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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 202, Number 2, Pages 264–277
DOI: https://doi.org/10.4213/tmf9836 (Mi tmf9836) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Semiclassical asymptotic behavior of the lower spectral bands of the Schrödinger operator with a trigonal-symmetric periodic potential

A. Yu. Anikinab, M. A. Vavilovab

a Ishlinsky Institute for Problems in Mechanics, RAS, Moscow, Russia
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Oblast, Russia
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DOI: https://doi.org/10.4213/tmf9836
Abstract: We study the semiclassical approximation of the lower bands of the Schrödinger operator with a periodic two-dimensional potential with a trigonal symmetry and consider the cases where the potential has one or two wells in the elementary cell. We obtain the exponentially small asymptotic behavior of the band width and find the dispersion relations. We investigate the form of the Bloch functions. Solving this problem is the first step in studying the more complicated (and more physically interesting) problem of tunnel effects in rotating dimers.
Keywords: periodic Schrödinger operator, semiclassical asymptotic behavior, spectral band, tunnel effect.
Funding agency Grant number
Russian Foundation for Basic Research 18-31-00273
This research is supported by Russian Foundation for Basic Research (Grant No. 18-31-00273).
Received: 23.10.2019
Revised: 23.10.2019
English version:
Theoretical and Mathematical Physics, 2020, Volume 202, Issue 2, Pages 231–242
DOI: https://doi.org/10.1134/S0040577920020063
Bibliographic databases:
Document Type: Article
MSC: 41A60
Language: Russian
Citation: A. Yu. Anikin, M. A. Vavilova, “Semiclassical asymptotic behavior of the lower spectral bands of the Schrödinger operator with a trigonal-symmetric periodic potential”, TMF, 202:2 (2020), 264–277; Theoret. and Math. Phys., 202:2 (2020), 231–242
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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