Characteristics of Coherence and Information for the Davydov Soliton Field

Home , Davydov soliton

Journal of Modern Physics, 2012, 3, 1907-1913 http://dx.doi.org/10.4236/jmp.2012.312240 Published Online December 2012 (http://www.SciRP.org/journal/jmp)

Bi Qiao1, Kongzhi Song2, Harry E. Ruda3 1Physics Department of Wuhan University of Technology, Wuhan, China 2Institute of Space Medico-Engineering, Beijing, China 3The Center of Advanced Nanotechnology, University of Toronto, Toronto, Canada Email: [email protected]

Received September 17, 2012; revised October 29, 2012; accepted November 8, 2012

ABSTRACT In this work, a generalized Davydov soliton field (DSF) has been investigated. The characteristics of correlation and information for the filed are emphasized and studied. It is a sort of correlation among so called generalized solitons so that the field may appear to some macroscopic quantum properties such as the superconductivity at room temperature. Secondly, the character of information for the field can be described by a nonlinear Liouville equation in the quantum information representation. This provides a basis to express information quality of DSF, which means that DSF can influence or drive object by using (soliton type of) quantum information density. All these two aspects provide a foundation which possibly explains many potential biological functions of human body such as some complex bio-electromagnetic phenomena and their interactions with objects.

Keywords: Soliton; Nonlinear Interaction; Biological Field; Quantum Information; Coherence

1. Introduction another place. It is found in the experiment (3 - 7) × 1010 Hz field frequency that soliton resonance light decompose For many years, the bio-photonics experiments have into excitons and local deformation, corresponding to a discovered that the complex human body likes a set of new band in 1650 cm−1, with amide-I exciton infrared many molecules and atoms to have particle type of dis- absorption spectra observed on the 1666 cm−1 line. This crete characteristic frequency as a stably entire body. This proves that there is a red shift of 16 cm−1 corresponding to symbolizes human body to have distinctive quantum ex- the formation of just soliton bound energy. This shows the citation field. Not only that, the human body in various new metabolism possibilities in the presence of excitons function status experiments often be measured with visi- and phonon interaction as well collective excitation of ble color light and a variety of electromagnetic waves as coherence. However, Davydov soliton in the presence of well as acoustic wave phenomena [1-7]. short duration is serious obstacle to explain it as a basic Some scholars from the physical point of view to ex- information transmission unit. After that, Pang Xiaofeng plore this kind of phenomena, and think the characteristic improved and developed Davydov soliton model, and frequency existence due to nonlinear interaction within established a frame of biological soliton transmission the system units continuously exchange energy between theory based on his nonlinear quantum theory [15,16]. body and environment, which results in the coherent ex- The above phenomena and explorations demonstrate citation of organisms with long-range correlations. This that the human body is a quantum field system. This means the coherence can be achieved by nonlinear inter- quantum field has complex nonlinear elicitors, biological action in organism internal subunits. Thereby they put solitons, and its main interaction may be related to forward entire concepts about human quantization of bio-electromagnetic field, which is manifested by the dissipative structure in self-organization [8-14]. presence of sensitive absorption and emission character- In fact in early 1973 Davydov proposed protein mole- istic frequency and complex spectrum. This is the starting cules excited “solitary” model of the energy transport. point for further research. According to this theory, the protein molecule three spiral micro-vibration and lattice distortion of amide-I exciton 2. Physical Model interactions produce collective excitations as formed soliton, along the helix propagation, so that ATP mole- Let us start from the Davydov soliton perspective and cules hydrolyzed to produce energy from one place to extend the Pang Xiaofeng introduced concepts about the

Copyright © 2012 SciRes. JMP 1908 Q. BI ET AL. domain and the human body biological field to DSF. We greater than 1, then corresponding field is strongly cor- can take DSF as a dissipative structure of non-equilibrium related. thermodynamic system. This DSF system consists of Concerning in present calculation easily to bear sim- generalized solitons or generalized nonlinear excitations, plicity and dropping more than 6 higher order terms, the which represents a local oscillation with characteristics of free energy density F is expressed as: quasi particles and can transmit from a quantum energy NN 241 2 level to other quantum energy level. We extend the theo- F Fi0 nn  nn  r retical model of the domain, and believe that a domain is a nn112m N generalized nonlinear excitation or generalized soliton,  nn n11  nn  n (2) the most important interaction is with the electromagnetic n1 field, and in addition the generalized soliton is through the N   exchange of virtual bosons (e.g. virtual phonon or virtual   nn n11  n n  nnqnnqn       photon) to form the non-local correlation. It is this corre- nn,'1 lation role that can cause entire cooperation of DSF, thus where F0 represents the disorder of the free energy illustrate a macroscopic quantum effect of DSF under the n  0 , N is localized particle number. Also consider condition of the correlation strength and correlation dis- the generalized coordinates n and the generalized tance increase. momentum n , the Lagrange density is Consider a strongly correlated situation, then between 11NN  generalized solitons (may also include a finite object Lm *  m  F (3) 22nn nn interacted with DSF) there exist exchange of virtual pho- nn11 non or virtual photon. This forms a harmoniously entire where the former two are the kinetic energy of the system, biological field correlation or orderly self-organization and F is equivalent to the potential energy. whose wave function is quantized as an operator  . In the continuous approximation, taking minimum of Although the human body system is considered as an open  F equilibrium free energy functional as  0 , the Euler dissipative structure of non-equilibrium thermodynamic  system, but if adding the correlation part caused by in- equation is given by teraction with the system, then the system can be seen as a total equilibrium system. Thus, according to the second  t itt2   2  law of thermodynamics, the free energy density tends to t (4) minimum. 24 24tt   tt  Local generalized soliton density is square modulus of     2 field operator  , where  can be defined as an order where im   . This is a non-linear Schrodinger equa- parameter, where   0 as disordered situation,   0 tion, which can be viewed as an extension of four orders as orderly condition. When DSF forms disorderly to or- for the soliton equation proposed by Pang Xiaofeng at derly transition, in near the transformation point  ATP hydrolysis in helix proteins producing collective should be small, thus the free energy density F can be excitations [15-17]. Hence, this equation can be defined as 2 expanded by  , i.e. a basic equation describing DSF in highly correlated 24 states. In considering the human field high order coherent FF   (1) 0 nn nn conditions, higher order of extension of this equation is Now let one consider two adjacent domains to form also possible, in that situation the solution is usually as- correlation by the exchange of virtual bosons (e.g. virtual sociated with multiple well potentials. phonon or virtual photons). We define first order of cor- In fact for the second order of approximation, the soli-  ton type of solution is given by [17] relation as nnn11  nn  n , and second order of correlation as 1 2    x     rt, sech v t t m      .    g 0  nn n11 n n nnqnnqn     (5) 2 A higher order of correlation also is possible. It is these vvggt expi  2 generalized solitons with various order of correlations  2 4 m produce a highly delocalized coherent field in the human  body, which enable the body to become overall highly where the envelop wave is ordered field. Here  ,  ,  .  are the expansion   x  coefficients of free energy density F , where  ,  are  sech    vttg 0 m , relevant with the strength of the correlation; if they are far  

the velocity of wave is vg , and the carrier is as a har- super-conductor because the electron and virtual phonon monic wave nonlinear interactions prevent electron energy dispersion and thereby form a stable superconducting electronic— 2  vvggt  expi  2. Cooper pair. The corresponding energy represents as  2 4 m 2rr , which is just a binding energy for the elec- Thus the introduction  rt, as order parameter =  biological field. The order parameter (field operator) tronic bound of the Bose-Cooper pair. So this Cooper pair  rt, composes of DSF which describes cooperative is not else, but a kind of soliton. Hence the supercon- behaviors of many particles as an entirety; therefore it is ducting electrons are also to form a kind of solitons. Pang called as macroscopic wave function or order parameter Xiaofeng has pointed out this in [17]. based on the Landau second type of phase transition the- We want to emphasize here the above similarity be- ory [18]. This highly ordered biological field can be fur- tween the theoretical model of superconductivity and the ther integrated with only one field function expression  correlation model of DSF. Superconducting critical tem- and keep step with consistent with overall vibration to perature can be obtained by considering the soliton for- show macroscopic quantum effect that can be seen as an mula, the finite temperature gap equation and the quasi- origin of many human biological function or potential Fermi particle distribution [19], special features of nonlinear quantum mechanics. 1  In short, biological DSF systems rely on the non-linear g0 Tcp1.14 e (9) interactions among internal sub-units and the energy exchange process of self-organization with environment to where g 0 is the density of states. The key is the nonlinear coupling coefficient  in the nonlinear inter- maintain their order and perfect ceaselessly, and form its 4 own characteristic frequency. These presences of multiple action  of Equation (4). If  becomes bigger, biological elicitor and soliton may be key mechanism to superconducting transition temperature increases. It is support a variety of special features of the human body precisely  influencing the correlation strength en- functions. These biological elicitor and soliton in the body hancement, so that the superconducting transition tem- cycle tracks are probably so called acupuncture channels. perature is increased. This demonstrates that the superconductivity for DSF model even at room temperature is 3. Superconductivity in Room Temperature possible. But the high temperature superconducting mechanism One interesting notice here is that the above second-order and theory has not finally been settled, and the room tem- approximation equation corresponding to the potential perature superconductor effect either experimentally or field can be expressed as: theoretically is very thorny problem. Moreover, the hy- 24 Urt,2  rt,2,rt (6) pothesis as superconductive electrons form a solitary is also required to confirm in relevant experiments of high It is a double potential well (because the original equa- temperature superconductor. Also from experimental tion is of the second-order), there are two minima for perspective, human superconducting phenomenon has not been found, and some experiments only discovered that 2 the acupuncture channels resistance is smaller than other 0 rt,  (7) 4 direction resistor. Whether or not there exist some special functional states whose resistance closes to zero? This sort Not in the point  rt, 0. If   2 , then   0 , 0 of experiment needs to be investigated in future. then it gives Thus, we suggest performing an experiment in which  1 2 DSF is applied to the appropriate materials to induce room 0 temperature superconductor. If this can be realized, then  4 0 rt,   (8) in a considerable extent it demonstrates that our proposed  2 2 above generalized soliton field theory is a key mechanism 0   4 to explain many phenomena of the bio-electromagnetic experiments, at the same time, also gives quit important There is clearly to show these ground state changes contribution for the high (room) temperature supercon- have the symmetry broken, which has consistency same ducting mechanism. as the situation of electro-acoustic superconductor system. In fact in the electro-acoustic superconductors, when 4. Biological Information Field the electrons in the two equivalent ground states, the above two energy minima are just ground states of the The above Equation (4) is for describing DSF in human

Copyright © 2012 SciRes. JMP 1910 Q. BI ET AL. body, whose solution is a kind of generalized biological Furthermore, for a classical system it can also be proved soliton under certain conditions which can propagate over that the classical Liouville equation can be written by [25]. distance without decaying inside or outside the human Therefore, the description of the generalized soliton can body. These solitons are considered to be the basic units of be extended into a concept of the generalized quantum human biological information transmission. This intro- information density, since the corresponding nonlinear duces a biological information problem in human body. Schrodinger equation stunned into generalized Liouville Further, DSF can also be generalized to a kind of bio- equation given by logical information field. We can even consider what  information density equation to drive or control DSF and iLR (14) t produces some special physiological functions above the threshold of energy information intensity, because in the where R is the nonlinear self-interaction term. Be- real world, there may exist effective interaction between low, we deduce some specific forms of R explicitly. human body biological field and environment, such as a Suppose that a general expression for the distribution variety of spectroscopy, magnetic spectrum radiation function is given by treatment as a role of physiotherapy instrument for human F   e (15) body [20,21]. Here character of information for DSF may be de- The corresponding non-equilibrium Liouville equation scribed by an information representation of the nonlinear is Liouville equation [22-25]. To explain clearly, we firstly d iLR (16) define a quantum information density as dtt I  ln (10) For example:  Then the information representation of quantum Liu- iL e (17) ville equation is deduced by following calculations: t

2  According to the above point of view, more broadly, ii i tt whole world is composed of quantum information density 2 driven by energy, and all kinds of objects only presented HH,,   H, various information density distribution. Often this in-  (11) formation distribution at different frequency, with various  waveform amplitudes, but by the driving from a type of iH nn,,11nH  quantum soliton information density field, the target in-   formation distribution with different frequency and wave- n  H, for any integer n , form amplitudes will tend to a synchronous resonance, so that the target information density distribution become the which illustrates that a quantum information density same distribution as the quantum soliton information (QID), I   ln  , to meet the Liouville equation by the density field. The both become an entire form to possess power series of  expanding as possibly macroscopic quantum effect to render many I iLIHI, (12) specific potential functions of human body. t For example: by introducing a quantum information

ln     iiln i H ,  ln   H ,  tt   t HHHH       ln  ln pq  qp   pq  qp HHHH   ln  ln ln  ln (3) pq  qp   p  q  q  p H  ln H ln  ln  ln    pq  q qp  p HHln   ln H,ln pq  qp

density potential (PQID), make the human biological This V   can be analytic function for any  0,1 , information field to drive an object: ln  and can commute with , and satisfies condition (111),   ob (18) 1  which establishes a general nonlinear Liouville equation Thus, an equation of information density of the bio- as logical field and the object is entirely written as:   1 iLV  (28) iLV  (19) t t 2 The above type of Liouville equation may have soliton where    . ob type of solution. The physical meaning can be considered Then the use of Baker-Hausdorff formula and Magnus that this equation consists of a kind of nonlinear lemma [26], one gets Schrödinger equations. For instance, for a pure ensemble dlnln system,   , if constructing R   2 , then one  V , (20) d1t   gets  where defining iH, 2 t 0 n  x,,yx yyy,, (21) 2 HH00  (29)

Therefore one obtains 1122 HH   d ddln  0022 ln ln  ddttdt which gives the nonlinear Schrödinger equation described (22) ln  as VVln , 1    1 2 iH0   , (30) Introducing the non-equilibrium and irreversible con- t 2 dition, having   1 2 iH  (31) dln t 0 2 ln VVln  , 0 (23) dt 1  where notice the nonlinear part of the Hamiltonian is not which enables one to have self-adjoint, showing the system may be an open system with the evolution symmetric broken. This shows the V ln 0 above equation with R    2 is related to the soli- and tons through the nonlinear Schrödinger equations men- tioned. However, it is not restricted the solitons since the ln  V  ,0 (24) nonlinear term R  could be functional of  , such 1  as exp  ,  ln  , sech exp  , and so on, which may describe more general nonlinear interactions. This allows one to obtain the type of PQID as As an example of the application, suppose that a hu- ln  man biological field is described by VV   (25) 1     iH0 ,e  (32) ln  t were V is a functional of , and a simple form can 1  where   1 is quite week introduced by the field sub- be jects to the attack such as sick, disturbing, etc. Then one can use the nonlinear series of pulses (e.g. from medical ln  V   (26) device) such as e1t  , e2t  , e3t  ,, to allows 1  ee   nt  n (33) this shows  0,1 ，and V   is analytic, i.e. n so that ln 1 1 2 11    1  12  3  nt n iH0 ,ee  (27) t nn211 n (34) 11    n H0 ,e

Copyright © 2012 SciRes. JMP 1912 Q. BI ET AL. where    1 is magnified, which enables the sys- the target atom or molecule separation, aggregation, dis- tem to return to health state by agitating. A concrete placement and finally accompanied by the wave carrier driving pulse function can be considered as strength reaching a threshold, some macro-quantum effects (such as macro-quantum tunnelling, the room su- f  Ameitmm (35) mm perconductor phenomenon, etc.) can be shown as men- and a corresponding density operator is tioned in previous description. f tftA eitmn  mn  mn m n mn mn (36) 5. Conclusion itmn  mn  Amne mn The coherence and information aspects for DSF theory th th have been investigated. We firstly emphasize the correla- where mn is a transition from m state to n state, tion characteristics of the filed. It is this sort of correla- m is an initial phase for m state, mn is a frequency which is related to m and n states. Therefore a series tion between so called generalized solitons, some mac- of multiplied pulses can be constructed by roscopic quantum effects are possible such as the superconducting at room temperature. Secondly, a nonlinear t  23tt e,e1 22,e,, (37) Liouville equation in the quantum information represen- which allows a driving PQID f  from an external tation has been represented, which provides a basis to source to be expressed by describe information character of DSF. This means that DSF can be influenced or driven by object using (soliton nt n f   e nn (38) type of) PQID. All these two elements provide a founda- n tion possibly to explain many potential functions of hu- and is proportional to the original V   e by ad- man body and relevant interactions with objects. justing frequency n . Here f   is an analytic function of  . For instance, by choosing 6. Acknowledgements 11 This work was supported by the grants from Canada by n ln , nt n! t NSERC, MITACS, CIPI, MMO, and CITO. such as   REFERENCES 0  , 1  , t t [1] P. N. Prasad, “Introduction to Biophotonics,” Wiley-Inter- 11 11 science, New York, 2003. doi:10.1002/0471465380  ln ,  ln , 2 22tt3 36tt [2] K. Z. Song, “The Existence and Significance of Parapsy- chological Function,” Journal of International Society of 11 11 Life Information Science (ISLIS), Vol. 17, No. 1, 1999, pp.  ln ,  ln , , 4 424tt5 5tt 120 198-214. [3] Q. Y. Wu, et al., “Research of Electromagnetic Radiation e so that  can be magnified by the driving PQID from Human Body,” Chinese Journal of Somatic Science, f  , namely for any   1, Vol. 3, No. 4, 1991, pp. 166-167. f  exp  [4] B. J. Wu, et al., “The Dynamic Study of Magnetic Signal (39) Frequency-Power Spectrum from Different Points by Su- 112314 5 perconducting Biomagnetometer,” Chinese Journal of So- 1      o  2624 matic Science, Vol. 4, No. 2, 1994, pp. 81-82. In brief, by considering the significance of  as a [5] K. Z. Song, “The Research on Characteristics and Physio- minimum information density, generally speaking, the logical Foundation of Human Body Parapsychological Function,” Chinese Journal of Somatic Science, Vol. 5, new equation driving object information density  ob No. 4, 1995, pp. 147-155. has a solitary type of solution, which provides certain PQID to drive the quantum information density of object [6] J. C. Shen, et al., “Examination and Thinking of Soul- Controlled Energy Gathering by Sun Chulin,” Chinese to tend to a kind of resonance synchronous, so that the Journal of Somatic Science, Vol. 6, No. 1, 1996, pp. 10- both become highly coherent as information solitons with 15. a variety of macroscopic quantum effect. Extremely, it is [7] J. C. Shen, et al., “To Explore the Secret of Human Body possible that the information wave (envelope) to around Magnetic Field-The Quantitative Determination of the the object form an entire soliton, so that the carrier of Human Body Magnetic Field under the Qigong State,” waves in the solitons have resonance with each others as Chinese Journal of Somatic Science, Vol. 7, No. 1, 1997, a sort of strongly non-local correlations. This may make pp. 3-7.

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