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D. Matrasulov

Publications and source records attributed to D. Matrasulov.

At least 19 recordsLinked to original sources
arXiv2025

Optical high harmonic generation in Dirac materials

We study high-order harmonic generation by optically driven one- and two-dimensional hydrogenlike atoms formed by Coulomb imurities in graphene. The time-dependent Dirac equations with Coulomb plus time-periodic monochromatic field potentials are solved for both cases. Such characteristics of the optical high harmonic generation, as average dipole moment and high harmonic generation spectra, are computed. A sketch for table-top experimental realization of the considered models is proposed.

cond-mat.mes-hall↗
arXiv2024

Discrete Schrodinger equation on graphs: An effective model for branched quantum lattice

We propose an approach to quantize discrete networks (graphs with discrete edges). We introduce a new exact solution of discrete Schrodinger equation that is used to write the solution for quantum graphs. Formulation of the problem and derivation of secular equation for arbitrary quantum graphs is presented. Application of the approach for the star graph is demonstrated by obtaining eigenfunctions and eigenvalues explicitely. Practical application of the model in conducting polymers and branched molecular chains is discussed.

quant-ph↗
arXiv2024

PT-symmetric dynamical confinement: Fermi acceleration, quantum force and Berry phase

We consider a quantum particle under the dynamical confinement caused by PT-symmetric box with a moving wall. The latter is described in terms of the time-dependent Schr\"{o}dinger equation obeying the time-dependent PT-symmetric boundary conditions. The class of the functions, describing time-dependence of the wall's position and keeping the system as PT-symmetric is found. Physically observable characteristics, such as average kinetic energy and the average quantum force are calculated as a function of time. Also, geometric phase is calculated for the harmonically oscillating wall regime. Experimental realization of the proposed model is discussed.

quant-ph↗
arXiv2024

Dirac particle under dynamical confinement: Fermi acceleration, trembling motion and quantum force

Quantum dynamics of a Dirac particle in a 1D box with moving wall is studied. Dirac equation with time-dependent boundary condition is mapped onto that with static one, but with time-dependent mass. Exact analytical solution of such modified Dirac equation is obtained for massless particle. For massive particle the problem is solved numerically. Time-dependences of the main characteristics of the dynamical confinement, such as average kinetic energy and quantum force are analyzed. It is found that the average kinetic energy remains bounded for the interval length bounded from below, in particular for the periodically oscillating wall.

quant-ph↗
arXiv2023

Quantum particle under dynamical confinement: From quantum Fermi acceleration to high harmonic generation

Quantum dynamics of a particle confined in a box with time-dependent wall is revisited by considering some unexplored aspects of the problem. In particular, the case of dynamical confinement in a time-dependent box in the presence of purely time-varying external potential is treated by obtaining exact solution. Also, some external potentials approving separation of space and time variables in the Schrodinger equation with time-dependent boundary conditions are classified. Time-dependence of the average kinetic energy and average quantum force are analyzed. A model for optical high harmonic generation in the presence of dynamical confinement and external linearly polarized monochromatic field is proposed.

quant-ph↗
arXiv2021

Nonlocal Nonlinear Schrodinger Equation on Metric Graphs

We consider PT-symmetric, nonlocal nonlinear Schrodinger equation on metric graphs. Vertex boundary conditions are derived from the conservation laws. Soliton solutions are obtained for simplest graph topologies, such as star and tree graphs. Integrability of the problem is shown by proving existence of infinite number of conservation laws.

nlin.SI↗
arXiv2019

Branched Josephson junctions: Current carrying solitons in external magnetic fields

We consider branched Josephson junction created by planar superconductors connected to each other through the Y-junction insulator. Assuming that the structure interacts with the external constant magnetic field, we study static sine-Gordon solitons in such system by modeling them in terms of the stationary sine-Gordon equation on metric graph. Exact analytical solutions of the problem are obtained and their stability is analyzed.

cond-mat.mes-hall↗
arXiv2019

High harmonic generation under dynamical confinement: An atom-in-box model

We consider optical high harmonic generation in a hydrogen atom confined in a breathing spherical box by considering atomic nucleus as fixed at the center of sphere. In such spherically symmetric, dynamical trap, the high harmonic generation spectrum is calculated at different values of the oscillation amplitude, confinement size and atomic nucleus charge.

quant-ph↗
arXiv2018

Quantum dynamics of a hydrogen-like atom in a time-dependent box: non-adiabatic regime

We consider a hydrogen atom confined in time-dependent trap created by a spherical impenetrable box with time-dependent radius. For such model we study the behavior of atomic electron under the (non-adiabatic) dynamical confinement caused by the rapidly moving wall of the box. The expectation values of the total and kinetic energy, average force, pressure and coordinate are analyzed as a function of time for linearly expanding, contracting and harmonically breathing boxes. It is shown that linearly extending box leads to de-excitation of the atom, while the rapidly contracting box causes the creation of very high pressure on the atom and transition of the atomic electron into the unbound state. In harmonically breathing box diffusive excitation of atomic electron may occur in analogy with that for atom in a microwave field.

physics.atom-ph↗
arXiv2018

Charged solitons in branched conducting polymers

We consider dynamics of charged solitons in branched conducting polymers. An effective model based on the sine-Gordon equation on metric graphs is used for computing the charge transport and scattering of charge carriers at the polymer branching points. Condition for the ballistic charge carrier transport is revealed.

nlin.PS↗
arXiv2018

Thermal diffusion in branched structures: Metric graph based approach

We consider the problem of heat diffusion in branched systems and networks on the basis of a model described in terms of heat equation on metric graphs. Using the explicit analytical solutions of the latter, evolution of the temperature profile and heat flow on each branch are computed. Extension of the study for nonlinear regime is considered using a nonlinear heat equation on metric graphs. It is found that in nonlinear regime is more intensive than that in linear case.

physics.class-ph↗
arXiv2017

Nonlinear standing waves on planar branched systems: Shrinking into metric graph

We treat the stationary nonlinear Schroodinger equation on two-dimensional branched domains, so-called fat graphs. The shrinking limit when the domain becomes one-dimensional metric graph is studied by using analytical estimate of the convergence of fat graph boundary conditions into those for metric graph. Detailed analysis of such convergence on the basis of numerical solution of stationary nonlinear Schrodinger equation on a fat graph is provided. Possibility for reproducing different metric graph boundary conditions studied in earlier works is shown. Practical applications of the proposed model for such problems as Bose-Einstein condensation in networks, branched optical media, DNA, conducting polymers and wave dynamics in branched capillary networks are discussed.

nlin.PS↗
arXiv2016

The stationary sine-Gordon equation on metric graphs: Exact analytical solutions for simple topologies

We consider the stationary sine-Gordon equation on metric graphs with simple topologies. The vertex boundary conditions are provided by flux conservation and matching of derivatives at the star graph vertex. Exact analytical solutions are obtained. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.

nlin.SI↗
arXiv2014

Scattering theory and ground-state energy of Dirac fermions in graphene with two Coulomb impurities

We study the physics of Dirac fermions in a gapped graphene monolayer containing two Coulomb impurities. For the case of equal impurity charges, we discuss the ground-state energy using the linear combination of atomic orbitals (LCAO) approach. For opposite charges of the Coulomb centers, an electric dipole potential results at large distances. We provide a nonperturbative analysis of the corresponding low-energy scattering problem.

cond-mat.mes-hall↗
arXiv2014

Electric dipole induced universality for Dirac fermions in graphene

We study electric dipole effects for massive Dirac fermions in graphene and related materials. The dipole potential accomodates towers of infinitely many bound states exhibiting a universal Efimov-like scaling hierarchy. The dipole moment determines the number of towers, but there is always at least one tower. The corresponding eigenstates show a characteristic angular asymmetry, observable in tunnel spectroscopy. However, charge transport properties inferred from scattering states are highly isotropic.

cond-mat.mes-hall↗
arXiv2009

Soliton solutions of nonlinear Schroedinger equation on simple networks

We show soliton solutions of nonlinear Schroedinger equation on simple networks consisting of vertices and bonds, where the strength of cubic nonlinearity is different from bond to bond. We concentrate on reflectionless propagation of Zakharov-Shabat's solitons through a branched chain, namely, a primary star graph consisting of three semi-infinite bonds connected at a vertex. The conservation of the norm and the global current elucidates: (1) the solution on each bond is a part of the universal soliton solution on a simple 1-dimensional (1-d) chain but multiplied by the inverse of square root of bond-dependent nonlinearity; (2) nonlinearities at individual bonds around each vertex must satisfy a sum rule. Under these conditions, all other conservation rules for a simple 1-d chain have proved to hold for multi-soliton solutions on graphs. The argument is extended to other graphs, i.e., general star graphs, tree graphs, loop graphs and their combinations. Numerical evidence is also given on the reflectionless propagation of a soliton through a branched chain.

cond-mat.mes-hall↗
arXiv2009

Quantum Transport in Ladder-Type Networks: Role of nonlinearity, topology and spin

We investigate quantum transport of electrons, phase solitons, etc. through mesoscopic networks of zero-dimensional quantum dots. Straight and circular ladders are chosen as networks with each coupled with three semi-infinite leads (with one incoming and the other two outgoing). Two transmission probabilities (TPs) as a function of the incident energy $ε$ show a transition from anti-phase aperiodic to degenerate periodic spectra at the critical energy $ε_c$ which is determined by a bifurcation point of the bulk energy dispersions. TPs of the circular ladder depend only on the parity of the winding number. Introduction of a single missing bond (MB) or missing step doubles the period of the periodic spectra at $ε>ε_c$ . Shift of the MB by lattice constant results in a striking switching effect at $ε<ε_c$. In the presence of the electric-field induced spin-orbit interaction (SOI), an obvious spin filtering occurs against the spin-unpolarized injection. Against the spin-polarized injection, on the other hand, the spin transport shows spin-flip (magnetization reversal) oscillations with respect to SOI. We also show a role of soliton in the context of its transport through the ladder networks.

cond-mat.mes-hall↗