Bogolyubov Institute for Theoretical Physics

List of Departments Topmost Scientific Results

Department of Theory of Nonlinear Processes in Condensed Matter

2024
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2016

Equations for the superconducting nematic order parameter, critical temperature, and chemical potential for a two-dimensional rectangular lattice are derived, taking into account carrier hopping (electrons and holes) through the nearest and next-nearest neighbors. Solving the resulting equations revealed that the symmetry of the order parameter and other superconducting properties strongly depend on the sign and magnitude of the nearest-neighbor hopping matrix element, as well as on doping. The possible transition of the system from Bose-Einstein condensation to Bardeen-Cooper-Schrieffer superconducting regimes with increasing electron density is analyzed. As shown, the crossover, which can be tuned both by doping and by nearest-neighbor hopping, occurs only in the s-channel at physically significant values of these parameters. A possible connection of the obtained results with the properties of doped high-temperature cuprate superconductors is discussed
Acad. NAS of Ukraine V.M. Loktev
Within the framework of a new approach based on the exact solution of the Dirac equation with the Coulomb potential, radiation corrections were calculated, which eliminate the random degeneracy in the spectrum of the relativistic hydrogen atom and lead to a modification of the Coulomb law. Taking into account these corrections, the energy spectrum of the hydrogen atom was obtained and the Lembski shift for the lowest energy states was calculated
Acad. NAS of Ukraine V.M. Loktev, L.S. Bryzhyk, O.O. Eremko
Based on the solutions of the Dirac equation, the energy spectrum of quasi-one-dimensional electrons in an atomic chain was calculated. It is shown that the presence of a complete set of integrals of motion, which includes the Hamiltonian of the system and the projections onto the chain axis of the electron momentum vectors, its total angular momentum and the relativistic spin polarization vector, ensures the integrability of the Dirac equation, the exact solutions of which describe the one-dimensional motion of electrons bound by the Coulomb field of the chain atoms. An additional spinor integral of motion (invariant) has been found, the presence of which explains the so-called "random" degeneracy of the electron spectrum with respect to the spin quantum number
Acad. NAS of Ukraine V.M. Loktev, L.S. Bryzhik, O.O. Eremko
It is shown that the electron spectrum of graphene, as in other low-dimensional systems, can exhibit a sharp impurity resonance near the Dirac point due to the presence of a single weakly coupled impurity described by the Fano model. This is demonstrated by the fact that, according to the established scenario, the electronic band structure of graphene undergoes a kind of transformation, namely: the type of avoided crossing, when the concentration of such short-range impurities increases. In this transformation process, the main events unfold close to the impurity resonance energy, and, therefore, they belong to the most intriguing region of the energy spectrum of graphene. The avoided cross-transformation develops in a threshold manner. Namely, it begins when the impurity concentration exceeds a critical value, which is determined by a significant spatial overlap of the states of individual impurities. In contrast to previous cases of such band structure transformations in low-dimensional systems, our findings reveal the formation of a new — impurity — Dirac point in the spectrum next to the original one, which doubles their number in the disordered system. The regions of band edge blurring in the old and newly formed Dirac points, where electronic states are also localized, turn out to be quite narrow. The analysis shows that controlling the position of the Fermi level in a disordered system can allow observation of repeated metal-insulator transitions. The Fermi level entering and leaving the mobility gap causes metal-insulator and insulator-metal transitions
Acad. NAS of Ukraine V.M. Loktev, Y.V. Skrypnyk
For a one-dimensional molecular chain with an excess electron in the presence of a time-varying harmonic magnetic field, a modified nonlinear Schrödinger equation with additional terms describing the influence of the magnetic field on the dynamics of both the electron and the phonon sublattice is derived. It is shown that in an external time-periodic magnetic field, the dynamics of Davydovsky solitons significantly depends on the orientation of the field. The wave functions of the soliton are calculated in two cases, when the field is parallel to the molecular chains and perpendicular. In the first case, the soliton dynamics is a superposition of the dynamics of a harmonic oscillator in an external periodic magnetic field in a plane perpendicular to the chains and the motion of a free soliton along the chain. In a perpendicular magnetic field, the dynamics of a soliton is a superposition of plane waves in a plane perpendicular to the chains and the longitudinal motion of the soliton with parameters that depend on both the amplitude and frequency of the external field. The velocity of the soliton is calculated and shown to contain harmonics with the frequency of the field and multiple frequencies. This causes the soliton to emit sound and electromagnetic waves. Using perturbation theory based on the inverse scattering problem method, the dependence of the soliton parameters on the magnetic field is found and the existence of a resonant frequency is shown at which the soliton intensively absorbs the field energy and emits it in the form of linear waves. Such dynamic properties of the soliton affect the processes of charge transport in electrically conductive low-dimensional compounds and in redox processes in biological systems
L.S. Bryzhik
Dynamic equations for an excess electron and deformation of an anharmonic quasi-two-dimensional lattice are derived, taking into account the electron-phonon interaction in the adiabatic approximation. For this purpose, the Hamiltonian of such a system is written in the nodal representation. It is shown that this system of equations can be reduced to a coupled system of the nonlinear Schrödinger equation and the Kadomtsev-Petviashvili equation of the second kind. A solution to this system of coupled equations is found. The existence of nonlinear Lolized modes in the form of stable coupled electron-phonon states for a wide range of system parameter values is shown
L.S. Bryzhik
The Sagnac effect in graphene is found to be determined by the mass of the free electron, making it about a million times stronger than in light-based interferometers, even though monolayer graphene has zero effective carrier mass and linear dispersion similar to that of light. Our study provides a deeper understanding of the fundamental principles of quantum physics as applied to rotating solid-state systems. The Sagnac effect is the phase shift between two coherent beams traveling in opposite directions in an interferometer mounted on a rotating disk, a principle that underlies many modern navigation systems
S.G. Sharapov
Using effective low-energy theory, the phenomenon of Landau level collapse in graphene nanoribbons of finite width and semi-infinite geometry subjected to a perpendicular magnetic field and a planar electric field applied perpendicular to the zigzag and armchair edges was investigated
S.G. Sharapov
It was shown that in semi-infinite geometry, hole (electron)-like Landau levels collapse when the ratio of the electric and magnetic fields reaches a critical value +(-)1
S.G. Sharapov
The energies of the electron (hole)-like levels remain different near the edge and inside the sample, asymptotically approaching each other for the same critical value. In finite geometry, it is shown that electron (hole)-like levels become denser and merge, forming a zone
S.G. Sharapov
Based on the methods of quantum electrodynamics, a contribution to the modification of Coulomb's law of vacuum polarization by the electric field of the nucleus has been found. Modification of Coulomb's law due to the so-called radiation corrections leads to the removal of the "random" degeneracy of electronic levels, namely, the splitting of the 2S_1/2 and 2P_1/2 states in the hydrogen atom (known as the Lemb shift)
O.O. Eremko
The Lemb shift was calculated within the framework of the traditional Hamiltonian description in quantum mechanics using exact solutions of the Dirac equation with the Coulomb potential and taking into account all radiation corrections as perturbations. At the same time, the contribution of the vacuum polarization by the electric field of the nucleus (the dependence of the vacuum energy on the external electric field) was calculated for the first time
O.O. Eremko
The influence of thermal fluctuations on the current-voltage characteristics of a Josephson junction with a biharmonic current-phase dependence was investigated. An analytical model of the soliton dynamics in such a junction was constructed taking into account the action of white Gaussian noise. A stochastic dynamics equation was obtained for the probability distribution function of the Josephson phase in the system. Using numerical methods, the dynamics of the soliton were simulated, the time dependence of its center of mass and the distribution of the Josephson phase in the contact were constructed. The diffusion coefficient that occurs in the process of soliton dynamics in a Josephson contact with a biharmonic current-phase dependence under the action of thermal noise was calculated. The current-voltage characteristics of such a contact were constructed, the influence of thermal fluctuations on them and on the dynamics of the soliton, respectively, was analyzed. The working range of system parameter values was obtained, at which an analytical description of the stochastic process of soliton dynamics is possible
Zolotaryuk Ya.O., I.O. Starodub
The influence of electron-vibronic and interelectron interactions on the tunneling current through a molecular device in the case of two- and four-fold order of level degeneracy on the molecule is shown
O.O. Ponezha
The motion of a fluxon in an array of Josephson contacts with a non-sinusoidal current-phase dependence was investigated. The equation of the motion of a fluxon in such an array with a dipole spatial impurity located in the dielectric layer of one of the Josephson contacts of the array was obtained. Such an impurity models a qubit inductively coupled to the array, the state of which can be read by determining the fluxon passage time along the array. It is shown that changing the polarity of the inhomogeneity significantly affects the mobility and dynamics of the fluxon in such a discrete environment. The threshold current of fluxon pinning on the impurity is calculated. Using numerical calculations, the dependence of the threshold pinning current on the amplitude of the impurity, discreteness and dissipation in the array is constructed. Analytical and numerical calculations are compared, the region of system parameters is analyzed, at which the proposed analytical description of the model is correct
Ya.O. Zolotaryuk, I.O. Starodub
The dynamics of the fluxon in a discrete Josephson transmission line with a non-sinusoidal current-phase relationship is modeled and the possibility of the coexistence of fluxons with different equilibrium velocities for the same value of the external current is shown. The influence of the second harmonic of the current-phase dependence on the sensitivity of fluxon dynamics to initial conditions is analyzed. Based on the Fourier analysis, the process of formation of allowed and forbidden regions of fluxon existence parameters in the described discrete medium is explained
Ya.O. Zolotaryuk, I.O. Starodub
The transport spectroscopy method was used, which consists in measuring the differential conductivity as a function of the voltage on the electrodes and the voltage on the gate and constructing stable diagrams. Using this method, it was established through which of the ground and excited levels on the molecule the tunneling occurs depending on the applied voltages, as well as how the spins are oriented at these levels
O.O. Ponezha
It is shown that competition in the population of levels leads to the appearance of regions on stable diagrams with negative differential conductivity
O.O. Ponezha
Within the framework of the molecular dynamics method, a study of abnormally bent conformations of natural polyamine molecules - spermidine3+, interacting with the DNA double helix was performed. It was shown that the abnormally bent conformations of the spermidine3+ molecule are the result of the interaction of all three amino groups of the polyamine with the phosphate groups of DNA from the side of the minor groove of the double helix. Changes in the torsion angles of the bent spermidine3+ molecule are explained in terms of conformational transformations of six- and seven-membered rings, similar to cyclohexane and cycloheptane. Analysis of the location of spermidine3+ molecules along the DNA macromolecule revealed the specificity of the nucleotide sequence with a pronounced predominance of A-tracts from the side of the minor groove. The formation of abnormally bent conformations of spermidine3+ in a complex with the DNA double helix may be of paramount importance for understanding the mechanisms underlying the biological function of DNA
S.M. Perepelytsya
The interaction of bis-acridine orange (BAO) dyes with the DNA double helix was studied. Molecular dynamics simulations were performed to explain the higher efficiency of BAO-1, BAO-2, and BAO-3 dyes under polymerase chain reaction (PCR) conditions compared to the commercial dye EvaGreen (EG), despite the fact that these dyes differ only in the structure of the linker. It was shown that the transition from the folded to the unfolded conformation requires less energy for BAO-1 and BAO-3 dyes than for EG. This means that compared to EG, the BAO-3 equilibrium is shifted towards the unfolded conformation, which explains the stronger binding to double-stranded DNA and the better performance of BAO-3 in PCR
S.M. Perepelytsya
During May 21-23, 2024, a school-seminar on computational DNA physics was held at the Institute of Theoretical Physics named after M.M. Bogolyubov of the NAS of Ukraine (hereinafter referred to as the ITF). The event was organized in a mixed offline-online format by the joint efforts of the ITF and the Kyiv Academic University (hereinafter referred to as the KAU). Among the participants were more than 30 students from various universities of Ukraine. The lecturers and teachers of the school were leading scientists in this field. The lectures were devoted to modern methods of numerical modeling of DNA at different levels of organization of its structure. Practical classes were also held using the computational cluster of the Institute of Theoretical Physics named after M.M. Bogolyubov of the NAS of Ukraine. Recordings of all lectures can be viewed on YouTube
S.M. Perepelytsya
Within the framework of quantum-chemical calculations, optimized geometries of complexes of the Li+ ion with phosphate groups PO4 in the presence of water molecules and chlorine ion were obtained. These characteristic complexes were taken from molecular-dynamic simulation of the behavior of several DNA molecules in a solution with a high concentration of lithium ions. The vibrational spectra of such complexes were calculated and the obtained frequencies were compared with the experiment
D.V. Piatnytskyi
Based on the data obtained from molecular dynamics for the behavior of a DNA macromolecule in an aqueous solution with potassium ions, quantum-chemical calculations of the interaction energies of a monovalent potassium ion K+ with water molecules at distances from 5 Å to 10 Å from the backbone of the DNA molecule were performed. For each distance, up to 25 fragments of the molecular-dynamic trajectory were used, for which the final results were averaged and the mean square deviations were determined
D.V. Piatnytskyi
The effects of alkali metal ions (Li+, Na+, K+, Rb+ and Cs+) on the vibrational dynamics of the DNA ion-hydrate shell were studied using the atomistic molecular dynamics method. As a result, the vibrational spectra of DNA-water-ion systems were calculated within the framework of two different approaches. The influence of the regions of the DNA double helix (minor and major grooves, and phosphate groups) on the vibrational dynamics of ions and water molecules was analyzed. It was found that the calculated spectra have a qualitatively different shape in the case of ions with different hydration characteristics (structure-forming and structure-destroying). This difference becomes more pronounced for ions interacting with DNA, especially in the case of structure-destroying ions localized in the minor groove of the double helix. In the case of the calculated absorption spectra of DNA, it is shown that the influence of counterions is insignificant on the vibrations of the atomic groups of the double helix, with the exception of Li+, which enhances the intensity of the vibration modes of phosphate groups. It is shown that in the spectra of vibrations of water molecules around ions, an isosbestic point is observed at ~70 cm-1, which arises due to the interaction with DNA and counterions
T.L. Bubon
The department also conducted research on the problem of aging. In the telomeric model of aging, telomeric structures contain guanine-rich repeating sequences that are able to fold into four-stranded so-called G-quadruplexes, consisting of three horizontally arranged G-quartets. It is shown that the G-quartet exists in two conformations: one with the lowest minimum energy, and the other higher by only 0.2 kcal/mol, but which is always drawn in textbooks. Their uniqueness is manifested in the fact that they pass into each other through a tiny barrier of 0.3 kcal/mol. This means significant flexibility (floppiness) of hydrogen bonds in the G-tetrad and that for the n-stacking of the G-quadruplex there are actually 2n isomers. The conformation with the lowest minimum energy is formed in a complex with the G-quadruplex due to four bifurcated weaker hydrogen bonds N-H…O with "overcoordinated" oxygen atoms
E.S. Kryachko
The work results in the distinct chemical nature of the hydrogen bonding interactions of the overcoordinated oxygen atoms in the “bare” G-quadruplex. This information is obtained by performing a topological analysis of the Laplacian of the charge density, ∇2(r), identifying regions of local concentration and charge depletion near the overcoordinated oxygen atoms, and superimposing this topology on the bonding paths found by the topological analysis (r). The topological analysis shows that the longer H-bond is unconventional, since the hydrogen bond does not coordinate with any of the lone oxygen pairs, but rather agrees with the minimum charge concentration between them! That is, the subatomic features of the supercoordinated oxygen atoms in the “bare” G-quadruplex show that the unconventional hydrogen bonds are actually examples of chalcogen bonds, where the donor atom is hydrogen
E.S. Kryachko
A representation of zero curvature for a new integrative nonlinear model of pseudoexciton excitations on a regular two-chain lattice is constructed and a system of evolution equations of this lattice model is formulated. The most important local conservation laws for the specified integrative nonlinear system are found
O.O. Vakhnenko
A transformation of the field amplitudes of the system to a physically motivated canonical form is proposed. The prototypical integrable nonlinear system is split into the actual nonlinear dynamic lattice system and a spatially independent parametric actuator that modulates the parameters of the internodal interaction of the main nonlinear system in time
O.O. Vakhnenko
The Hamiltonian of the physically motivated parametrically actuated version of the integrable nonlinear model of pseudoexciton excitations on a regular two-chain lattice is found and a system of dynamic equations of this parametrically actuated nonlinear model in the explicit canonical Hamiltonian form is obtained
O.O. Vakhnenko
A new integrated nonlinear evolutionary model of two coupled oscillatory subsystems on a quasi-one-dimensional lattice with local and spatially distributed mass parameters and, accordingly, positive and negative elastic moduli has been constructed
O.O. Vakhnenko
The features of the electronic spectrum of a number of conjugated oligomers are studied. Namely, an exact solution of the eigenvalue problem for conjugated oligomers of polyparaphenylene and polynaphthalene of different lengths, which can serve as structural blocks for armchair and (2m,m) graphene nanoribbons, is presented. It is shown that the electronic spectrum of polynaphthalene includes localized states, unlike the spectrum of polyparaphenylene, which consists (like the spectra of armchair graphene nanoribbons of arbitrary width) only of unlocalized states. Explicit analytical expressions for the coefficients of the wave function expansion of the considered conjugated oligomers are also found
L.I. Malysheva
On the basis of the formalism of the strong coupling theory and the Green function technique, all matrix elements of the Green functions for a chain under the action of a uniformly varying field were obtained. Exact and approximate expressions for the transmission coefficient and current-voltage characteristics for the Wannier-Stark ladder of interacting levels were found. Analytical expressions for the current-voltage characteristics through atomic wires at zero temperature were obtained. The proposed approximate expressions for the current-voltage characteristics quite accurately approximate the corresponding exact analytical dependences
L.I. Malysheva
A phenomenological theory of d-wave altermagnets was constructed. It is shown that in these materials non-collinear magnetization structures, such as domain walls or skyrmions, have spontaneous magnetization. The dynamics of the domain wall in altermagnets are studied. It is shown that the moving wall deforms, resulting in a critical bifurcation value of the velocity, which separates two types of motion: translational and precessional types of dynamics for velocities smaller and larger than the critical value, respectively
V.P. Kravchuk
For films of d-wave altermagnets, a piezoelectric effect induced by thermal excitation of magnons is predicted. The magnetic moment is linear with respect to the applied mechanical stress and oriented perpendicular to the film. The orientation of the moment (up or down) is determined by the direction of application of the mechanical stress relative to the crystallographic axes. In these same systems, the effect of temperature spin conductivity is predicted, the effect of spin current generation in response to an applied temperature gradient
V.P. Kravchuk
The appearance of a phasic sliding mode of a quasi-skyrmion lattice formed in a monolayer of iron on the surface of iridium has been experimentally found and theoretically explained. The phasic mode arises as a result of the incommensurability of the magnetic and atomic subsystems, when in a certain direction the ratio of the periods of the atomic and magnetic structures is not a rational number
V.P. Kravchuk
An analytical expression for the density of states of Josephson plasmons in a ladder-shaped array of Josephson junctions that is infinite in one direction and contains an arbitrary finite number of rows N) in the opposite direction has been obtained. It has been established that the density of states has 3N-2 singularities. The dependence of the density of states on the constant anisotropy (the ratio of the horizontal critical current to the vertical), dimensionless inductance and external current was analyzed. It was shown that the constant anisotropy has the greatest impact on the density of states, leading to significant shifts of its singularities along the frequency axis
Ya.O. Zolotaryuk, I.O. Starodub, D. Bukatova
The density of states and the differential entropy per particle for Dirac electrons in graphene, which are under the action of a perpendicular magnetic field and a plane electric field, were obtained and analyzed. The study considered ballistic electrons, and also took into account the effect of weak scattering by impurities. In the latter case, the zero magnetic field limit and the so-called collapse of Landau levels in graphene were analytically investigated. Comparing the results with numerical calculations on graphene ribbons, it is demonstrated that the Landau procedure for calculating the number of states must be modified for Dirac-like electrons, which leads to a field-dependent degeneracy coefficient of the Landau levels
S.G. Sharapov

It is shown that introduced earlier new invariant of the Dirac equation with the Coulomb potential supplements the kown Dirac and Johnson-Lippmann invariants and they all form algebra. This allows to solve the equation using the algebraic method. It is found that different solutions of the equation are different presentations of the algebra of the spinor invariants. Within the group theory and using this algebra, relations between different presentations are found and all properties of the exact general solution are obtained in such algebraic approach. The hidden SU(2) symmetry (invariance with respect to the rotation in the Hilbert space of all eigen states) of the Dirac equation is demonstrated.
L. Brizhik, A.A. Eremko, V.M Loktev
An integrable nonlinear dynamical system of gauge-coupled intrasite excitations and lattice vibrations on an infinite one-dimensional regular lattice has been studied. Depending on the relationships between the two physically distinct spatial scaling parameters the system can manifest itself in three qualitatively distinct dynamical regimes referred to as the monopole regime, dipole regime, and threshold regime. The phenomenon of dipole-monopole crossover for the spatial distribution of pseudoexcitons is shown to initiate the partial splitting between the pseudoexcitonic and vibrational subsystems in the threshold dynamical regime specified by the threshold value of the localization parameter. This partial splitting is manifested by the complete elimination of one pseudoexcitonic component accompanied by the actual conversion of another pseudoexcitonic component into a pseudoexcitonic chargeless half mode. The integrable nonlinear pseudoexciton-phonon system under study is expected to be applicable for modeling the nonlinear dynamical properties of properly designed PT-symmetric metamaterials.
O.O. Vakhnenko and V.O. Vakhnenko
Within the framework of Green's function formalism, the pi-electron spectra of polyparaphenylene and polynaphthalene oligomers, which are the building blocks of armchair and chiral (2m,m) nanoribbons of arbitrary width, are found, analyzed and compared. In particular, it is shown that the spectrum of polynaphthalene (in contrast to polyparaphenylene) includes localized states.
L.I. Malysheva
The influence of discreteness on the fluxon interaction with the spatial dipole impurity in the Josephson transmission line is studied. This impurity is used to model the qubit inductively coupled to the Josephson transmission line. Fluxon assisted readout process of the qubit state is based on measuring the passage time it takes to pass through the dipole impurity. The discreteness of the medium plays an important role in this process. It was found that the fluxon delay time on the qubit impurity increases significantly if the discreteness of the medium increases, which is favorable for the sensitivity of the readout process. It is shown that the difference between the fluxon threshold currents for the qubit in different states decreases with the increase of discreteness, which in turn worsens the sensitivity of the readout process.
I.O. Starodub, Y. Zolotaryuk
The spectrum of spin waves propagating along a skyrmion string was obtained for the case when a spin-polarized current flows along the string. It was shown that the presence of the current leads to instability of the string translational mode. For an infinitely long string in an ideal ferromagnet, the instability effect is thresholdless and takes place for an infinitely small current.
V.P. Kravchuk
It is proposed and verified computationally, within the density functional approach, the concept of pre-fragmentation bonding that governs the ionization fragmentation in some amino acids under the influence of ionizing radiation.
E.S. Kryachko
Within the framework of the molecular dynamics simulations, the conformational space of natural polyamine molecules, interacting with the DNA double helix was studied. In particular, the system of DNA with spermidine3+ molecules was analyzed. The results showed that conformations of the spermidine3+ molecule (over 2000) can be classified into seven conformational modes. DNA macromolecule strongly influence the relative population of conformational states of polyamines, in particular two of the seven conformational modes of the spermidine3+ molecule appear only in complex with DNA. Interacting with DNA, the spermidine3+ molecules can significantly bend, inducing local conformational changes in the double helix. The obtained results are important for understanding the role of natural polyamines in the mechanisms of DNA biological functioning.
Perepelytsya S.M.

The new invariant of the Diraq equation with the Coulomb potential is found. It supplements Diraq and Johnson-Lippman invariants, so that they together form algebra. It is shown that various solutions of the equation are various representations of this algebra. In frame of the group theory using the algebra of the spinor invariants the relation between different representations is found. The general solution of the Diraq equation is found within the algebraic approach. It is shown that the principal quantum number is not a mere combination of other quantum numbers, as it follows from the direct solving of the equation, but is a fundamental characteristic of the hydrogen atom.
L. Brizhik, A.A. Eremko, V.M Loktev
It is known that in two-dimensional relativistic Dirac systems placed in orthogonal uniform magnetic and electric fields, the Landau levels collapse as the applied in-plane electric field reaches a critical value $\pm E_c$. We study this phenomenon for a distinct field configuration with in-plane constant radial electric field. The Dirac equation for this configuration does not allow analytical solutions in terms of known special functions. The results are obtained by using both the WKB approximation and the exact diagonalization and shooting methods. It is shown that the collapse occurs for positive values of the total angular momentum quantum number, the hole (electron)-like Landau levels collapse as the electric field eaches the value +(-) E_c/2. The investigation of the Landau level collapse in the case of gapped graphene shows a number of distinctive features in comparison with the gapless case.
S.G. Sharapov
A one-dimensional nonlinear dynamical system of intra-site excitations and lattice vibrations coupled via gauge-like mechanism is studied. The system admits the semi-discrete zero-curvature representation and therefore it proves to be integrable in the Lax sense. Relaying upon an appropriately developed Darboux-Bäcklund dressing technique the explicit four-component analytical solution to the system is found and analyzed in details. Due to mutual influence between the interacting subsystems the physically meaningful solution arises as the essentially nonlinear superposition of two principally distinct types of traveling waves. The interplay between the two typical spatial scales relevant to these traveling waves causes the criticality of system's dynamics manifested as the dipole-monopole transition in the spatial distribution of intra-site excitations. The under-critical and over-critical regimes of system's dynamics are comprehensively illustrated graphically.
O.O. Vakhnenko
Using the solution of the Schrödinger equation with the Hückel-type Hamiltonian for carbon nanotubes (2m,m), analytical expressions for wave functions were obtained within the framework of the tight-binding model, and the relationship between the transmission coefficient and the band structure of chiral and achiral carbon nanotubes was analyzed. The influence of chirality on the coefficient of electron transmission through a system with a step-like potential is determined and it is shown that (2m,m) nanotubes with an average chiral angle exhibit intermediate transport properties compared to achiral (arnchair and zigzag) nanotubes.
L. Malysheva
A new class of topologically non-trivial solutions of the Landau-Lifshitz equation in the form of screw dislocations was found and investigated. The screw dislocations are realized in a helical phase of the cubic chiral magnets. A type of dislocation was found, which is continuously deformed into a skyrmion string under the action of an external magnetic field.
V.P. Kravchuk
A model of double helix deformation was built to describe changes in the macromolecule structure. In addition to elastic components (bending, twisting, stretching), the presented model includes conformational rearrangements of the macromolecule, as well as describes the relationship between the external and internal degrees of freedom of the DNA structure. The obtained shapes, values and energy of the DNA deformation sites allow us to propose a probable mechanism of recognition of key DNA sequences due to their deformation, as well as to explain the high accuracy of genetic information reproduction processes.
P.P. Kanevska, S.N. Volkov
Using the density functional theory method in the presence of a physiological environment the structure and energy of formation of atomic molecular complexes are determined groups of nucleic bases of the DNA macromolecule with hydrogen peroxide molecules and water It is shown that hydrogen peroxide forms stable complexes with atomic grains of DNA, blocking the centers of specific recognition of the macromolecule.
D.V. Pyatnytskyi

A new spin relevant invariant of the Dirac equation with the Coulomb potential is constructed. It does not commute with the known Dirac and Johnson-Lippman invariants and defines the spin degree of freedom. The general solution of the Dirac equation is found. It is described by the full set of quantum numbers which characterize hydrogen-like energy states. Spatial distribution of the charge density and spin orientation meanvalue are calculated and shown to depend significantly on the spin invariant. This can be manifested experimentally.
Acad. of the NAS of Ukraine V.M. Loktev, L. Brizhik, O. Eremko
The nonlinear dynamics of coupled PT-symmetric excitations and Toda-like vibrations on a onedimensional lattice are studied analytically and elucidated graphically. The nonlinear exciton-phonon system as the whole is shown to be integrable in the Lax sense inasmuch as it admits the zero-curvature representation supported by the auxiliary linear problem of third order. Inspired by this fact, we have developed in detail the Darboux-Bäcklund integration technique appropriate to generate a higher-rank crop solution by dressing a lower-rank (supposedly known) seed solution. In the framework of this approach, we have found rather non-trivial four-component analytical solution exhibiting the crossover between the monopole and dipole regimes in the spatial distribution of intra-site excitations. This effect is inseparable from the pronounced mutual influence between the interacting subsystems in the form of specific nonlinear superposition of two essentially distinct types of travelling waves. We have established the criterion of monopole-dipole transition based upon the interplay between the localization parameter of Toda mode and the intersubsystem coupling parameter.
О.О. Vakhnenko
Using solution of the Schroedinger equation with Hukkel type Hamiltonian for carbon nanotubes (2m,m) the analytical expressions for the wavefunctions are obtained in the model of strong coupling. The relation between the transmission coefficient and band structure of chiral and non-chiral nanotubes is analyzed. It is found the impact of non-chirality on the transmission coefficient for electrons across the system with the step-like potential. Range of parameter values is given, at which experimental observation of chirality impact on transport characteristics of carbon nanotubes is obtained.
L.I. Malysheva
Spin waves of skirmion lattices in many-layered ferromagnetic heterostructures are studied theoretically and experimentally. It is shown that strong dipole-dipole interaction leads to significant change of the positions of magnon modes which have non-zero magnetic moment. From the comparison of experimental and theoretical evolutions of spectra in the magnetic field Dzyaloshinsky-Morria coupling constant is calculated for the heterostructure Ir/Fr/Co/Pt.
V.P. Kravchuk
The structure and energy formation of molecular complexes of DNA atomic groups of sugar-phosphate backbone with molecules of hydrogen peroxide and water are studied. Using the method of molecular mechanics, approaches of quantum chemistry and the presence of a physiological environment, the interaction energies are calculated and the spatial configurations of molecular complexes of peroxide with phosphate of DNA backbone are optimized. Calculations show that under physiological conditions, hydrogen peroxide can stay near phosphate groups of DNA for a long time, blocking the centers of genetic activity of the macromolecule.
D.V. Piatnytskyi, O.O. Zdorevskyi, S.N. Volkov
The formation of a double helix of DNA in aqueous solution with hydrogen peroxide molecules and Na + counterions is modeled. Molecular mechanics shows that hydrogen peroxide molecules bind to the oxygen atoms of the phosphate groups of the double helix and thus replace the water molecules of the hydrated shell of the macromolecule. Three layers of hydrogen peroxide ordering around the phosphate groups of the DNA helix with centers of density around 2.6 and 3.3 angstroms, as well as a wide band with a center around 5 angstroms were determined. Thus, hydrogen peroxide molecules that interact with phosphates can inhibit the formation of hydrogen bonds necessary for the biological functioning of DNA.
S.N. Volkov, S.M. Perepelytsya
Equations for the scattering data and discrete spectrum were obtained for the one-dimensional Schroedinger equation with the piecewise-constant potential. The asymptotical three-scale method of squeezing the system to zero width has been developed. It has been shown that the boundary conditions in the singular point make sense only when the mutual divergence cancellation in the connection matrix is possible. Two types of the transcendental equations for the resonance sets have been derived.
O.O. Zolotaryuk, Y.O. Zolotaryuk
The dispersion law for plasmons in the quasi-one-dimensional array of Josephson junctions, that consists of the finite number of rows N and the infinite numbers of columns, is derived. If external bias is absent then the spectrum has a N-fold degenerate flat band. The degeneracy is lifted when the external bias is applied and, as a result, only one flat branch remains.
D.V. Bukatova, Y.O. Zolotaryuk

The description of the collective magnetorheological effect induced by magnetic field in elastomers with uniaxial ferromagnetic particles is proposed. The condition of consistency is used between magnetic and mechanic momenta of forces exerted on these particles in elastomer at their magnetization. The study shows that even in the case of their small concentration, the value of magnetically-induced shear can be anomalously large, reaching up to tens of percent. The deformation of magneto-active elastomer can evolve critically as a second-order phase transition if magnetic field is aligned along the easy axis of particles.
Acad. of the NAS of Ukraine V.M. Loktev
A novel family of disordered systems is proposed. This family belongs to the class of systems containing random substitutional non-Hermitian impurities. The consideration is limited by a rather simple case when the presence of substitutional point defects results in the model Hamiltonian featuring a diagonal disorder. In contrast to known models of non-Hermitian impurities, the nonzero density of states for each isolated from the host impurity is restricted to a continuous band of finite width. A method to construct corresponding impurity Hamiltonians is provided.
Yu.V. Skrypnyk, Acad. of the NAS of Ukraine V.M. Loktev
Using the methods of density functional and molecular mechanics, it has been shown that hydrogen peroxide molecules form stable complexes with the phosphate group of the DNA macromolecule. Under physiological conditions, such complexes are more energetically favourable than similar complexes with a water molecule. The energy advantage for complexes with hydrogen peroxide is achieved, in particular, due to the presence in the molecule of a torsional degree of freedom, which makes it more flexible compared to the water molecule. These results show that in living tissues, hydrogen peroxide can remain near the phosphate groups of DNA for a long time, blocking the genetic activity of the macromolecule.
S.N. Volkov, D.V. Piatnytskyi, O.O. Zdorevskyi
Two families of point interactions with bound state energy are realized from a heterostructure composed of two parallel homogeneous layers in the limit as their width and the distance between them tend to zero simultaneously. Under certain conditions described by transcendental equations, a resonant-tunneling transmission of electrons through this limit structure is shown to occur. A particular example of the singular potential having the form of the derivative of the Dirac delta-function is generalized to a whole family of point interactions, for which a single bound state does exist, contrary to the widespread opinion on the non-existence of bound states in δ-like systems.
A. Zolotaryuk, Ya. Zolotaryuk
The nonlinear model of three dynamical subsystems, coupled both in their kinetic and potential parts, has been suggested. Due to the quasi-one-dimensional spatial structure of its underlying lattice the model grasps several degrees of freedom capable to imitate the dynamical behavior of long macromolecules both natural and synthesized origins. The model admits a clear Hamiltonian formulation with the standard form of fundamental Poisson brackets and it demonstrates the complex-conjugate symmetry between two subsystems of a Toda type. The integrability of system equations is supported by their zero-curvature representation based upon the auxiliary linear problem with the relevant spectral operator of third order. In view of these facts, we have developed an appropriate two-fold Darboux-Bäcklund dressing technique capable to generate the nontrivial crop solution embracing all three coupled subsystems. The explicit crop solution to the nonlinear model is found to be of a pronounced pulson character.
O.O. Vakhnenko
The theory of curvilinear one-dimensional antiferromagnets has been developed. It has been established that the achiral antiferromagnetic spin chain behaves like a biaxial chiral magnet with effective anisotropy and Dzialoshinsky-Moria interaction. The geometry-induced Dyaloshinsky-Moria interaction leads to hybridization of magnons in the chain.
K.V. Yershov, V.P. Kravchuk
We study the manifestation of the Nernst effect in the Corbino disk subjected to the normal external magnetic field and to the radial temperature gradient. The Corbino geometry offers a precious opportunity for the direct measurement of the magnetization currents that are masked by the kinetic contributions to the Nernst current in the conventional geometry. The magnetization currents, also referred to as the edge currents, do not depend on the conductivity of the sample which is why they can be conveniently described within the thermodynamic approach. They can be related to the Landau thermodynamic potential for an infinite system. We demonstrate that the observable manifestation of this, purely thermodynamic, Nernst effect occurs as strong oscillations of the magnetic field measured in the center of the disk as a function of the external field. The oscillations depend on the temperature difference at the edges of the disk. Dirac fermions and 2D electrons with a parabolic spectrum are characterized by oscillations of different phase and frequency. We predict qualitatively different power dependencies of the magnitude of the Nernst signal on the chemical potential for normal and Dirac carriers.
S.G. Sharapov

Based on the Dirac quantum theory of the spinor field, the generelized operator of the spin-orbit interaction is found. It is shown that this operator contains not only the known Thomas-Frenkel correction, but also a new term, so that the consistent description of the influence of the spin-orbit interaction on electrons in the external potential in frame of the non-relativistic Schroedinger equation is possible only with the account of this generelized operator.
L.S. Brizhik. O.O. Eremko, Acad. of the NAS of Ukraine V.M. Loktev
An explanation is proposed for the recently observed a giant increase of the Drude peak width under applied uniaxial strain in optical spectra of monolayer graphene. The underlying mechanism of this increase can be based on resonant scattering of carriers from inevitably present impurities such as adsorbed atoms that can be described by the Fano-Anderson model. It is demonstrated that the often neglected scalar deformation potential plays the essential role in this process. The conditions necessary for the maximum effect of the giant Drude peak broadening are determined.
V.O. Shubnyi, Yu.V. Skrypnyk, S.G. Sharapov, Acad. of the NAS of Ukraine V.M. Loktev
Two types of general nonlinear integrable systems on infinite quasi-one-dimensional regular lattices are proposed. The method is suggested which allows to unify the Toda-like vibration subsystem and the self-trapping-like exciton subsystem into a single integrable system, thereby substantially extending the range of realistic physical problems that can be rigorously modeled. Several lowest conserved densities associated with either of the relevant infinite hierarchies of local conservation laws are found explicitly in terms of prototype field functions.
O.O. Vakhnenko
The properties of embedded solitons (solitons that exist despite their resonance with the linear spectrum of the system and have only isolated values of velocity) in the discrete double sine-Gordon equation with next-neighbor and second-neighbor interactions are investigated. This model describes the DC biased array of the superconductor/ferromagnet/ superconductor junctions. Depending on the sign of these interactions they can be either destructive or favorable for the embedded soliton creation. The embedded soliton existence area depends on the width of the linear spectrum: narrowing of the spectrum widens the embedded soliton existence range and vice versa.
Y. Zolotaryuk, I. Starodub
An approach to define single-point interactions under the application of external fields has been developed. The essential feature is an asymptotic method based on the one-point approximation of multi-layered heterostructures that are subject to bias potentials. In the zero-thickness limit, the matrix connecting the two-sided boundary conditions of wave function at the point of singularity has been obtained. The dependence of the reflection and transmission coefficients on the bias potential has been studied. Several "one-point" models of two- and three-terminal devices in the semiconductor physics have been elaborated. The notion of a "point" transistor has been introduced, and the existence of extremely sharp peaks as an applied voltage tunes, forming a resonance set for this one-point interaction, is shown.
A.V. Zolotaryuk, Y. Zolotaryuk
The interaction of hydrogen peroxide and water molecules with the regions of specific and non-specific recognition of DNA molecules by proteins is analyzed. These interactions are important for explanation of beam therapy of cancer. On the basis of density functional theory, the interaction energies of water and hydrogen peroxide molecules with DNA nuclear bases are calculated and optimal geometries of stable complexes are determined. The positions are found where binding of hydrogen peroxide molecule exceeds the one for water molecule.
S.N. Volkov, D.V. Piatnytskyi, O.O. Zdorevskyi
The interaction of polyamines with the DNA macromolecule was studied using molecular dynamics simulations. The polyamines molecules were found to be localized mostly in the minor groove of the double helix in the region with the specific sequence of nucleotides of A-tract type. The results of the study agree with the existing experimental data and explain the preferential localization of polyamines molecules in the DNA sites with characteristic nucleotide sequence.
S.M. Perepelytsya

It is shown that inhomogeneous curvature of magnetic wire induces motion of a domain wall in the direction of the curvature gradient increasing. An asymptotic domain wall velocity is found. The resuts are verified by micromagnetic simulations.
Yu.B. Gaididei, V.P. Kravchuk, K.V. Yershov
The two-stage mechanism of the appearance of threshold deformations in a DNA macromolecule under the action of external force is proposed. At the first stage the appearance of a bistable state and the formation of domains with different conformations in the macromolecule chain occur for some critical value of external force. On the second stage the cooperative process of the domain walls propagation happens in the macromolecule. Thus, the emergence of bistability causes the threshold effect of deformation. The calculated parameters of the threshold elongation of DNA double helix are consistent with the experimental data.
S.N. Volkov
The character of hydration of Na+, K+, Cs+ and Mg2+ counterions interacting with DNA double helix is studied using molecular dynamics simulations. The results show that structuring of the first and the second hydration shells of the ions is essential for the specific interactions with DNA. In particular, Na+ and Mg2+ interact with the DNA mostly via water molecules of the first hydration shell, while K+ and Cs+ may be dehydrated and penetrate deep into the minor groove of the double helix.
S.M. Perepelytsya
It is shown that with the accuracy of the second order relativistic corrections the Hamiltonian of particles and antiparticles in an external field can be reduced to the Hamiltonian of non-interacting electrons and positrons. Operator invariants are obtained which describe spin states of relativistic particles. The Hamiltonian of electrons in the non-relativistic approximation is shown to contain both known and new relativistic corrections.
A.A. Eremko, L.S. Brizhik, Acad. of the NAS of Ukraine V.M. Loktev
Discrete time nonlinear quantum walk dynamics are studied. In the linear limit the spectrum of this model can be reduced to the complete flat band shape, what means the absence of transport and presence of the compact localized states. Existence of the soliton-like exitations that can propagate with constant velocity has been demonstrated. Due to the flatness of the linear spectrum the soliton does not resonate with it. The absence of the linear waves also causes the super-exponential [~exp(-exp(x))] decay of the soliton amplitude.
Ya. Zolotaryuk
The new nonlinear integrable system of classical intra-molecular excitations on a ladder lattice with three structural elements in the unit cell is suggested. The Poisson structure and the Hamiltonian formulation of the system are found. In the framework of Darboux transformation for an auxiliary spectral problem the system's multicomponent soliton solution is obtained.
O.O. Vakhnenko

A new mechanism of point mutation formation in biological systems that takes into account the fluctuation appearance of complementary pairs preopened by water in the DNA double helix has been proposed. The possible proton transitions in the preopened A-T pair have been analyzed within the density functional theory, and their energies have been numerically obtained. It is shown that under formation of an opened pair, irregular tautomeric forms of the nucleic bases can be stabilized and be the origin of point mutations. The estimated probability of the occurrence of these mutations in DNA falling in the interval of 10^-10-10^-11 explains the known experimental facts.
E.S. Kryachko, S.N. Volkov
The mixed set of primary and intermediate fields for the integrable nonlinear Schrödinger system on a triangular ladder lattice is found out. Having been written in terms of these field variables the system is shown to split into two subsystems with qualitatively different properties of excitations. The crossover effect in the system dynamical behavior at the critical value of background parameter is established.
О.О. Vakhnenko

It is known that the Shubnikov - de Haas oscillations can be observed in the Hall resistivity, although their amplitude is much weaker than the amplitude of the diagonal resistivity oscillations. Employing a model of two-dimensional massive Dirac fermions that exhibits anomalous Hall effect, we demonstrate the amplitude of the Shubnikov - de Haas oscillations of the anomalous Hall conductivity is the same as that of the diagonal conductivity. We argue that the oscillations of the anomalous Hall conductivity can be observed by studying the valley Hall effect in graphene superlattices and the spin Hall effect in the low-buckled Dirac materials.
S.G. Sharapov
It is shown that the curvature and torsion of a ferromagnetic nanowire significantly affect the spin-polarized current induced domain wall motion along the wire. We consider the simplest case of constant curvature and torsion, corresponding nanowires in the form of three-dimensional helix. It is shown that the curvature leads to Walker breakdown, i.e. the emergence of a critical density of spin-polarized current j_c, which separates two modes of motion: translational motion when j<j_c and oscillating motion for j> j_c. In the point j = j_c a saddle-node bifurcation takes place. The nanowire torsion, in turn, leads to a shift of the material parameter of spin torque nonadiabaticity. The shift is proportional to the product of the helix chirality to the topological charge of the domain walls. This shift can be negative, that can lead to negative domain wall mobility. Basing on the obtained results we propose a practical method of experimental measurement of the nonadiabaticity parameter and the damping coefficient.
Yu.B. Gaididei, V.P. Kravchuk, K.V. Yershov
The analytical expression for the spectrum of electrons in quasi-two-dimensional space (so called 2D electrons) is found within the fundamental Dirac equation. Such system describes layered heterostructures, interfaces, crystal surfaces, etc. It is shown that the exact solution contains several spin invariants, which means possibility of the existence of many spin states of quasi-2D electrons with different spin polarization and different effects of spin-orbit interaction on the energy spectrum. The exact solution is found for electrons confined by asymmetric potential well, which includes free parameters, whose value corresponds to certain invariants. In the general case the spin quantum number determines certain value of the linear combination of all invariants. These results allow to ascertain the conditions at which the given spin state is realized, which opens new perspectives to control the spin degree of freedom of charge carriers in spintronics.
A.A. Eremko, V.M. Loktev, L.S. Brizhik
We present the analytic analysis of the spectral problem for bounded graphene fragments and finite polyene chains. The solutions of the transcendental equation for the characteristic quantum numbers are thoroughly examined and their accurate approximations are proposed. The obtained results are used for analysis of the fundamental and technologically significant properties of graphene and its daughter structures (i.e., zigzag and armchair graphene nanoribbons), and finite polyene chains of various length.
L.I. Malysheva
The variativity of governing coupling parameters in the integrable nonlinear Schrödinger system on a triangular-lattice ribbon is shown to ensure the important qualitative rearrangements in the system dynamics. Thus the longitudinal coupling parameters regulated mainly by the background values of concomitant field variables are responsible for the bifurcation of primary integrable nonlinear system into the integrable nonlinear system of Ablowitz-Ladik type. As a consequence in a critical point the number of independent field variables is reduced by a half and the system Poisson structure turns out to be degenerate. On the other hand the transverse coupling parameters regulated basically by the choice of their a priori arbitrary dependencies on time are capable to incorporate the effect of external linear potential. As a consequence the primary integrable nonlinear system with appropriately adjusted parametrical driving becomes isomorphic to the system modelling the Bloch oscillations of charged nonlinear carriers in an electrically biased ribbon of triangular lattice.
O.O. Vakhnenko
Molecular force field (CHARM), which is commonly used in computer simulations to study the structure and dynamics of macromolecules in biological systems, is modified. A new type of potential function allows us to study the processes of chemical bonds breaks, the rupture of valence angles and dihedral interactions in molecules. Modified force field implemented in the software package MBN Explorer.
S.N. Volkov
The structure functions of the mirror nuclei ¹⁴С and ¹⁴O are studied within a model "three alpha-particles plus two extra nucleons". The charge density distributions, form factors, pair correlation functions, and the momentum distributions of particles are found for these nuclei. Two spatial configurations are revealed in the ground state of ¹⁴С and ¹⁴O nuclei. The unknown experimental charge r.m.s. radius of ¹⁴O nucleus is predicted.
B.E. Grinyuk, D.V. Piatnytskyi

Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine

Bogolyubov Institute for Theoretical Physics
of the National Academy of Sciences of Ukraine