34 citations · 234 across the 33 of their papers we have counts for
33 papers
Discrete Dirac equation on quantum graphs: A model of a Dirac particle in a branched lattice
Mashrab Akramov, Carsten Trunk, Davron Matrasulov
We study the one-dimensional time-independent discrete Dirac equation on graphs with discrete edges. Both continuous and discrete formulations of the graphs are considered, with pa…
Transparent boundary conditions for the spatially discrete Schrödinger equation: Reflectionless quantum transport in 1D lattices
Mashrab E. Akramov, Jambul R. Yusupov, Matthias Ehrhardt +1
We construct exact transparent boundary conditions (TBCs) for a time-continuous, spatially discrete Schrödinger equation that models a one-dimensional quantum lattice. Using a rece…
Discrete Schrodinger equation on graphs: An effective model for branched quantum lattice
M. Akramov, C. Trunk, J. Yusupov +1
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 solu…
Coulomb impurities in graphene driven by fast ions
Saparboy Rakhmanov, Reinhold Egger, Doniyor Jumanazarov +1
We provide a theoretical model for electronic transitions in a two-dimensional (2D) artificial atom in a graphene monolayer. The artificial atom is due to the presence of a charged…
Transparent boundary conditions for the stationary Schroedinger equation via Weyl-Titchmarsh theory
V. A. Derkach, C. Trunk, J. R. Yusupov +1
We propose a general approach for deriving transparent boundary conditions for the stationary Schroedinger equation with arbitrary potential. It is proven that the transparent boun…
Transparent PT-symmetric nonlinear networks
Mashrab Akramov, Jambul Yusupov, Matthias Ehrhardt +2
We consider reflectionless wave propagation in networks modeled in terms of the nonlocal nonlinear Schrödinger (NNLS) equation on metric graphs, for which transparent boundary cond…
PT-symmetric dynamical confinement: Fermi acceleration, quantum force and Berry phase
S. Rakhmanov, C. Trunk, M. Znojil +1
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 Schrödinger equ…
Dirac particle under dynamical confinement: Fermi acceleration, trembling motion and quantum force
J. Dittrich, S. Rakhmanov, D. Matrasulov
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 ti…
Coulomb impurities in graphene driven by ultrashort electromagnetic pulses: Excitation, ionization, and pair creation
Saparboy Rakhmanov, Reinhold Egger, Davron Matrasulov
We provide a theory for electronic transitions induced by ultrashort electromagnetic pulses in two-dimensional artificial relativistic atoms which are created by a charged impurity…
Quantum particle under dynamical confinement: From quantum Fermi acceleration to high harmonic generation
S. Rakhmanov, C. Trunk, D. Matrasulov
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 c…
Discrete sine-Gordon equation on metric graphs: A simple model for Josephson junction networks
M. E. Akramov, J. R. Yusupov, I. N. Askerzade +1
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. Ex…
Transparent boundary conditions for the nonlocal nonlinear Schroedinger equation: A model for reflectionless propagation of PT-symmetric solitons
M. E. Akramov, J. R. Yusupov, M. Ehrhardt +2
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 o…
Manakov system on metric graphs: Modeling the reflectionless propagation of vector solitons in networks
J. R. Yusupov, Kh. Sh. Matyokubov, M. Ehrhardt +1
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 con…
Reflectionless propagation of Manakov solitons on a line:A model based on the concept of transparent boundary conditions
K. K. Sabirov, J. R. Yusupov, M. M. Aripov +2
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 reflect…
Transparent boundary conditions for the sine-Gordon equation:Modeling the reflectionless propagation of kink solitons on a line
K. K. Sabirov, J. R. Yusupov, M. Ehrhardt +1
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 p…
Dirac particles on periodic quantum graphs
J. R. Yusupov, K. K. Sabirov, D. U. Matrasulov
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…
Exciton dynamics in branched conducting polymers: Quantum graphs based approach
J. R. Yusupov, Kh. Matyakubov, K. K. Sabirov +1
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 t…
Charged solitons in branched conducting polymers
D. Babajanov, H. Matyoqubov, D. Matrasulov
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 tra…
Quantum dynamics of PT-symmetrically kicked particle confined in a 1D box
J. Yusupov, S. Rakhmanov, D. U. Matrasulov +1
We study quantum particle dynamics in a box and driven by PT-symmetric, delta-kicking complex potential. Such dynamical characteristics as the average kinetic energy as function of…
PT-symmetric quantum graphs
D. U. Matrasulov, K. K. Sabirov, J. R. Yusupov
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…
Bogoliubov de Gennes equation on metric graphs
K. K. Sabirov, D. Jumanazarov, J. Yusupov +1
We consider Bogoliubov de Gennes equation on metric graphs. The vertex boundary conditions providing self-adjoint realization of the Bogoliubov de Gennes operator on a metric star…
Classical and quantum dynamics of a kicked relativistic particle in a box
J. R. Yusupov, D. M. Otajanov, V. E. Eshniyazov +1
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 kinet…
Nonlinear standing waves on planar branched systems: Shrinking into metric graph
Z. Sobirov, D. Babajanov, D. Matrasulov
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 metri…
Quantum dynamics of a hydrogen-like atom in a time-dependent box: non-adiabatic regime
S. Rakhmanov, D. Matrasulov, V. I. Matveev
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 elect…