arXiv subjects

Mashrab Akramov

Publications and source records attributed to Mashrab Akramov.

2 recordsLinked to original sources

arXiv2026

Discrete Dirac equation on quantum graphs: A model of a Dirac particle in a branched lattice

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 particular focus on star graphs with three edges as a simple example. Exact solutions for eigenstates and spectra are derived and compared with the continuum case, showing good agreement in tabulated results. This approach offers a systematic framework for analyzing relativistic quantum transport on branched structures relevant to nanostructures and quantum device design.

quant-ph↗

arXiv2024

Transparent PT-symmetric nonlinear networks

We consider reflectionless wave propagation in networks modeled in terms of the nonlocal nonlinear Schrödinger (NNLS) equation on metric graphs, for which transparent boundary conditions are imposed at the vertices. By employing the ``potential approach" previously used for the nonlinear Schrödinger equation, we derive transparent boundary conditions for the NNLS equation on metric graphs. These conditions eliminate backscattering at graph vertices, which is crucial for minimizing losses in signal, heat, and charge transfer in various applications such as optical fibers, optoelectronic networks, and low-dimensional materials.

math-ph↗