arXiv subjects

Y. Zolotaryuk

Publications and source records attributed to Y. Zolotaryuk.

At least 19 recordsLinked to original sources

arXiv2023

Bound states and point interactions of the one-dimensional pseudospin-one Hamiltonian

The spectrum of a one-dimensional pseudospin-one Hamiltonian with a three-component potential is studied for two configurations: (i) all the potential components are constants over the whole coordinate space and (ii) the profile of some components is of a rectangular form. In case (i), it is illustrated how the structure of three (lower, middle and upper) bands depends on the configuration of potential strengths including the appearance of flat bands at some special values of these strengths. In case (ii), the set of two equations for finding bound states is derived. The spectrum of bound-state energies is shown to depend crucially on the configuration of potential strengths. Each of these configurations is specified by a single strength parameter $V$. The bound-state energies are calculated as functions of the strength $V$ and a one-point approach is developed realizing correspondent point interactions. For different potential configurations, the energy dependence on the strength $V$ is described in detail, including its one-point approximation. From a whole variety of bound-state spectra, four characteristic types are singled out.

quant-ph↗

arXiv2023

Bound states of a one-dimensional Dirac equation with multiple delta-potentials

Two approaches are developed for the study of the bound states of a one-dimensional Dirac equation with the potential consisting of $N$ $δ$-function centers. One of these uses the Green's function method. This method is applicable to a finite number $N$ of $δ$-point centers, reducing the bound state problem to finding the energy eigenvalues from the determinant of a $2N\times2N$ matrix. The second approach starts with the matrix for a single delta-center that connects the two-sided boundary conditions for this center. This connection matrix is obtained from the squeezing limit of a piecewise constant approximation of the delta-function. Having then the connection matrices for each center, the transmission matrix for the whole system is obtained by multiplying the one-center connection matrices and the free transfer matrices between neighbor centers. An equation for bound state energies is derived in terms of the elements of the total transfer matrix. Within both the approaches, the transcendental equations for bound state energies are derived, the solutions to which depend on the strength of delta-centers and the distance between them, and this dependence is illustrated by numerical calculations. The bound state energies for the potentials composed of one, two, and three delta-centers ($N=1,\,2,\,3$) are computed explicitly. The principle of strength additivity is analyzed in the limits as the delta-centers merge at a single point or diverge to infinity.

quant-ph↗

arXiv2019

Point interactions with bias potentials

We develop an approach on how to define single-point interactions under the application of external fields. The essential feature relies on an asymptotic method based on the one-point approximation of multi-layered heterostructures that are subject to bias potentials. In this approach , the zero-thickness limit of the transmission matrices of specific structures is analyzed and shown to result in matrices connecting the two-sided boundary conditions of the wave function at the origin. The reflection and transmission amplitudes are computed in terms of these matrix elements as well as biased data. Several one-point interaction models of two- and three-terminal devices are elaborated. The typical transistor in the semiconductor physics is modeled in the "squeezed limit'' as a $δ$- and a $δ'$-potentialand referred to as a "point" transistor. The basic property of these one-point interaction models is the existence of several extremely sharp peaks as an applied voltage tunes, at which the transmission amplitude is non-zero, while beyond these resonance values, the heterostructure behaves as a fully reflecting wall. The location of these peaks referred to as a "resonance set" is shown to depend on both system parameters and applied voltages. An interesting effect of resonant transmission through a $δ$-like barrier under the presence of an adjacent well is observed. This transmission occurs at a countable set of the well depth values.

quant-ph↗

arXiv2018

Almost compact moving breathers with fine-tuned discrete time quantum walks

Discrete time quantum walks are unitary maps defined on the Hilbert space of coupled two-level systems. We study the dynamics of excitations in a nonlinear discrete time quantum walk, whose fine-tuned linear counterpart has a flat band structure. The linear counterpart is, therefore, lacking transport, with exact solutions being compactly localized. A solitary entity of the nonlinear walk moving at velocity $v$ would therefore not suffer from resonances with small amplitude plane waves with identical phase velocity, due to the absence of the latter. That solitary excitation would also have to be localized stronger than exponential, due to the absence of a linear dispersion. We report on the existence of a set of stationary and moving breathers with almost compact superexponential spatial tails. At the limit of the largest velocity $v=1$ the moving breather turns into a completely compact bullet.

nlin.PS↗

arXiv2012

Controlling a resonant transmission across the $δ'$-potential: the inverse problem

Recently, the non-zero transmission of a quantum particle through the one-dimensional singular potential given in the form of the derivative of Dirac's delta function, $λδ'(x) $, with $λ\in \R$, being a potential strength constant, has been discussed by several authors. The transmission occurs at certain discrete values of $λ$ forming a resonance set ${λ_n}_{n=1}^\infty$. For $λ\notin {λ_n}_{n=1}^\infty$ this potential has been shown to be a perfectly reflecting wall. However, this resonant transmission takes place only in the case when the regularization of the distribution $δ'(x) $ is constructed in a specific way. Otherwise, the $δ'$-potential is fully non-transparent. Moreover, when the transmission is non-zero, the structure of a resonant set depends on a regularizing sequence $Δ'_\varepsilon(x)$ that tends to $δ'(x)$ in the sense of distributions as $\varepsilon \to 0$. Therefore, from a practical point of view, it would be interesting to have an inverse solution, i.e. for a given $\barλ \in \R$ to construct such a regularizing sequence $Δ'_\varepsilon(x)$ that the $δ'$-potential at this value is transparent. If such a procedure is possible, then this value $\barλ$ has to belong to a corresponding resonance set. The present paper is devoted to solving this problem and, as a result, the family of regularizing sequences is constructed by tuning adjustable parameters in the equations that provide a resonance transmission across the $δ'$-potential.

math-ph↗

arXiv2008

Vortex and translational currents due to broken time-space symmetries

We consider the classical dynamics of a particle in a $d=2,3$-dimensional space-periodic potential under the influence of time-periodic external fields with zero mean. We perform a general time-space symmetry analysis and identify conditions, when the particle will generate a nonzero averaged translational and vortex currents. We perform computational studies of the equations of motion and of corresponding Fokker-Planck equations, which confirm the symmetry predictions. We address the experimentally important issue of current control. Cold atoms in optical potentials and magnetic traps are among possible candidates to observe these findings experimentally.

cond-mat.stat-mech↗

arXiv2006

Kinks in dipole chains

It is shown that the topological discrete sine-Gordon system introduced by Speight and Ward models the dynamics of an infinite uniform chain of electric dipoles constrained to rotate in a plane containing the chain. Such a chain admits a novel type of static kink solution which may occupy any position relative to the spatial lattice and experiences no Peierls-Nabarro barrier. Consequently the dynamics of a single kink is highly continuum like, despite the strongly discrete nature of the model. Static multikinks and kink-antikink pairs are constructed, and it is shown that all such static solutions are unstable. Exact propagating kinks are sought numerically using the pseudo-spectral method, but it is found that none exist, except, perhaps, at very low speed.

nlin.PS↗

arXiv2004

Resonant enhancement of the jump rate in a double-well potential

We study the overdamped dynamics of a Brownian particle in the double-well potential under the influence of an external periodic (AC) force with zero mean. We obtain a dependence of the jump rate on the frequency of the external force. The dependence shows a maximum at a certain driving frequency. We explain the phenomenon as a switching between different time scales of the system: interwell relaxation time (the mean residence time) and the intrawell relaxation time. Dependence of the resonant peak on the system parameters, namely the amplitude of the driving force A and the noise strength (temperature) D has been explored. We observe that the effect is well pronounced when A/D > 1 and if A/D 1 the enhancement of the jump rate can be of the order of magnitude with respect to the Kramers rate.

nlin.CD↗

arXiv2004

Ratchet-like dynamics of fluxons in annular Josephson junctions driven by bi-harmonic microwave fields

Experimental observation of the unidirectional motion of a topological soliton driven by a bi-harmonic ac force of zero mean is reported. The observation is made by measuring the current-voltage characteristics for a fluxon trapped in an annular Josephson junction that was placed into a microwave field. The measured dependence of the fluxon mean velocity (rectified voltage) at zero dc bias versus the phase shift between the first and second harmonic of the driving force is in qualitative agreement with theoretical expectations.

cond-mat.supr-con↗

arXiv2002

Discrete kink dynamics in hydrogen-bonded chains I: The one-component model

We study topological solitary waves (kinks and antikinks) in a nonlinear one-dimensional Klein-Gordon chain with the on-site potential of a double-Morse type. This chain is used to describe the collective proton dynamics in quasi-one-dimensional networks of hydrogen bonds, where the on-site potential plays role of the proton potential in the hydrogen bond. The system supports a rich variety of stationary kink solutions with different symmetry properties. We study the stability and bifurcation structure of all these stationary kink states. An exactly solvable model with a piecewise ``parabola-constant'' approximation of the double-Morse potential is suggested and studied analytically. The dependence of the Peierls-Nabarro potential on the system parameters is studied. Discrete travelling-wave solutions of a narrow permanent profile are shown to exist, depending on the anharmonicity of the Morse potential and the cooperativity of the hydrogen bond (the coupling constant of the interaction between nearest-neighbor protons).

nlin.PS↗

arXiv2002

Simple Mechanical Equivalents of Stepping Rotary Dynamics in F$_1$-ATPase

Two simple (rotator and one-particle) mechanistic models are suggested to describe simultaneously at a minimal level of sophistication two basic functions of F$_1$-ATPase: a motor regime driven by ATP hydrolysis and its inverted function as ATP synthesis. This description is consistent with the so-called rotary binding-change mechanism, a milestone of functioning ATP synthase, and uses a stepping (driving) function associated with two sequences of time instants, at which hydrolysis and synthesis reactions occur. It is useful to analyse experimental data and numerical simulations indeed predict corresponding dynamic behavior.

physics.bio-ph↗

arXiv2002

Broken space-time symmetries and mechanisms of rectification of ac fields by nonlinear (non)adiabatic response

We consider low-dimensional dynamical systems exposed to a heat bath and to additional ac fields. The presence of these ac fields may lead to a breaking of certain spatial or temporal symmetries which in turn cause nonzero averages of relevant observables. Nonlinear (non)adiabatic response is employed to explain the effect. We consider a case of a particle in a periodic potential as an example and discuss the relevant symmetry breakings and the mechanisms of rectification of the current in such a system.

cond-mat.stat-mech↗

arXiv2001

Broken symmetries and directed collective energy transport

We study the appearance of directed energy current in homogeneous spatially extended systems coupled to a heat bath in the presence of an external ac field E(t). The systems are described by nonlinear field equations. By making use of a symmetry analysis we predict the right choice of E(t) and obtain directed energy transport for systems with a nonzero topological charge Q. We demonstrate that the symmetry properties of motion of topological solitons (kinks and antikinks) are equivalent to the ones for the energy current. Numerical simulations confirm the predictions of the symmetry analysis and, moreover, show that the directed energy current drastically increases as the dissipation parameter $α$ reduces. Our results generalize recent rigorous theories of currents generated by broken time-space symmetries to the case of interacting many-particle systems.

nlin.PS↗

arXiv2001

Breathers in Josephson junction ladders: resonances and electromagnetic waves spectroscopy

We present a theoretical study of the resonant interaction between dynamical localized states (discrete breathers) and linear electromagnetic excitations (EEs) in Josephson junction ladders. By making use of direct numerical simulations we find that such an interaction manifests itself by resonant steps and various sharp switchings (voltage jumps) in the current-voltage characteristics. Moreover, the power of ac oscillations away from the breather center (the breather tail) displays singularities as the externally applied dc bias decreases. All these features can be mapped to the spectrum of EEs that has been derived analytically and numerically. Using an improved analysis of the breather tail, a spectroscopy of the EEs is developed. The nature of breather instability driven by localized EEs is established.

cond-mat.supr-con↗

arXiv2000

Rectification of current in ac-driven nonlinear systems and symmetry properties of the Boltzmann equation

We study rectification of a current of particles moving in a spatially periodic potential under the influence of time-periodic forces with zero mean value. If certain time-space symmetries are broken a non-zero directed current of particles is possible. We investigate this phenomenon in the framework of the kinetic Boltzmann equation. We find that the attractor of the Boltzmann equation completely reflects the symmetries of the original one-particle equation of motion. Especially, we analyse the limits of weak and strong relaxation. The dc current increases by several orders of magnitude with decreasing dissipation.

nlin.CD↗

arXiv2000

Discrete breathers in classical spin lattices

Discrete breathers (nonlinear localised modes) have been shown to exist in various nonlinear Hamiltonian lattice systems. In the present paper we study the dynamics of classical spins interacting via Heisenberg exchange on spatial $d$-dimensional lattices (with and without the presence of single-ion anisotropy). We show that discrete breathers exist for cases when the continuum theory does not allow for their presence (easy-axis ferromagnets with anisotropic exchange and easy-plane ferromagnets). We prove the existence of localised excitations using the implicit function theorem and obtain necessary conditions for their existence. The most interesting case is the easy-plane one which yields excitations with locally tilted magnetisation. There is no continuum analogue for such a solution and there exists an energy threshold for it, which we have estimated analytically. We support our analytical results with numerical high-precision computations, including also a stability analysis for the excitations.

cond-mat↗

arXiv2000

Directed current due to broken time-space symmetry

We consider the classical dynamics of a particle in a one-dimensional space-periodic potential U(X) = U(X+2π) under the influence of a time-periodic space-homogeneous external field E(t)=E(t+T). If E(t) is neither symmetric function of t nor antisymmetric under time shifts $E(t \pm T/2) \neq -E(t)$, an ensemble of trajectories with zero current at t=0 yields a nonzero finite current as $t\to \infty$. We explain this effect using symmetry considerations and perturbation theory. Finally we add dissipation (friction) and demonstrate that the resulting set of attractors keeps the broken symmetry property in the basins of attraction and leads to directed currents as well.

chao-dyn↗

arXiv1999

Observation of breathers in Josephson ladders

We report on the observation of spatially-localized excitations in a ladder of small Josephson junctions. The excitations are whirling states which persist under a spatially-homogeneous force due to the bias current. These states of the ladder are visualized using a low temperature scanning laser microscopy. We also compute breather solutions with high accuracy in corresponding model equations. The stability analysis of these solutions is used to interpret the measured patterns in the I-V characteristics.

cond-mat↗