Dirac particles on periodic quantum graphs
Quantum Physics
2021-08-11 v2 Mesoscale and Nanoscale Physics
Mathematical Physics
math.MP
Abstract
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 energy spectrum of the Dirac particles on periodic quantum graphs is obtained. Band spectra of the periodic quantum graphs of different topologies are calculated. Universality of the probability to be in the spectrum for certain graph topologies is observed.
Cite
@article{arxiv.2011.02278,
title = {Dirac particles on periodic quantum graphs},
author = {J. R. Yusupov and K. K. Sabirov and D. U. Matrasulov},
journal= {arXiv preprint arXiv:2011.02278},
year = {2021}
}