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The solution of the Dirac equation with the Coulomb potential is used to analyze bound electron states in a hydrogen atom. The analysis is based on the fact that such states are characterized by a set of quantum numbers which describe definite values of the complete set of physical quantities that can be determined simultaneously. This set includes the energy, square of the total angular momentum, one of its component and a spinor invariant. The latter, spinor invariant gives two-valued quantum number which determines the sign of its eigenvalue. In addition to the known Dirac and Johnson–Lippman invariant, there exists a new one. Operators of these three spinor invariants do not commute between themselves which results in the degeneracy of the energy levels with respect to the two-valued quantum number. Three different systems of the eigenbispinor corresponding to the three spinor invariants are obtained and the generalized solution with free parameters is calculated. Variation of the free parameters transforms one particular solution into any other. It is shown that the electron probability densities and spin polarizations in an electron cloud depend essentially on the invariant set, demonstrating physical difference of the states corresponding to different spinor invariants. [ABSTRACT FROM AUTHOR]

All relativistic corrections to the Scrodinger equation which determine the interlink between spin and orbit of moving particles, are directly calculated from the Dirac equation using the spin invariant operators. It is shown that among the second order corrections there are not only the well-known Darwin and Thomas terms, but also the new ones. Only with the account of the latter corrections the energies found with the obtained spin-orbit interaction operator, coincide with the energies of the Dirac equation exact solution. The problem of electron spectrum in the quantum well type structures is studied in details and the physical reasons for the appearance of spin- orbit interaction operators in the Dresselhaus or Rashba form, are analyzed. [ABSTRACT FROM AUTHOR]

We study the long-range electron and energy transfer mediated by solitons in a quasi-one-dimensional molecular chain (conjugated polymer, alpha-helical macromolecule, etc.) weakly bound to a donor and an acceptor. We show that for certain sets of parameter values in such systems an electron, initially located at the donor molecule, can tunnel to the molecular chain, where it becomes self-trapped in a soliton state, and propagates to the opposite end of the chain practically without energy dissipation. Upon reaching the end, the electron can either bounce back and move in the opposite direction or, for suitable parameter values of the system, tunnel to the acceptor. We estimate the energy efficiency of the donor-acceptor electron transport depending on the parameter values. Our calculations show that the soliton mechanism works for the parameter values of polypeptide macromolecules and conjugated polymers. We also investigate the donor-acceptor electron transport in thermalized molecular chains. [ABSTRACT FROM AUTHOR]

We study the ratchet drift of large polarons (solitons) in molecular diatomic chains induced by unbiased time periodic electric fields at nonzero temperature below its critical value. We show that, at a nonzero temperature, the critical value of the intensity of the electric field above which the ratchet phenomenon takes place is lower than at zero temperature for the same frequency of the field. We show that there is a range of temperatures for which the polaron drift is larger than that at zero temperature. We also show that temperature decreases the value of the lowest critical period of the field. And, finally, we demonstrate that there is a stochastic resonance in a polaron ratchet, namely that there is an optimal temperature at which the polaron drift is a maximum. The values of the stochastic resonance temperature, the lowest critical values of the field intensity, and its period depend on various parameters of the system and, in particular, on the anisotropy of the chain parameters. This temperature induced decrease of the critical value of the field intensity and its period, as well as the stochastic resonance itself, may be important for practical applications of the ratchet phenomenon in systems involving conducting polymers and other low-dimensional materials. They may also be important in some biological macromolecules where the ratchet phenomenon could take place in biomotors and energy and/or charge transport. [ABSTRACT FROM AUTHOR]

In this study, it is shown that two added, excess electrons with opposite spins in one-dimensional crystal lattices with quartic anharmonicity may form a bisolectron, which is a localized bound state of the paired electrons to a soliton-like lattice deformation. It is also shown that when the Coulomb repulsion is included, the wave function of the bisolectron has two maxima, and such a state is stable in lattices with strong enough electron (phonon/soliton)-lattice coupling. Furthermore, the energy of the bisolectron is shown to be lower than the energy of the state with two separate, independent electrons, as even with account of the Coulomb repulsion the bisolectron binding energy is positive. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011 [ABSTRACT FROM AUTHOR]

We show that in anharmonic one-dimensional crystal lattices pairing of electrons or holes in a localized bisolectron state is possible due to the coupling between the charges and the lattice deformation that can overcome the Coulomb repulsion. Such localized states appear as traveling ground singlet states of two extra electrons bound in the potential well created by the local lattice solitonlike deformation. We also find the first excited localized state of two electrons given by a triplet state of two electrons. The results of the analytical study of interacting electrons in a lattice with cubic anharmonicity are compared with the numerical simulations of two electrons in an anharmonic lattice with Morse interactions and taking into account the single-site Hubbard electron-electron repulsion. We find quite a good qualitative agreement between both approaches for a broad range of parameter values. For illustration we give expressions for the bisolectron binding energy with parameter values that are typical for biological macromolecules. We also estimate threshold values of the Coulomb repulsion above which the bisolectron splits into two solectrons. [ABSTRACT FROM AUTHOR]

We show that when anharmonicity is added to the electron-phonon interaction it facilitates electron pairing in a localized state. Such localized state appears as singlet state of two electrons bound with the traveling local lattice soliton distortion, which survives when Coulomb repulsion is included. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012 [ABSTRACT FROM AUTHOR]

We show that in nonlinear systems dynamical order can be reached through the flows of matter, energy, and information, which can be non uniformly spread over the organism due to self-trapping induced by the correlated coherence domains of interfacial water. Endogenous electromagnetic field is self trapped in these domains and forms the dynamical pathways as wave-guides, along which these flows can occur via soliton mechanisms. Solitons in the pathways can be stimulated either by intrinsic dynamics or by external stimuli and can be visualized in the infrared range as bright or dark solitons. The formation of such pathways is the consequence of coherence-non coherence transitions occurring in the biological cycle of the organism. A rational therapy appears then to be the induction of conditions for soliton existence necessary for maintaining the coherence of the system. [ABSTRACT FROM AUTHOR]

The conditions for spontaneous localization of electrons in an isotropic two-dimensional electron–phonon lattice are investigated within the zero adiabatic approximation. It is shown that the localization occurs when the electron–phonon coupling takes values within certain finite interval of values g[sub c,1]g[sub c,2] the strong localization on one lattice site takes place. In this paper we introduce an ansatz which, under a variational principle, allows us to describe all three regimes at the same time. The radius of the electron localization, as a function of electron–phonon coupling constant, is evaluated analytically and shown to fit well the numerical data. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Electrosolitons that provide charge transport in biological systems (e.g., in respiratory processes) create alternating electromagnetic fields having a characteristic frequency. This frequency is determined by the soliton velocity and is in the microwave range. Because of this radiation the long-range interaction of solitons results in the synchronization of their motion. This effect can contribute to the self-regulation of metabolic processes in an organism. In addition, such regulation can be stimulated by external radiation with the same characteristic frequency, thus providing one mechanism to explain microwave resonant therapy. [ABSTRACT FROM AUTHOR]

The influence of electromagnetic radiation (EMR) on charge and energy transport processes in biological systems is studied in the light of the soliton model. It is shown that in the spectrum of biological effects of EMR there are two frequency resonances corresponding to qualitatively different frequency dependent effects of EMR on solitons. One of them is connected with the quasiresonance dynamic response of solitons to the EMR. At EMR frequencies close to the dynamic resonance frequency the solitons absorb energy from the field and generate intensive vibrational modes in the macromolecule. The second EMR resonance is connected with soliton decay due to the quantum mechanical transition of the system from the bound soliton state into the excited unbound states. [ABSTRACT FROM AUTHOR]

We study the long-range electron and energy transfer mediated by a polaron on an α-helix polypeptide chain coupled to donor and acceptor molecules at opposite ends of the chain. We show that for specific parameters of the system, an electron initially located on the donor can tunnel onto the α helix, forming a polaron, which then travels to the other extremity of the polypeptide chain, where it is captured by the acceptor. We consider three families of couplings between the donor, the acceptor, and the chain and show that one of them can lead to a 90% efficiency of the electron transport from donor to acceptor. We also show that this process remains stable at physiological temperatures in the presence of thermal fluctuations in the system. [ABSTRACT FROM AUTHOR]

We study the localized states of an extra electron in an anisotropic quasi-two-dimensional system in which the electron-lattice interaction and the anharmonicity of the lattice vibrations are dominant in one direction. This model describes layers of polydiacetylene or other polymer chains, beta sheets of polypeptides, multilevel microstructures of conjugated polymers, and other low-dimensional systems. It is shown that for appropriate parameter values of the system an extra electron can excite a soliton-like mobile wave of the lattice deformation, within which it can get self-trapped. Such a bound state of an electron and the lattice deformation form a nonlinear two-component polaron-like entity, which can propagate with minimum of the energy dissipation. Our findings are based on the variational approach and the full numerical solution of the coupled system of nonlinear equations. These results suggest that the experimentally measured charge and energy transport over macroscopic distances in the above-mentioned systems can be provided by the soliton mechanism and thus have a potential impact on the theoretical background of the numerous applications of low-dimensional materials in nanoelectronics.

Glucose is a natural chemical compound and is one of the most abundant organic molecules in nature. Plants and algae are able to produce it from water and carbon dioxide during photosynthesis, using energy of photons coming from the sun. It is very important in life processes because, in energy metabolism, Glucose is the most important source of energy in all organisms. As energy reservoir it is partially stored as a polymer, in plants mainly as starch and amylopectin and in animals as glycogen. Moreover it is used as cellulose, the most abundant carbohydrate, to strengthen plants and algae cell walls. In this paper we study the Delayed Luminescence from Glucose and its polymers, Amylose and Cellulose, composed by chains of glucose connected by different bond, as well as Glucose water solution, in order to acquire new knowledge on the mechanisms responsible for this phenomenon and check the possibility to give in-depth analysis of possible collective states present in Glucose-based structures. The phenomenon of DL in biological systems is not a byproduct, as one can naively expect. Instead, it is a property and necessity of the condensed matter, which can be also used as a tool to study the latter. It is a manifestation of the physical and biochemical processes in the system, on one hand side, and, on the other hand side, of its structural properties, in particular, of the presence and type of crystal-like structure, resulting in specific energy spectrum and electron transitions, as will be presented below. We show that the quantum yield and time trends of the Delayed Luminescence depend on the structure of systems under study. Significant differences in Delayed Luminescence parameters from cellulose before and after imbibition have been observed, indicating that Delayed Luminescence could be used to discriminate between various structures and follow the formation or demolition of them. The experimental results qualitatively agree with the soliton mechanism of the Delayed luminescence., (Copyright © 2019 Elsevier B.V. All rights reserved.)

We present here a model of meridians in the formalism of the gauge theory paradigm of quantum field theory with spontaneous breakdown of symmetry. We discuss the origin and dynamic self-focusing propagation of the electromagnetic field in coherent states and the role it plays in our meridian modeling. Within this frame, we consider the formation of solitary waves on proteins and anatomical filamentary structures and discuss nondissipative energy transport. Finally, we analyze the relation of meridians with anatomical filamentary structures, the reciprocal actions between meridians, and biochemical activity and the key role played by free energy, internal energy, and entropy., (Copyright © 2019. Published by Elsevier B.V.)

Biological organisms are complex open dissipative systems whose dynamical stability is sustained due to the exchange of matter, energy and information. Dynamical stability occurs through a number of mechanisms that sustain efficient adaptive dynamics. Such properties of living matter can be the consequence of a self-consistent state of matter and electromagnetic field (EMF). Based on the soliton model of charge transport in redox processes, we describe a possible mechanism of the origin of endogenous EMF and coherence. Solitons are formed in polypeptides due to electron-lattice interaction. Solitons experience periodical potential barrier, as a result of which their velocity oscillates in time, and, hence, they emit electromagnetic radiation (EMR). Under the effect of such radiation from all other solitons, the synchronization of their dynamics takes place, which significantly increases the intensity of the general EMF. The complex structure of biological molecules, such as helical structure, is not only important for "structure-function" relations, but also the source of the stability of biophysical processes, e.g. effectiveness of energy and charge transport on macroscopic distances. Such a complex structure also provides the framework for the spatiotemporal structure of the endogenous EMF. The highly hierarchical organization of living organisms is a manifestation of their complexity, even at the level of simple unicellular organisms. This complexity increases the dynamical stability of open systems and enhances the possibility of information storage and processing. Our findings provide a qualitative overview of a possible biophysical mechanism that supports health and disease adaptive dynamics.

We have performed a series of experiments applying high voltage between two electrodes, immersed in two beakers containing bidistilled water in a way similar to experiments conducted by Fuchs and collaborators, which showed that a water bridge can be formed between the two containers. We also observed the formation of water bridge. Moreover, choosing different pairs of electrodes depending on the material they are made up of, we observed that copper ions flow can pass along the bridge if the negative electrode is made up of copper. We show that the direction of the flux not only depends on the applied electrostatic field but on the relative electronegativity of the electrodes too. These results open new perspectives in understanding the properties of water. We suggest a possible explanation of the obtained results.

It is shown that electromagnetic fields affect dynamics of Davydov's solitons which provide charge transport processes in macromolecules during metabolism of the system. There is a resonant frequency of the field at which it can cause the transition of electrons from bound soliton states into delocalised states. Such decay of solitons reduces the effectiveness of charge transport, and, therefore, inhibits redox processes. Solitons radiate their own electromagnetic field of characteristic frequency determined by their average velocity. This self-radiated field leads to synchronization of soliton dynamics and charge transport processes, and is the source of the coherence in the system. Exposition of the system to the oscillating electromagnetic field of the frequency, which coincides with the eigen-frequency of solitons can enhance eigen-radiation of solitons, and, therefore, will enhance synchronization of charge transpor, stimulate the redox processes and increase coherence in the system. Electromagnetic oscillating field causes also ratchet phenomenon of solitons, i.e., drift of solitons in macromolecules in the presence of unbiased periodic field. Such additional drift enhances the charge transport processes. It is shown that temperature facilitates the ratchet drift. In particular, temperature fluctuations lead to the lowering of the critical value of the intensity and period of the field, above which the drift of solitons takes place. Moreover, there is a stochastic resonance in the soliton dynamics in external electromagnetic fields. This means, that there is some optimal temperature at which the drift of solitons is maximal.

A brilliant scientist and an outstanding personality who was one of the founders of modern photochemistry-Michael Kasha-is the subject of this Essay. Kasha's rule and the Kasha effect both bear his name, and he also discovered the chemical production of singlet molecular oxygen, and was a pioneer of excited-state proton transfer systems. Kasha combined his passion for chemistry and physics with that for music, photography, and botany., (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

It has been reported that the colors perceived behind closed eyes provide an indication of the psychophysical state of a subject. We discuss this phenomenon in the light of recently developed approaches to living organisms, based on the interplay between matter organization, biochemistry and electrodynamics. "When there is no energy, there is no color, no shape, no life." Caravaggio (1571-1610)., (Copyright © 2010 Korean Pharmacopuncture Institute. Published by .. All rights reserved.)

We study effects of periodic fields on charge transport in macromolecules and show that solitons acquire complex dynamics induced by the interplay between the periodic in time external field, energy dissipation, and depends on the molecule symmetry. Soliton dynamics is a superposition of the oscillations of the soliton c.m.c. with the frequency of the external field and directed current. Even unbiased periodic in time fields can cause drift of solitons (the ratchet effect) in the Peierls-Nabarro periodic potential. This effect has a threshold with respect to the intensity and frequency of the field. We calculate the dependence of the amplitude of soliton oscillations and the velocity of the drift on the intensity of the field, its frequency, and energy dissipation. Thus, we show that nonlinear charge transport processes in a field which is periodic in time acquire completely different dynamics than linear processes. This clearly plays a role in metabolism of biosystems.

The nonlinear mechanism for the origin of the weak biophoton emission from biological systems is suggested. The mechanism is based on the properties of solitons that provide energy transfer and charge transport in metabolic processes. Such soliton states are formed in alpha-helical proteins. Account of the electron-phonon interaction in macromolecules results in the self-trapping of electrons in a localized soliton-like state, known as Davydov's solitons. The important role of the helical symmetry of macromolecules is elucidated for the formation, stability and dynamical properties of solitons. It is shown that the soliton with the lowest energy has an inner structure with the many-hump envelope. The total probability of the excitation in the helix is characterized by interspine oscillations with the frequency of oscillations, proportional to the soliton velocity. The radiative life-time of a soliton is calculated and shown to exceed the life-time of an excitation on an isolated peptide group by several orders of magnitude.

We investigate some aspects of the soliton dynamics in an alpha-helical protein macromolecule within the steric Davydov-Scott model. Our main objective is to elucidate the important role of the helical symmetry in the formation, stability, and dynamical properties of Davydov's solitons in an alpha helix. We show, analytically and numerically, that the corresponding system of nonlinear equations admits several types of stationary soliton solutions and that solitons which preserve helical symmetry are dynamically unstable: once formed, they decay rapidly when they propagate. On the other hand, the soliton which spontaneously breaks the local translational and helical symmetries possesses the lowest energy and is a robust localized entity. We also demonstrate that this soliton is the result of a hybridization of the quasiparticle states from the two lowest degenerate bands and has an inner structure which can be described as a modulated multihump amplitude distribution of excitations on individual spines. The complex and composite structure of the soliton manifests itself distinctly when the soliton is moving and some interspine oscillations take place. Such a soliton structure and the interspine oscillations have previously been observed numerically [A. C. Scott, Phys. Rev. A 26, 578 (1982)]. Here we argue that the solitons studied by Scott are hybrid solitons and that the oscillations arise due to the helical symmetry of the system and result from the motion of the soliton along the alpha helix. The frequency of the interspine oscillations is shown to be proportional to the soliton velocity.

We generalize the correlated soliton model in order to describe the delayed luminescence arising from biological systems after their exposition to the irradiation by relatively high dose (high intensity and/or long duration of irradiation). The quantum yield of the delayed luminescence is calculated as a function of the irradiation and is shown to depend nonlinearly on the intensity and dose of the irradiation. At relatively low intensity, the yield of luminescence increases with increasing dose, and monotonously reaches saturation. At high intensity of the irradiation, the yield of the photosystem under study is restricted from above by the concentration of photosystem units. As a result, the total yield of the delayed luminescence first increases with the dose till the maximum value that, in the general case, is less than the maximum number of available photosystem units. With further increase of the dose, the yield gradually decreases, reaching the saturation value at large dose of illumination. These results are obtained within the steady state approximation in the description of the luminescence kinetics. To check the applicability of this approximation at high levels and large time of illumination, the corrections to the steady state solution have been calculated, and shown to decrease exponentially with increase in time till the small finite constant value. The results of the theoretical model are shown to describe well the experimental data on the dose dependence of the quantum yield of the luminescence of algae Acetabularia acetabulum, for which the correlated soliton model describes well the kinetics of the delayed luminescence at low levels of irradiation.