arXiv subjects

D. U. Matrasulov

Publications and source records attributed to D. U. Matrasulov.

At least 19 recordsLinked to original sources

arXiv2026

One-dimensional relativistic hydrogen-like atom in Dirac materials: Energy spectra and supercritical states

We consider a model of 1D relativistic hydrogen-like atom, formed by a Coulomb impurity in graphene nanoribbon. Describing the electron motion in terms of the one-dimensional Dirac equation for Coulomb potential taking into account the finite-size of the atomic nucleus, we compute the eigenvalues and eigenfunctions of the atomic electron. The cases of unconfined atom and atomin-box system are considered. Special focus is given calculation of supercritical energy levels and the critical charge. The latter is the value of the atomic nucleus charge, when the electronic state reaches the border of the Dirac sea. It is found that for confined atom the value of the critical charge is larger than that of free atom. Experimentally measurable characteristics, local density of states is also plotted for both cases. Existence of strong localization for atom-in-box system is shown.

cond-mat.mes-hall↗

arXiv2025

Burgers equation on networks: Metric graph based approach

Weconsider Burgers equation on metric graphs for simplest topologies such as star, loops, and tree graphs. Exact traveling wave solutions are obtained for the vertex boundary conditions providing mass conservation and continuity of the solution at the nodes. Constraints for the nonlinearity coefficients ensuring integrability of the Burgers equation are derived. Numerical treatment of the soliton dynamics and their transmission through the graph vertex is presented.

nlin.SI↗

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↗

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

Soliton generation in optical fiber networks

We consider the problem of soliton generation in branched optical fibers. A model based on the nonlinear Schrodinger equation on metric graphs is proposed. Number of generated solitons is computed for different branching topologies considering different initial pulse profiles. Experimental realization of the model is discussed.

nlin.PS↗

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

Interference effects in the reradiation of ultrashort electromagnetic pulses

Reradiation of a spatially non-uniform ultrashort electromagnetic pulse interacting with the linear chain of multielectron atoms is studied in the framework of sudden perturbation approximation. Angular distributions of the reradiation spectrum for arbitrary number of atoms are obtained. It is shown that interference effects for the photon radiation amplitudes lead to appearing of "diffraction" maximums. The obtained results can be extended to the case of two- and three-dimensional crystal lattices and atomic chains. The approach developed allows also to take into account thermal vibrations of the lattice atoms.

physics.atom-ph↗

arXiv2018

Dynamics of Dirac solitons in networks

We study dynamics of Dirac solitons in prototypical networks modeling them by the nonlinear Dirac equation on metric graphs. Soliton solutions of the nonlinear Dirac equation on simple metric graphs are obtained. It is shown that these solutions provide reflectionless vertex transmission of the Dirac solitons under suitable conditions. The constraints for bond nonlinearity coefficients, allowing reflectionless transmission over a Y-junction are derived. The analytical results are confirmed by direct numerical simulations.

nlin.PS↗