3 papers
math-ph2026
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…
quant-ph2024
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…
cond-mat.mes-hall2024
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…