34 citations · 234 across the 33 of their papers we have counts for
6 papers · 1 filter
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…