arXiv subjects

J. R. Yusupov

Publications and source records attributed to J. R. Yusupov.

At least 19 recordsLinked to original sources

arXiv2025

Kink-antikink soliton solutions of the nonlinear Klein-Gordon equation on branched structures

In this paper, we investigate the nonlinear Klein-Gordon equation on a metric star graph with three semi-infinite bonds. At the branching point, we impose a weighted continuity condition and a generalized weighted Kirchhoff condition for the derivatives of the wave function. By employing both analytical methods and numerical techniques, we construct exact and numerical soliton solutions that satisfy the vertex conditions and conserve energy and momentum. The results of analytic calculations are confirmed through numerical experiments, which demonstrate reflectionless propagation of kink-antikink soliton solutions. We compute and analyze the reflection coefficient, study the impact of various nonlinearity parameters, and further extend the formulation to other graph topologies, such as tree and loop graphs.

nlin.PS↗

arXiv2024

Transparent boundary conditions for the stationary Schroedinger equation via Weyl-Titchmarsh theory

We propose a general approach for deriving transparent boundary conditions for the stationary Schroedinger equation with arbitrary potential. It is proven that the transparent boundary conditions can be written in terms of the Weyl-Titchmarsh coefficients. As examples for the application of the proposed approach, two special cases for the stationary Schroedinger equation with the harmonic potential and the Poeschl-Teller potential are considered.

math-ph↗

arXiv2024

Fast forward problem for adiabatic quantum dynamics: Estimation of the energy cost

We consider the problem of energy cost needed for acceleration (deceleration) of the evolution of a quantum system using the Masuda-Nakamura fast forward protocol. In particular, we focus on dynamics by considering models for a quantum box with a moving wall and harmonic oscillator with time-dependent frequency. For both models we computed the energy needed for acceleration (deceleration) as a function of time. The results obtained are compared with those of other acceleration (deceleration) protocols

quant-ph↗

arXiv2024

Fast forward evolution in heat equation:Tunable heat transport in adiabatic regime

We consider the problem of fast forward evolution of the processes described in terms of the heat equation. The matter is considered on an adiabatically expanding time-dependent box. Attention is paid to acceleration of heat transfer processes. So called shortcuts to adiabaticity, implying fast forwarding of the adiabatic states are studied. Heat flux and temperature profiles are analyzed for standard and fast forwarded regimes.

quant-ph↗

arXiv2023

Driven transparent quantum graphs

In this paper, we discuss the concept of quantum graphs with transparent vertices by considering the case where the graph interacts with an external time-independent field. In particular, we address the problem of transparent boundary conditions for quantum graphs, building on previous work on transparent boundary conditions for the stationary Schrodinger equation on a line. Physically relevant constraints making the vertex transparent under boundary conditions in the form of (weight) continuity and Kirchhoff rules are derived using two methods, the scattering approach and transparent boundary conditions for the time-independent Schrodinger equation. The latter is derived by extending the transparent boundary condition concept to the time-independent Schrodinger equation on driven quantum graphs. We also discuss how the eigenvalues and eigenfunctions of a quantum graph are influenced not only by its topology, but also by the shape(type) of a potential when an external field is involved.

quant-ph↗

arXiv2023

Discrete sine-Gordon equation on metric graphs: A simple model for Josephson junction networks

We consider discrete sine-Gordon equation on branched domains. The latter is modeled in terms of the metric graphs with discrete bonds having the form of the branched 1D chains. Exact analytical solutions of the problem are obtained for special case of the constraints given by in terms of simple sum rule. Numerical solution is obtained when the constraint is not fulfilled.

nlin.SI↗

arXiv2022

Transparent boundary conditions for the nonlocal nonlinear Schroedinger equation: A model for reflectionless propagation of PT-symmetric solitons

We consider the problem of reflectionless propagation of PT-symmetric solitons described by the nonlocal nonlinear Schroedinger equation on a line in the framework of the concept of transparent boundary conditions for evolution equations. Transparent boundary conditions for the nonlocal nonlinear Schroedinger equation are derived. The absence of backscattering at the artificial boundaries is confirmed by the numerical implementation of the transparent boundary conditions.

nlin.SI↗

arXiv2022

Manakov system on metric graphs: Modeling the reflectionless propagation of vector solitons in networks

We consider the reflectionless transport of Manakov solitons in networks. The system is modelled in terms of the Manakov system on metric graphs subject to transparent boundary conditions at the branching points. Simple constraints combining the equivalent usual Kirchhoff vertex conditions with the transparent conditions are derived in terms of nonlinearity coefficients. Although the method is used for a metric star graph, an extension to more complicated graph topologies is easily possible.

nlin.SI↗

arXiv2021

Dirac particles on periodic quantum graphs

We consider the Dirac equation on periodic networks (quantum graphs). The self-adjoint quasi periodic boundary conditions are derived. The secular equation allowing us to find the energy spectrum of the Dirac particles on periodic quantum graphs is obtained. Band spectra of the periodic quantum graphs of different topologies are calculated. Universality of the probability to be in the spectrum for certain graph topologies is observed.

quant-ph↗

arXiv2021

Reflectionless propagation of Manakov solitons on a line:A model based on the concept of transparent boundary conditions

We consider the problem of absence of backscattering in the transport of Manakov solitons on a line. The concept of transparent boundary conditions is used for modeling the reflectionless propagation of Manakov vector solitons in a one-dimensional domain. Artificial boundary conditions that ensure the absence of backscattering are derived and their numerical implementation is demonstrated.

nlin.SI↗

arXiv2020

Transparent boundary conditions for the sine-Gordon equation:Modeling the reflectionless propagation of kink solitons on a line

We consider the reflectionless transport of sine-Gordon solitons on a line. Transparent boundary conditions for the sine-Gordon equation on a line are derived using the so-called potential approach. Our numerical implementation of these novel boundary conditions proves the absence of the backscattering in transmission of sine-Gordon solitons through the boundary of the considered finite domains.

nlin.SI↗

arXiv2020

Dirac Particles in Transparent Quantum Graphs: Tunable transport of relativistic quasiparticles in branched structures

We consider the dynamics of relativistic spin-half particles in quantum graphs with transparent branching points. The system is modeled by combining the quantum graph concept with the one of transparent boundary conditions applied to the Dirac equation on metric graphs. Within such an approach, we derive simple constraints, which turn the usual Kirchhoff-type boundary conditions at the vertex equivalent to the transparent ones. Our method is applied to quantum star graph. An extension to more complicated graph topologies is straightforward.

quant-ph↗

arXiv2020

Exciton dynamics in branched conducting polymers: Quantum graphs based approach

We consider dynamics of excitons in branched conducting polymers. An effective model based on the use of quantum graph concept is applied for computing of exciton migration along the branched polymer chain Condition for the regime, when the transmission of exciton through the branching point is reflectionless is revealed.

cond-mat.mes-hall↗

arXiv2019

Transparent nonlinear networks

We consider the reflectionless transport of solitons in networks. The system is modeled in terms of the nonlinear Schrödinger equation on metric graphs, for which transparent boundary conditions at the branching points are imposed. This allows to derive simple constraints, which link equivalent usual Kirchhoff-type vertex conditions to the transparent ones. Our approach is applied to a metric star graph. An extension to more complicated graph topologies is straight forward.

nlin.PS↗

arXiv2019

Networks with point like nonlinearities

We study static nonlinear waves in networks described by a nonlinear Schrodinger equation with point-like nonlinearities on metric graphs. Explicit solutions fulfilling vertex boundary conditions are obtained. Spontaneous symmetry breaking caused by bifurcations is found.

nlin.PS↗

arXiv2018

Transparent Quantum Graphs

We consider quantum graphs with transparent branching points. To design such networks, the concept of transparent boundary conditions is applied to the derivation of the vertex boundary conditions for the linear Schrodinger equation on metric graphs. This allows to derive simple constraints, which use equivalent usual Kirchhoff-type boundary conditions at the vertex to the transparent ones. The approach is applied to quantum star and tree graphs. However, extension to more complicated graph topologies is rather straight forward.

quant-ph↗

arXiv2018

PT-symmetric quantum graphs

We consider branched quantum wires, whose connection rules provide PT-symmetry for the Schrodinger equation on graph. For such PT-symmetric quantum graph we derive general boundary conditions which keep the Hamiltonian as PT-symmetric with real eigenvalues and positively defined norm. Explicit boundary conditions which are consistent with the general PT-symmetric boundary conditions are presented. Secular equations for finding the eigenvalues of the quantum graph are derived. Breaking of the Kirchhoff rule at the branching point is shown. Experimental realization of PT-symmetric quantum graphs on branched optical waveguides is discussed.

quant-ph↗

arXiv2018

Classical and quantum dynamics of a kicked relativistic particle in a box

We study classical and quantum dynamics of a kicked relativistic particle confined in a one dimensional box. It is found that in classical case for chaotic motion the average kinetic energy grows in time, while for mixed regime the growth is suppressed. However, in case of regular motion energy fluctuates around certain value. Quantum dynamics is treated by solving the time-dependent Dirac equation for delta-kicking potential, whose exact solution is obtained for single kicking period. In quantum case, depending on the values of the kicking parameters the average kinetic energy can be quasi periodic or, fluctuating around some value. Particle transport is studied by considering spatio-temporal evolution of the Gaussian wave packet and by analyzing trembling motion.

quant-ph↗