ESI NEWS Volume 4, Issue 1, Summer 2009
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Arxiv:1509.06955V1 [Physics.Optics]
Statistical mechanics models for multimode lasers and random lasers F. Antenucci 1,2, A. Crisanti2,3, M. Ib´a˜nez Berganza2,4, A. Marruzzo1,2, L. Leuzzi1,2∗ 1 NANOTEC-CNR, Institute of Nanotechnology, Soft and Living Matter Lab, Rome, Piazzale A. Moro 2, I-00185, Roma, Italy 2 Dipartimento di Fisica, Universit`adi Roma “Sapienza,” Piazzale A. Moro 2, I-00185, Roma, Italy 3 ISC-CNR, UOS Sapienza, Piazzale A. Moro 2, I-00185, Roma, Italy 4 INFN, Gruppo Collegato di Parma, via G.P. Usberti, 7/A - 43124, Parma, Italy We review recent statistical mechanical approaches to multimode laser theory. The theory has proved very effective to describe standard lasers. We refer of the mean field theory for passive mode locking and developments based on Monte Carlo simulations and cavity method to study the role of the frequency matching condition. The status for a complete theory of multimode lasing in open and disordered cavities is discussed and the derivation of the general statistical models in this framework is presented. When light is propagating in a disordered medium, the system can be analyzed via the replica method. For high degrees of disorder and nonlinearity, a glassy behavior is expected at the lasing threshold, providing a suggestive link between glasses and photonics. We describe in details the results for the general Hamiltonian model in mean field approximation and mention an available test for replica symmetry breaking from intensity spectra measurements. Finally, we summary some perspectives still opened for such approaches. The idea that the lasing threshold can be understood as a proper thermodynamic transition goes back since the early development of laser theory and non-linear optics in the 1970s, in particular in connection with modulation instability (see, e.g.,1 and the review2). -
Questions in Quantum Physics: a Personal View
Questions in quantum physics: a personal view Rudolf Haag Waldschmidtstraße 4b, D–83727 Schliersee-Neuhaus, Germany Abstract An assessment of the present status of the theory, some immediate tasks which are suggested thereby and some questions whose answers may require a longer breath since they relate to significant changes in the conceptual and mathematical structure of the theory. 1 Introduction Personal views are shaped by past experiences and so it may be worth while pondering a little about accidental circumstances which channelled the course of one’s own thinking. Meeting the right person at the right time, stumbling across a book or article which suddenly opens a new window. Fifty years ago, as eager students at Munich University just entering the phase of our own scientific research, we were studying the enormous papers by Julian Schwinger on Quantum Electrodynamics, following the arguments line by line but not really grasping the message. I remember the feelings of frustration, realizing that we were far away from the centers of action. But, mixed with this, also some dismay which did not only refer to the enormous arsenal of formalism in the new arXiv:hep-th/0001006v1 3 Jan 2000 developments of QED but began with the standard presentation of the interpretation of Quantum Theory. I remember long discussions with my thesis advisor Fritz Bopp, often while circling some blocks of streets ten times late in the evening, where we looked in vain for some reality behind the enigma of wave-particle dualism. Why should physical quantities correspond to operators in Hilbert space? Why should probabilities be described as absolute squares of amplitudes?, etc., etc. -
From Algebraic Quantum Field Theory to Effective Quantum Gravity
Algebraic approach to QFT Quantum gravity Locality and beyond: from algebraic quantum field theory to effective quantum gravity Kasia Rejzner University of York Local Quantum Physics and beyond in memoriam Rudolf Haag, 26.09.2016 Kasia Rejzner Locality and beyond 1 / 26 Algebraic approach to QFT Quantum gravity Outline of the talk 1 Algebraic approach to QFT AQFT LCQFT pAQFT 2 Quantum gravity Effective quantum gravity Observables The author of a beautiful book Local Quantum Physics. One of the fathers of LQP. We will all miss him. AQFT Algebraic approach to QFT LCQFT Quantum gravity pAQFT The father of Local Quantum Physics Rudolf Haag (1922 – 2016). Kasia Rejzner Locality and beyond 2 / 26 One of the fathers of LQP. We will all miss him. AQFT Algebraic approach to QFT LCQFT Quantum gravity pAQFT The father of Local Quantum Physics Rudolf Haag (1922 – 2016). The author of a beautiful book Local Quantum Physics. Kasia Rejzner Locality and beyond 2 / 26 We will all miss him. AQFT Algebraic approach to QFT LCQFT Quantum gravity pAQFT The father of Local Quantum Physics Rudolf Haag (1922 – 2016). The author of a beautiful book Local Quantum Physics. One of the fathers of LQP. Kasia Rejzner Locality and beyond 2 / 26 AQFT Algebraic approach to QFT LCQFT Quantum gravity pAQFT The father of Local Quantum Physics Rudolf Haag (1922 – 2016). The author of a beautiful book Local Quantum Physics. One of the fathers of LQP. We will all miss him. Kasia Rejzner Locality and beyond 2 / 26 It started as the axiomatic framework of Haag-Kastler[ Haag & Kastler 64]: a model is defined by associating to each region O of Minkowski spacetime the algebra A(O) of observables that can be measured in O. -
Conclusion: the Impact of Statistical Physics
Conclusion: The Impact of Statistical Physics Applications of Statistical Physics The different examples which we have treated in the present book have shown the role played by statistical mechanics in other branches of physics: as a theory of matter in its various forms it serves as a bridge between macroscopic physics, which is more descriptive and experimental, and microscopic physics, which aims at finding the principles on which our understanding of Nature is based. This bridge can be crossed fruitfully in both directions, to explain or predict macroscopic properties from our knowledge of microphysics, and inversely to consolidate the microscopic principles by exploring their more or less distant macroscopic consequences which may be checked experimentally. The use of statistical methods for deductive purposes becomes unavoidable as soon as the systems or the effects studied are no longer elementary. Statistical physics is a tool of common use in the other natural sciences. Astrophysics resorts to it for describing the various forms of matter existing in the Universe where densities are either too high or too low, and tempera tures too high, to enable us to carry out the appropriate laboratory studies. Chemical kinetics as well as chemical equilibria depend in an essential way on it. We have also seen that this makes it possible to calculate the mechan ical properties of fluids or of solids; these properties are postulated in the mechanics of continuous media. Even biophysics has recourse to it when it treats general properties or poorly organized systems. If we turn to the domain of practical applications it is clear that the technology of materials, a science aiming to develop substances which have definite mechanical (metallurgy, plastics, lubricants), chemical (corrosion), thermal (conduction or insulation), electrical (resistance, superconductivity), or optical (display by liquid crystals) properties, has a great interest in statis tical physics. -
Research Statement Statistical Physics Methods and Large Scale
Research Statement Maxim Shkarayev Statistical physics methods and large scale computations In recent years, the methods of statistical physics have found applications in many seemingly un- related areas, such as in information technology and bio-physics. The core of my recent research is largely based on developing and utilizing these methods in the novel areas of applied mathemat- ics: evaluation of error statistics in communication systems and dynamics of neuronal networks. During the coarse of my work I have shown that the distribution of the error rates in the fiber op- tical communication systems has broad tails; I have also shown that the architectural connectivity of the neuronal networks implies the functional connectivity of the afore mentioned networks. In my work I have successfully developed and applied methods based on optimal fluctuation theory, mean-field theory, asymptotic analysis. These methods can be used in investigations of related areas. Optical Communication Systems Error Rate Statistics in Fiber Optical Communication Links. During my studies in the Ap- plied Mathematics Program at the University of Arizona, my research was focused on the analyti- cal, numerical and experimental study of the statistics of rare events. In many cases the event that has the greatest impact is of extremely small likelihood. For example, large magnitude earthquakes are not at all frequent, yet their impact is so dramatic that understanding the likelihood of their oc- currence is of great practical value. Studying the statistical properties of rare events is nontrivial because these events are infrequent and there is rarely sufficient time to observe the event enough times to assess any information about its statistics. -
Statistical Physics II
Statistical Physics II. Janos Polonyi Strasbourg University (Dated: May 9, 2019) Contents I. Equilibrium ensembles 3 A. Closed systems 3 B. Randomness and macroscopic physics 5 C. Heat exchange 6 D. Information 8 E. Correlations and informations 11 F. Maximal entropy principle 12 G. Ensembles 13 H. Second law of thermodynamics 16 I. What is entropy after all? 18 J. Grand canonical ensemble, quantum case 19 K. Noninteracting particles 20 II. Perturbation expansion 22 A. Exchange correlations for free particles 23 B. Interacting classical systems 27 C. Interacting quantum systems 29 III. Phase transitions 30 A. Thermodynamics 32 B. Spontaneous symmetry breaking and order parameter 33 C. Singularities of the partition function 35 IV. Spin models on lattice 37 A. Effective theories 37 B. Spin models 38 C. Ising model in one dimension 39 D. High temperature expansion for the Ising model 41 E. Ordered phase in the Ising model in two dimension dimensions 41 V. Critical phenomena 43 A. Correlation length 44 B. Scaling laws 45 C. Scaling laws from the correlation function 47 D. Landau-Ginzburg double expansion 49 E. Mean field solution 50 F. Fluctuations and the critical point 55 VI. Bose systems 56 A. Noninteracting bosons 56 B. Phases of Helium 58 C. He II 59 D. Energy damping in super-fluid 60 E. Vortices 61 VII. Nonequillibrium processes 62 A. Stochastic processes 62 B. Markov process 63 2 C. Markov chain 64 D. Master equation 65 E. Equilibrium 66 VIII. Brownian motion 66 A. Diffusion equation 66 B. Fokker-Planck equation 68 IX. Linear response 72 A. -
Chapter 7 Equilibrium Statistical Physics
Chapter 7 Equilibrium statistical physics 7.1 Introduction The movement and the internal excitation states of atoms and molecules constitute the microscopic basis of thermodynamics. It is the task of statistical physics to connect the microscopic theory, viz the classical and quantum mechanical equations of motion, with the macroscopic laws of thermodynamics. Thermodynamic limit The number of particles in a macroscopic system is of the order of the Avogadro constantN 6 10 23 and hence huge. An exact solution of 1023 coupled a ∼ · equations of motion will hence not be possible, neither analytically,∗ nor numerically.† In statistical physics we will be dealing therefore with probability distribution functions describing averaged quantities and theirfluctuations. Intensive quantities like the free energy per volume,F/V will then have a well defined thermodynamic limit F lim . (7.1) N →∞ V The existence of a well defined thermodynamic limit (7.1) rests on the law of large num- bers, which implies thatfluctuations scale as 1/ √N. The statistics of intensive quantities reduce hence to an evaluation of their mean forN . →∞ Branches of statistical physics. We can distinguish the following branches of statistical physics. Classical statistical physics. The microscopic equations of motion of the particles are • given by classical mechanics. Classical statistical physics is incomplete in the sense that additional assumptions are needed for a rigorous derivation of thermodynamics. Quantum statistical physics. The microscopic equations of quantum mechanics pro- • vide the complete and self-contained basis of statistical physics once the statistical ensemble is defined. ∗ In classical mechanics one can solve only the two-body problem analytically, the Kepler problem, but not the problem of three or more interacting celestial bodies. -
Quantum Statistical Physics: a New Approach
QUANTUM STATISTICAL PHYSICS: A NEW APPROACH U. F. Edgal*,†,‡ and D. L. Huber‡ School of Technology, North Carolina A&T State University Greensboro, North Carolina, 27411 and Department of Physics, University of Wisconsin-Madison Madison, Wisconsin, 53706 PACS codes: 05.10. – a; 05.30. – d; 60; 70 Key-words: Quantum NNPDF’s, Generalized Order, Reduced One Particle Phase Space, Free Energy, Slater Sum, Product Property of Slater Sum ∗ ∗ To whom correspondence should be addressed. School of Technology, North Carolina A&T State University, 1601 E. Market Street, Greensboro, NC 27411. Phone: (336)334-7718. Fax: (336)334-7546. Email: [email protected]. † North Carolina A&T State University ‡ University of Wisconsin-Madison 1 ABSTRACT The new scheme employed (throughout the “thermodynamic phase space”), in the statistical thermodynamic investigation of classical systems, is extended to quantum systems. Quantum Nearest Neighbor Probability Density Functions (QNNPDF’s) are formulated (in a manner analogous to the classical case) to provide a new quantum approach for describing structure at the microscopic level, as well as characterize the thermodynamic properties of material systems. A major point of this paper is that it relates the free energy of an assembly of interacting particles to QNNPDF’s. Also. the methods of this paper reduces to a great extent, the degree of difficulty of the original equilibrium quantum statistical thermodynamic problem without compromising the accuracy of results. Application to the simple case of dilute, weakly degenerate gases has been outlined.. 2 I. INTRODUCTION The new mathematical framework employed in the determination of the exact free energy of pure classical systems [1] (with arbitrary many-body interactions, throughout the thermodynamic phase space), which was recently extended to classical mixed systems[2] is further extended to quantum systems in the present paper. -
Quantum Mechanical Laws - Bogdan Mielnik and Oscar Rosas-Ruiz
FUNDAMENTALS OF PHYSICS – Vol. I - Quantum Mechanical Laws - Bogdan Mielnik and Oscar Rosas-Ruiz QUANTUM MECHANICAL LAWS Bogdan Mielnik and Oscar Rosas-Ortiz Departamento de Física, Centro de Investigación y de Estudios Avanzados, México Keywords: Indeterminism, Quantum Observables, Probabilistic Interpretation, Schrödinger’s cat, Quantum Control, Entangled States, Einstein-Podolski-Rosen Paradox, Canonical Quantization, Bell Inequalities, Path integral, Quantum Cryptography, Quantum Teleportation, Quantum Computing. Contents: 1. Introduction 2. Black body radiation: the lateral problem becomes fundamental. 3. The discovery of photons 4. Compton’s effect: collisions confirm the existence of photons 5. Atoms: the contradictions of the planetary model 6. The mystery of the allowed energy levels 7. Luis de Broglie: particles or waves? 8. Schrödinger’s wave mechanics: wave vibrations explain the energy levels 9. The statistical interpretation 10. The Schrödinger’s picture of quantum theory 11. The uncertainty principle: instrumental and mathematical aspects. 12. Typical states and spectra 13. Unitary evolution 14. Canonical quantization: scientific or magic algorithm? 15. The mixed states 16. Quantum control: how to manipulate the particle? 17. Measurement theory and its conceptual consequences 18. Interpretational polemics and paradoxes 19. Entangled states 20. Dirac’s theory of the electron as the square root of the Klein-Gordon law 21. Feynman: the interference of virtual histories 22. Locality problems 23. The idea UNESCOof quantum computing and future – perspectives EOLSS 24. Open questions Glossary Bibliography Biographical SketchesSAMPLE CHAPTERS Summary The present day quantum laws unify simple empirical facts and fundamental principles describing the behavior of micro-systems. A parallel but different component is the symbolic language adequate to express the ‘logic’ of quantum phenomena. -
Notas De Fisica CBPF-NF-058/99 November 1999
ISSN 0029-3865 BR0040497 CBPF - CENTRO BRASILEIRO PE PESQUISAS FISICAS Rio de Janeiro Notas de Fisica CBPF-NF-058/99 November 1999 New Concepts in Particle Physics from Solution of an Old Problem Bert Schroer 31/43 CNPq - Conselho Nacional de Desenvolvimento Cientifico e Tecnologico New Concepts in Particle Physics from Solution of an Old Problem Bert Schroer Institut fur Theoretische Physik FU-Berlin, Arnimallee 14, 14195 Berlin, Germany presently: CBPF, Rua Dr. Xavier Sigaud, 22290-180 Rio de Janeiro, Brazil [email protected] July 1999 Abstract Recent ideas on modular localization in local quantum physics are used to clarify the relation between on- and off-shell quantities in particle physics; in particular the relation between on-shell crossing symmetry and off-shell Einstein causality. Among the collateral results of this new non- perturbative approach are profound relations between crossing symmetry of particle physics and Hawking-Unruh like thermal aspects (KMS property, entropy attached to horizons) of quantum mat- ter behind causal horizons which hitherto were more related with Killing horizons in curved spacetime than with localization aspects in Minkowski space particle physics. The scope of this framework is wide and ranges from providing a conceptual basis for the d=l+l bootstrap-formfactor program for factorizable d=l+l models to a decomposition theory of QFT's in terms of a finite collection of unitarily equivalent chiral conformal theories placed a specified relative position within a common Hilbert space (in d=l+l a holographic relation and in higher dimensions more like a scanning). Al- though different from string theory, some of its concepts originated as string theory in the aftermath of the ill-fated S-matrix bootstrap approch of the 6O'es. -
Numdam:AIHPA 1996__64 4 385 0
ANNALES DE L’I. H. P., SECTION A RUDOLF HAAG IZUMI OJIMA On the problem of defining a specific theory within the frame of local quantum physics Annales de l’I. H. P., section A, tome 64, no 4 (1996), p. 385-393 <http://www.numdam.org/item?id=AIHPA_1996__64_4_385_0> © Gauthier-Villars, 1996, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section A » implique l’accord avec les conditions générales d’utilisation (http://www.numdam. org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Ann. Inst. Henri Poincare, Vol. 64, n° 4, 1996, 385 Physique theorique On the problem of defining a specific theory within the frame of local quantum physics Rudolf HAAG Waldschmidtstraße 4B D-83727 Schliersee, Germany. Izumi OJIMA Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-01, Japan. ABSTRACT. - The notion and use of germs of states are discussed. La notion de germe d’état et son utilisation sont 1’ objet de cette discussion. 1. INTRODUCTION The customary procedure of defining a specific theory or model in Quantum Field Theory starts by writing down a Lagrangean in terms of point-like fields. This defines first of all a classical field theory which is then subjected to a process called "quantization", either in the old fashioned form of replacing the numerical-valued fields by field operators with commutation relations or by a Feynman-Schwinger functional integral which should directly give the correlation functions of fields in the vacuum state. -
CV Alfred Kastler
Curriculum Vitae Prof. Dr. Alfred Kastler Name: Alfred Kastler Lebensdaten: 3. Mai 1902 ‐ 7. Januar 1984 Alfred Kastler war ein französischer Physiker. Seine Arbeiten bildeten die Grundlage für die Entwicklung von Maser und Laser. Für die Entdeckung und Entwicklung optischer Methoden zum Studium der elektromagnetischen Resonanzen in Atomen wurde er 1966 mit dem Nobelpreis für Physik ausgezeichnet. Akademischer und beruflicher Werdegang Alfred Kastler studierte von 1921 bis 1926 Physik an der École Normale Supérieure (ENS) in Paris. Anschließend war er als Physiklehrer tätig, zunächst an einem Lyceum in Mühlhausen, später in Colmar und Bordeaux. 1931 wurde er Assistent an der Universität Bordeaux. Von 1936 bis 1938 war er an der Universität in Clemont‐Ferrand tätig. 1938 bekam er eine Professur an der Universität in Bordeaux. Dort beschäftigte er sich mit dem Verfahren der Atomspektroskopie. 1941 ging er nach Paris, wo er die Physik‐Abteilung an der École Normale Supérieure in Paris leitete, die er als junger Mann selbst absolviert hatte. Von 1951 bis zu seinem Rücktritt 1972 war er Direktor des Laboratoire de Spectroscopie Hertzienne des ENS, das heute seinen Namen trägt. 1952 wurde er außerdem Professor an der Faculté de Science in Paris. In den Jahren 1953/54 war er als Gastprofessor an der Universität im belgischen Löwen tätig. Gemeinsam mit seinem Kollegen Jean Brossel entwickelte er spektroskopische Methoden in der Atomphysik, so etwa die Doppelresonanzmethode sowie den physikalischen Effekt des optischen Pumpens. Dieser bewirkt eine Besetzungsinversion durch optische Anregung und bildet zugleich die Grundlagen für die Theorie des Maser‐ sowie des Laserstrahls. Von 1968 bis 1972 war Kastler außerdem Direktor der französischen Forschungsorganisation Centre National de la Recherche Scientifique (CNRS).