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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 205, Number 3, Pages 349–367
DOI: https://doi.org/10.4213/tmf9958 (Mi tmf9958) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Fundamental solution of the stationary Dirac equation with a linear potential

I. Bogaevskyab

a Lomonosov Moscow State University, Moscow, Russia
b Scientific Research Institute for System Analysis of the Russian Academy of Sciences, Moscow, Russia
Full-text PDF (554 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf9958
Abstract: We explicitly express the fundamental solution of the stationary two-dimensional massless Dirac equation with a constant electric field in terms of Fourier transforms of parabolic cylinder functions. This solution describes the flux of quasiparticles in graphene emitted by a pointlike source of electrons that are partially converted into holes (antiparticles). Using our explicit formula, we calculate its semiclassical asymptotic behavior in the hole region.
Keywords: massless Dirac equation, semiclassical asymptotic behavior, fundamental solution, Green's matrix, parabolic cylinder function, graphene, quasiparticle.
Funding agency Grant number
Russian Foundation for Basic Research 19-51-50005
This research was supported in part by the Russian Foundation for Basic Research and the Japanese Society for the Advancement of Science in the framework of scientific project No. 19-51-50005.
Received: 15.07.2020
Revised: 15.07.2020
English version:
Theoretical and Mathematical Physics, 2020, Volume 205, Issue 3, Pages 1547–1563
DOI: https://doi.org/10.1134/S0040577920120016
Bibliographic databases:
Document Type: Article
PACS: 03.65.Pm
MSC: 35J08, 81Q20
Language: Russian
Citation: I. Bogaevsky, “Fundamental solution of the stationary Dirac equation with a linear potential”, TMF, 205:3 (2020), 349–367; Theoret. and Math. Phys., 205:3 (2020), 1547–1563
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf9958
  • https://doi.org/10.4213/tmf9958
  • https://www.mathnet.ru/eng/tmf/v205/i3/p349
    • This publication is cited in the following 3 articles:
    1. I. A. Bogaevsky, S. Yu. Dobrokhotov, A. A. Tolchennikov, “Arnold Lagrangian singularity in the asymptotics of the solution of a model two-dimensional Helmholtz equation with a localized right-hand side”, Theoret. and Math. Phys., 218:1 (2024), 19–40  mathnet  crossref  crossref  mathscinet  adsnasa
    2. A.I. Allilueva, A.I. Shafarevich, “Quasi-Classical Asymptotics Describing the Electron-Hole Interaction and the Klein Effect for the (2+1)-Dirac Equation in Abruptly Varying Fields”, Russ. J. Math. Phys., 31:3 (2024), 339  crossref
    3. A.I. Allilueva, A.I. Shafarevich, “Semiclassical Asymptotics and Particle-Antiparticle Interactions for the Dirac Equations with Abruptly Varying 4-Potential”, Russ. J. Math. Phys., 31:4 (2024), 577  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Full-text PDF :165
    References:62
    First page:25
     
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