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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2019 Volume 483, Pages 178–188 (Mi znsl6852)

Quasiphotons for the nonstationary 2D Dirac equation

M. V. Perel

Saint Petersburg State University

Abstract: The asymptotic expansions are obtained for the solution of the $ (2 + 1) $-dimensional nonstationary Dirac equation describing the wave function of a massive fermion in graphene, placed in an external inhomogeneous electric and magnetic field. The semiclassical asymptotics of the solution of the Cauchy problem for this equation with rapidly oscillating and rapidly decreasing initial data are found. This made it possible to find quasiphotons – asymptotic solutions describing Gaussian wave packets concentrated near a point running along a semiclassical trajectory.

Key words and phrases: Dirac equation, quasiphoton, semiclassical approximation, localized solution, Gaussian wave packets.

UDC: 517

Received: 05.11.2019



© Steklov Math. Inst. of RAS, 2024