HISTORY OF MATHEMATICS AND APPLICATIONS

Phases of semiclassical solutions of the two-dimensional massless Dirac equation with a constant electromagnetic field

D. Zh. Akpan^ab, I. A. Bogaevskii^cd, N. R. Ziatdinov^b, A. A. Oshemkov<sup>b

a</sup> Institute of Mathematics and Mathematical Modeling (Almaty, Kazakhstan)
^b Lomonosov Moscow State University (Moscow)
^c Scientific Research Institute of System Analysis (Moscow)
^d Guangdong Technion-Israel Institute of Technology (Guangdong, China)

Abstract: The phase graphs of semiclassical asymptotics of solutions to the two-dimensional massless Dirac equation with a localized initial condition in a constant (independent of position and time) electromagnetic field have been studied. The considered equation describes the propagation of quasiparticles (electrons and holes) in graphene, with the electric component of the field parallel to the graphene plane and the magnetic component perpendicular to it. Formulas for the phases have been obtained for all values of the electromagnetic field components.

Keywords: massless Dirac equation, semiclassical asymptotics, graphene, quasiparticles, Legendrian submanifolds.

UDC: 517.955.8

Received: 15.02.2025
Accepted: 17.10.2025

DOI: 10.22405/2226-8383-2025-26-4-474-485