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Journal of Modern Physics

Characteristics of Coherence and Information for the Davydov Soliton Field

Bi Qiao, Kongzhi Song, Harry E. Ruda

Published Jan 1, 2012• 5 citations
Publisher

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.

DOI
10.4236/jmp.2012.312240

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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.
In this work, a mechanism of macroscopic quantum tunneling is studied, which shows this sort of phenomena may exist even in the bio-field system. The relevant Davydov solitons fields and the Feynman digraph have been constructed based on the nonlinear Green function theory, which allows one to get a synchronous resonance model to explain the macroscopic quantum tunneling, such as in double potential wells system. Furthermore, the functional of quantum information density can also be applied to drive the object into a type of soliton structure of quantum information density, which allows the system to possess property of the macroscopic quantum tunneling.
In this work, some types of nonlinear Liouville equation (NLE) and nonlinear Master equations (NME) are studied. We found that the nonlinear terms in the equation can resist state of system damping so that an information solitonic structure appears. Furthermore, the power in the non-linear term is independent of limitation of the solution. This characteristic offers a possibility to construct complicated information solitons from some simple solutions, which allow one to solve complicated NLE or NME. The results obtained in this work may provide an innovated channel for the quantum information transmission over far distance against dissipation and decoherence, and also open a constructive way to resist age decaying of system by designing adjusted field interaction with the system nonlinearly.
A general definition of quantum coherence is developed from analysis of superposition, entanglement, chemical bonding behavior, and basic phenomena of classical mechanics. Various properties of atoms can be better explained if these particles are matter waves that embody a spectrum ranging from relatively coherent to decoherent states. It is demonstrated that quantum coherence so defined can comprehensively explain signal transmission in neurons and dynamics of the brain’s emergent electric field, including potential support for the claim that conscious volition is to some degree real rather than an illusion. Recent research in a physiological context suggests that electromagnetic radiation interacts with molecular structure to comprise integrated energy fields. A mechanism is proposed by which quantum coherence as accelerating electric currents in neurons may result in a broadened spectrum of electromagnetic radiation capable of interacting with molecular complexes in the brain and perhaps elsewhere in an organism to influence vibrational and structural properties. Research should investigate whether a consequent energy field is the basic perceptual substrate, with at least some additive electromagnetic wavelengths of this field involved in generating image percepts insofar as they arise from the body, and electromagnetic vibrations the signature of a more diverse phenomenon by which somewhat nondimensional features of perception such as sound, touch, taste, smell, interoceptive sensations, etc. partially arise. If examination of the brain reveals this organ to be composed of a coherence field, structured at least in part by broadened spectrums of EM radiation interacting with molecular components, this has major implications for furthering our model of the matter/mind interface and possibly physical reality in total.
Abstract We present a series of quantum states that are characterized by dark solitons of the nonlinear Schrödinger equation (i.e. the Gross–Pitaevskii equation) for the one-dimensional Bose gas interacting through the repulsive delta-function potentials. The classical solutions satisfy the periodic boundary conditions and we simply call them classical dark solitons. Through exact solutions we show corresponding aspects between the states and the solitons in the weak coupling case: the quantum and classical density profiles completely overlap with each other not only at an initial time but also at later times over a long period of time, and they move together with the same speed in time; the matrix element of the bosonic field operator between the quantum states has exactly the same profiles of the square amplitude and the phase as the classical complex scalar field of a classical dark soliton not only at the initial time but also at later times, and the corresponding profiles move together for a long period of time. We suggest that the corresponding properties hold rigorously in the weak coupling limit. Furthermore, we argue that the lifetime of the dark soliton-like density profile in the quantum state becomes infinitely long as the coupling constant approaches zero, by comparing it with the quantum speed limit time. Thus, we call the quantum states quantum dark soliton states.
Macroscopic fields such as electromagnetic, magnetohydrodynamic, acoustic or gravitational waves are usually described by classical wave equations with possible additional damping terms and coherent sources. The aim of this paper is to develop a complete macroscopic formalism including random/thermal sources, dissipation and random scattering of waves by environment. The proposed reduced state of the field combines averaged field with the two-point correlation function called single-particle density matrix. The evolution equation for the reduced state of the field is obtained by reduction of the generalized quasi-free dynamical semigroups describing irreversible evolution of bosonic quantum field and the definition of entropy for the reduced state of the field follows from the von Neumann entropy of quantum field states. The presented formalism can be applied, for example, to superradiance phenomena and allows unifying the Mueller and Jones calculi in polarization optics.
Coherence properties of quantum optical solitons in the normalized fundamental soliton states are discussed in terms of the integrated two-point field and intensity autocorrelation functions, which are the relevant quantities in the quantum description of soliton interference experiments and in the Hanbury-Brown and Twiss experiment, respectively. Both the spatial and the temporal correlation properties are considered. The correlation functions are shown to be stationary in general, which demonstrates the solitary behavior of quantum fundamental solitons and indicates their stability in propagation. Explicit evaluation of the correlation functions in some limit cases enables us to make comparisons between the classical and the quantum-mechanical results. Conditions leading to the classical limit are derived and the intrinsic quantum phenomena are identified. Of great importance is the contribution of the momentum superposition, which can make the quantum results differ significantly from the corresponding classical ones.