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Sbornik: Mathematics, 2017, Volume 208, Issue 10, Pages 1535–1556
DOI: https://doi.org/10.1070/SM8773 (Mi sm8773) 		 
This article is cited in 4 scientific papers (total in 4 papers)

A quasiclassical limit of the spectrum of a Schrödinger operator with complex periodic potential

D. V. Nekhaeva, A. I. Shafarevichbacd

a Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
b Lomonosov Moscow State University
c Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow
d National Research Centre "Kurchatov Institute", Moscow
English version PDF (643 kB) Citations (4) Russian version article
References:
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DOI: https://doi.org/10.1070/SM8773
Abstract: The quasiclassical asymptotics of the spectrum of a one-dimensional Schrödinger operator with periodic complex potential that arises in the statistical mechanics of a Coulomb gas are described. The spectrum is shown to concentrate in a neighbourhood of a tree in the complex plane; the vertices of this tree are calculated explicitly, and the position of its edges can be investigated comprehensively. Equations are derived from which the asymptotic eigenvalues are found; these equations are conditions that certain special periods of a holomorphic form on the Riemann surface of constant classical energy are integers.
Bibliography: 25 titles.
Keywords: quasiclassical asymptotics, nonselfadjoint operators, spectral graph, Stokes curves.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00378-а
14-01-00521-а
16-31-00339 мол_а
Ministry of Education and Science of the Russian Federation НШ-7962.2016.1
This research was carried out with the support of the Russian Foundation for Basic Research (grant nos. 16-01-00378-a, 14-01-00521-a and 16-31-00339-мол_а), and in the framework of the Programme of the President of the Russian Federation for State Support of Leading Scientific Schools of the Russian Federation (grant no. НШ-7962.2016.1).
Received: 01.07.2016 and 04.02.2017
Bibliographic databases:
Document Type: Article
UDC: 514.83+517.926
MSC: Primary 34E20, 34L20, 34L40; Secondary 47A10
Language: English
Original paper language: Russian
Citation: D. V. Nekhaev, A. I. Shafarevich, “A quasiclassical limit of the spectrum of a Schrödinger operator with complex periodic potential”, Sb. Math., 208:10 (2017), 1535–1556
Citation in format AMSBIB
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\by D.~V.~Nekhaev, A.~I.~Shafarevich
\paper A~quasiclassical limit of the spectrum of a~Schr\"odinger operator with complex periodic potential
\jour Sb. Math.
\yr 2017
\vol 208
\issue 10
\pages 1535--1556
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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