Phases of semiclassical solutions of the two-dimensional massless Dirac equation with a constant electromagnetic field
https://doi.org/10.22405/2226-8383-2025-26-4-475-486
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.
About the Authors
Dinmukhammed Zhuldyzbayuly Akpan
Lomonosov Moscow State University; Institute of Mathematics and Mathematical Modeling
Russian Federation
Russian Federation
Ilya Aleksandrovich Bogaevskii
Guangdong Technion-Israel Institute of Technology; Scientific Research Institute of System Analysis
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
Nail Ravilevich Ziatdinov
Lomonosov Moscow State University
Russian Federation
Russian Federation
Andrey Aleksandrovich Oshemkov
Lomonosov Moscow State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
References
1. Bogaevskii, I. A. 2018, “Sub-Lorentzian structures in R4: left-invariance and conformal normal forms”, Journal of Dynamical and Control Systems, vol. 24, no. 3, pp. 371–389.
2. Bogaevskii, I. A. 2020, “Fronts of control-affine systems in R3”, Journal of Singularities, vol. 21, pp. 15–29.
3. Dobrokhotov, S.Yu., Tolchennikov, A. A. 2019, “Solution of the two-dimensional Dirac equation with a linear potential and a localized initial condition”, Russian Journal of Mathematical Physics, vol. 26, no. 2, pp. 139–151.
4. Arnold, V. I. 1990, Singularities of Caustics and Wave Fronts, Kluwer, Dordrecht.
5. Vershik, A. M., Gershkovich, V.Ya. 1994, “Nonholonomic dynamical systems, geometry of distributions and variational problems”. Translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 16, 5–85 (1987) Dynamical systems. VII. Encycl. Math. Sci., vol. 16, pp. 1–81.
6. Dobrokhotov, S.Yu. , Nazaikinskii, V. E., Shafarevich, A. I. 2021, “Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations”, Russian Mathematical Surveys, vol. 76, no. 5, pp. 745–819.
Review
For citations:
Akpan D.Zh., Bogaevskii I.A., Ziatdinov N.R., Oshemkov A.A. Phases of semiclassical solutions of the two-dimensional massless Dirac equation with a constant electromagnetic field. Chebyshevskii Sbornik. 2025;26(4):475-486. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-4-475-486
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