBN 90-277-2775-9 31. G.J. Erickson and C.R. Smith (eds.): Maximum-Entropy and Bayesian Methods in Science and Engineering. Vol. I: Foundations. 1988 ISBN 90-277-2793-7 32. G.J. Erickson and C.R. Smith (eds.): Maximum-Entropy and Bayesian Methods in Science and Engineering. Vol. II: Applications. 1988 ISBN 90-277-2794-5 33. M.E. Noz and Y.S. Kim (eds.): Special Relativity and Quantum Theory. A Collection of Papers on the Poincaré Group. 1988 ISBN 90-277-2799-6 34. I.Yu. Kobzarev and Yu.I. Manin: Elementary Particles. Mathematics, Physics and Philosophy. 1989 ISBN 0-7923-0098-X 35. F. Selleri: Quantum Paradoxes and Physical Reality. 1990 ISBN 0-7923-0253-2 36. J. Skilling (ed.): Maximum-Entropy and Bayesian Methods. Proceedings of the 8th International Workshop (Cambridge, UK, 1988). 1989 ISBN 0-7923-0224-9 37. M. Kafatos (ed.): Bell’s Theorem, Quantum Theory and Conceptions of the Universe. 1989 ISBN 0-7923-0496-9 38. Yu.A. Izyumov and V.N. Syromyatnikov: Phase Transitions and Crystal Symmetry. 1990 ISBN 0-7923-0542-6 39. P.F. Fougère (ed.): Maximum-Entropy and Bayesian Methods. Proceedings of the 9th Interna- tional Workshop (Dartmouth, Massachusetts, USA, 1989). 1990 ISBN 0-7923-0928-6 40. L. de Broglie: Heisenberg’s Uncertainties and the Probabilistic Interpretation of Wave Mech- anics. With Critical Notes of the Author. 1990 ISBN 0-7923-0929-4 41. W.T. Grandy, Jr.: Relativistic Quantum Mechanics of Leptons and Fields. 1991 ISBN 0-7923-1049-7 42. Yu.L. Klimontovich: Turbulent Motion and the Structure of Chaos. A New Approach to the Statistical Theory of Open Systems. 1991 ISBN 0-7923-1114-0 43. W.T. Grandy, Jr. and L.H. Schick (eds.): Maximum-Entropy and Bayesian Methods. Proceed- ings of the 10th International Workshop (Laramie, Wyoming, USA, 1990). 1991 ISBN 0-7923-1140-X 44. P. Pták and S. Pulmannová: Orthomodular Structures as Quantum Logics. Intrinsic Properties, State Space and Probabilistic Topics. 1991 ISBN 0-7923-1207-4 45. D. Hestenes and A. Weingartshofer (eds.): The Electron. New Theory and Experiment. 1991 ISBN 0-7923-1356-9 Fundamental Theories of Physics
46. P.P.J.M. Schram: Kinetic Theory of Gases and Plasmas. 1991 ISBN 0 7923 1392 5 47. A. Micali, R. Boudet and J. Helmstetter (eds.): Clifford Algebras and their Applications in Mathematical Physics. 1992 ISBN 0 7923 1623 1 48. E. Prugovečki: Quantum Geometry. A Framework for Quantum General Relativity. 1992 ISBN 0 7923 1640 1 49. M.H. Mac Gregor: The Enigmatic Electron. 1992 ISBN 0 7923 1982 6 50. C.R. Smith, G. J. Erickson and P.O. Neudorfer (eds.): Maximum Entropy and Bayesian Methods. Proceedings of the 11th International Workshop (Seattle, 1991). 1993 ISBN 0 7923 2031 X 51. D.J. Hoekzema: The Quantum Labyrinth. 1993 ISBN 0 7923 2066 2 52. Z. Oziewicz, B. Jancewicz and A. Borowiec (eds.): Spinors, Twistors, Clifford Algebras and Quantum Deformations. Proceedings of the Second Max Born Symposium (Wroclaw, Poland, 1992). 1993 ISBN 0 7923 2251 7 53. A. Mohammad Djafari and G. Demoment (eds.): Maximum Entropy and Bayesian Methods. Proceedings of the 12th International Workshop (Paris, France, 1992). 1993 ISBN 0 7923 2280 0 54. M. Riesz: Clifford Numbers and Spinors with Riesz’ Private Lectures to E. Folke Bolinder and a Historical Review by Pertti Lounesto. E.F. Bolinder and P. Lounesto (eds.). 1993 ISBN 0 7923 2299 1 55. F. Brackx, R. Delanghe and H. Serras (eds.): Clifford Algebras and their Applications in Mathematical Physics. Proceedings of the Third Conference (Deinze, 1993) 1993 ISBN 0 7923 2347 5 56. J.R. Fanchi: Parametrized Relativistic Quantum Theory. 1993 ISBN 0 7923 2376 9 57. A. Peres: Quantum Theory: Concepts and Methods. 1993 ISBN 0 7923 2549 4 58. P.L. Antonelli, R.S. Ingarden and M. Matsumoto: The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology. 1993 ISBN 0 7923 2577 X 59. R. Miron and M. Anastasiei: The Geometry of Lagrange Spaces: Theory and Applications. 1994 ISBN 0 7923 2591 5 60. G. Adomian: Solving Frontier Problems of Physics: The Decomposition Method. 1994 ISBN 0 7923 2644 X 61. B.S. Kerner and V.V. Osipov: Autosolitons. A New Approach to Problems of Self Organization and Turbulence. 1994 ISBN 0 7923 2816 7 62. G.R. Heidbreder (ed.): Maximum Entropy and Bayesian Methods. Proceedings of the 13th International Workshop (Santa Barbara, USA, 1993) 1996 ISBN 0 7923 2851 5 63. J. Peřina, Z. Hradil and B. Jurčo: Quantum Optics and Fundamentals of Physics. 1994 ISBN 0 7923 3000 5 64. M. Evans and J. P. Vigier: The Enigmatic Photon. Volume 1: The Field 1994 ISBN 0 7923 3049 8 65. C.K. Raju: Time: Towards a Constistent Theory. 1994 ISBN 0 7923 3103 6 66. A.K.T. Assis: Weber’s Electrodynamics. 1994 ISBN 0 7923 3137 0 67. Yu. L. Klimontovich: Statistical Theory of Open Systems. Volume 1: A Unified Approach to Kinetic Description of Processes in Active Systems. 1995 ISBN 0 7923 3199 0; Pb: ISBN 0 7923 3242 3 68. M. Evans and J. P. Vigier: The Enigmatic Photon. Volume 2: Non Abelian Electrodynamics. 1995 ISBN 0 7923 3288 1 69. G. Esposito: Complex General Relativity. 1995 ISBN 0 7923 3340 3 Fundamental Theories of Physics
70. J. Skilling and S. Sibisi (eds.): Maximum Entropy and Bayesian Methods. Proceedings of the Fourteenth International Workshop on Maximum Entropy and Bayesian Methods. 1996 ISBN 0 7923 3452 3 71. C. Garola and A. Rossi (eds.): The Foundations of Quantum Mechanics Historical Analysis and Open Questions. 1995 ISBN 0 7923 3480 9 72. A. Peres: Quantum Theory: Concepts and Methods. 1995 (see for hardback edition, Vol. 57) ISBN Pb 0 7923 3632 1 73. M. Ferrero and A. van der Merwe (eds.): Fundamental Problems in Quantum Physics. 1995 ISBN 0 7923 3670 4 74. F.E. Schroeck, Jr.: Quantum Mechanics on Phase Space. 1996 ISBN 0 7923 3794 8 75. L. de la Peña and A.M. Cetto: The Quantum Dice. An Introduction to Stochastic Electro dynamics. 1996 ISBN 0 7923 3818 9 76. P.L. Antonelli and R. Miron (eds.): L agrange and Finsler Geometry. Applications to Physics and Biology. 1996 ISBN 0 7923 3873 1 77. M.W. Evans, J. P. Vigier, S. Roy and S. Jeffers: The Enigmatic Photon. Volume 3: Theory and Practice of the Field. 1996 ISBN 0 7923 4044 2 78. W.G .V. Rosser: Interpretation of Classical Electromagnetism. 1996 ISBN 0 7923 4187 2 79. K.M. Hanson and R.N. Silver (eds.): Maximum Entropy and Bayesian Methods. 1996 ISBN 0 7923 4311 5 80. S. Jeffers, S. Roy, J. P. Vigier and G. Hunter (eds.): The Present Status of the Quantum Theory of Light. Proceedings of a Symposium in Honour of Jean Pierre Vigier. 1997 ISBN 0 7923 4337 9 81. M. Ferrero and A. van der Merwe (eds.): New Developments on Fundamental Problems in Quantum Physics. 1997 ISBN 0 7923 4374 3 82. R. Miron: The Geometry of Higher Order Lagrange Spaces. Applications to Mechanics and Physics. 1997 ISBN 0 7923 4393 X 83. T. Hakioğlu and A.S. Shumovsky (eds.): Quantum Optics and the Spectroscopy of Solids. Concepts and Advances. 1997 ISBN 0 7923 4414 6 84. A. Sitenko and V. Tartakovskii: Theory of Nucleus. Nuclear Structure and Nuclear Interaction. 1997 ISBN 0 7923 4423 5 85. G. Esposito, A. Yu. Kamenshchik and G. Pollifrone: Euclidean Quantum Gravity on Manifolds with Boundary. 1997 ISBN 0 7923 4472 3 86. R.S. Ingarden, A. Kossakowski and M. Ohya: Information Dynamics and Open Systems. Classical and Quantum Approach. 1997 ISBN 0 7923 4473 1 87. K. Nakamura: Quantum versus Chaos. Questions Emerging from Mesoscopic Cosmos. 1997 ISBN 0 7923 4557 6 88. B.R. Iyer and C.V. Vishveshwara (eds.): Geometry, Fields and Cosmology. Techniques and Applications. 1997 ISBN 0 7923 4725 0 89. G.A. Martynov: Classical Statistical Mechanics. 1997 ISBN 0 7923 4774 9 90. M.W. Evans, J. P. Vigier, S. Roy and G. Hunter (eds.): The Enigmatic Photon. Volum e 4: N ew D irections. 1998 ISBN 0 7923 4826 5 91. M. Rédei: Quantum Logic in Algebraic Approach. 1998 ISBN 0 7923 4903 2 92. S. Roy: Statistical Geometry and Applications to Microphysics and Cosmology. 1998 ISBN 0 7923 4907 5 93. B.C. Eu: Nonequilibrium Statistical Mechanics. Ensembled Method. 1998 ISBN 0 7923 4980 6 Fundamental Theories of Physics
94. V. Dietrich, K. Habetha and G. Jank (eds.): Clifford Algebras and Their Application in Math- ematical Physics. Aachen 1996. 1998 ISBN 0-7923-5037-5 95. J.P. Blaizot, X. Campi and M. Ploszajczak (eds.): Nuclear Matter in Different Phases and Transitions. 1999 ISBN 0-7923-5660-8 96. V.P. Frolov and I.D. Novikov: Black Hole Physics. Basic Concepts and New Developments. 1998 ISBN 0-7923-5145-2; Pb 0-7923-5146 97. G. Hunter, S. Jeffers and J-P. Vigier (eds.): Causality and Locality in Modern Physics. 1998 ISBN 0-7923-5227-0 98. G.J. Erickson, J.T. Rychert and C.R. Smith (eds.): Maximum Entropy and Bayesian Methods. 1998 ISBN 0-7923-5047-2 99. D. Hestenes: New Foundations for Classical Mechanics (Second Edition). 1999 ISBN 0-7923-5302-1; Pb ISBN 0-7923-5514-8 100. B.R. Iyer and B. Bhawal (eds.): Black Holes, Gravitational Radiation and the Universe. Essays in Honor of C. V. Vishveshwara. 1999 ISBN 0-7923-5308-0 101. P.L. Antonelli and T.J. Zastawniak: Fundamentals of Finslerian Diffusion with Applications. 1998 ISBN 0-7923-5511-3 102. H. Atmanspacher, A. Amann and U. Müller-Herold: On Quanta, Mind and Matter Hans Primas in Context. 1999 ISBN 0-7923-5696-9 103. M.A. Trump and W.C. Schieve: Classical Relativistic Many-Body Dynamics. 1999 ISBN 0-7923-5737-X 104. A.I. Maimistov and A.M. Basharov: Nonlinear Optical Waves. 1999 ISBN 0-7923-5752-3 105. W. von der Linden, V. Dose, R. Fischer and R. Preuss (eds.): Maximum Entropy and Bayesian Methods Garching, Germany 1998. 1999 ISBN 0-7923-5766-3 106. M.W. Evans: The Enigmatic Photon Volume 5: O(3) Electrodynamics. 1999 ISBN 0-7923-5792-2 107. G.N. Afanasiev: Topological Effects in Quantum Mecvhanics. 1999 ISBN 0-7923-5800-7 108. V. Devanathan: Angular Momentum Techniques in Quantum Mechanics. 1999 ISBN 0-7923-5866-X 109. P.L. Antonelli (ed.): Finslerian Geometries A Meeting of Minds. 1999 ISBN 0-7923-6115-6 110. M.B. Mensky: Quantum Measurements and Decoherence Models and Phenomenology. 2000 ISBN 0-7923-6227-6 111. B. Coecke, D. Moore and A. Wilce (eds.): Current Research in Operation Quantum Logic. Algebras, Categories, Languages. 2000 ISBN 0-7923-6258-6 112. G. Jumarie: Maximum Entropy, Information Without Probability and Complex Fractals. Clas- sical and Quantum Approach. 2000 ISBN 0-7923-6330-2 113. B. Fain: Irreversibilities in Quantum Mechanics. 2000 ISBN 0-7923-6581 -X 114. T. Borne, G. Lochak and H. Stumpf: Nonperturbative Quantum Field Theory and the Structure of Matter. 2001 ISBN 0-7923-6803-7 115. J. Keller: Theory of the Electron. A Theory of Matter from START. 2001 ISBN 0-7923-6819-3 116. M. Rivas: Kinematical Theory of Spinning Particles. Classical and Quantum Mechanical Formalism of Elementary Particles. 2001 ISBN 0-7923-6824-X 117. A.A. Ungar: Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession. The Theory of Gyrogroups and Gyrovector Spaces. 2001 ISBN 0-7923-6909-2 118. R. Miron, D. Hrimiuc, H. Shimada and S.V. Sabau: The Geometry of Hamilton and Lagrange Spaces. 2001 ISBN 0-7923-6926-2 Fundamental Theories of Physics
119. M. Pavšič: The Landscape of Theoretical Physics: A Global View. From Point Particles to the Brane World and Beyond in Search of a Unifying Principle. 2001 ISBN 0792370066 120. R.M. Santilli: Foundations of Hadronic Chemistry. With Applications to New Clean Energies and Fuels. 2001 ISBN 1 402000871 121. S. Fujita and S. Godoy: Theory of High Temperature Superconductivity. 2001 ISBN 1402001495
KLUWER ACADEMIC PUBLISHERS – DORDRECHT / BOSTON / LONDON