Dirac particles on periodic quantum graphs
Jambul YusupovYeoju Technical Institute in Tashkent, 156 Usman Nasyr Street, 100121 Tashkent, UzbekistanK.K. SabirovTashkent State Technical University named after Islam Karimov, 2 Universitet Street, 100095 Tashkent, UzbekistanD. U. MatrasulovYeoju Technical Institute in Tashkent, 156 Usman Nasyr Street, 100121 Tashkent, Uzbekistan
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We consider the Dirac equation on periodic networks (quantum graphs). The self-adjoint quasiperiodic 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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