Quasiphotons for the nonstationary 2D Dirac equation

M. V. Perel

Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 49, Tome 483 (2019), pp. 178-188

Résumé

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.

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