arXiv subjects

M. Akramov

Publications and source records attributed to M. Akramov.

3 recordsLinked to original sources

arXiv2024

Discrete Schrodinger equation on graphs: An effective model for branched quantum lattice

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 solution for quantum graphs. Formulation of the problem and derivation of secular equation for arbitrary quantum graphs is presented. Application of the approach for the star graph is demonstrated by obtaining eigenfunctions and eigenvalues explicitely. Practical application of the model in conducting polymers and branched molecular chains is discussed.

quant-ph↗

arXiv2022

Discrete Nonlocal Nonlinear Schroedinger equation on Metric Graphs: Dynamics of PT-Symmetric Solitons in Discrete Networks

We consider PT-symmetric, discrete nonlocal nonlinear Schrödinger equation on metric graphs. Soliton solutions are obtained for simplest graph topologies, such as star and tree graphs. Integrability of the problem is shown by proving existence of infinite number of conservation laws.

nlin.SI↗

arXiv2021

Nonlocal Nonlinear Schrodinger Equation on Metric Graphs

We consider PT-symmetric, nonlocal nonlinear Schrodinger equation on metric graphs. Vertex boundary conditions are derived from the conservation laws. Soliton solutions are obtained for simplest graph topologies, such as star and tree graphs. Integrability of the problem is shown by proving existence of infinite number of conservation laws.

nlin.SI↗