Dirac particles on periodic quantum graphs
J.R. Yusupov, K.K. Sabirov, D.U. Matrasulov
TL;DR
This paper investigates the spectral properties of Dirac particles on periodic quantum graphs, deriving boundary conditions, secular equations, and analyzing band spectra across various topologies, revealing universal spectral probability features.
Contribution
It introduces a method to analyze Dirac particles on quantum graphs, deriving boundary conditions and secular equations, and explores spectral universality across different graph topologies.
Findings
Derived self-adjoint quasi-periodic boundary conditions.
Obtained secular equations for energy spectra.
Observed universality in spectral probability for certain topologies.
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.
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