34 citations · 234 across the 33 of their papers we have counts for
12 papers · 1 filter
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…
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…
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…
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…
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…
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…
Kicked Dirac particle in a box
V. E. Eshniyazov, D. U. Matrasulov, J. R. Yusupov
We study quantum dynamics of a kicked relativistic spin-half particle in a one dimensional box. Time-dependence of the average kinetic energy and evolution of the wave packet are e…
Ideal quantum gas in expanding cavity: nature of non-adiabatic force
K. Nakamura, S. K. Avazbaev, Z. A. Sobirov +2
We consider a quantum gas of non-interacting particles confined in the expanding cavity, and investigate the nature of the non-adiabatic force which is generated from the gas and a…