Geodesic
A~quasiclassical limit of the spectrum of a~Schr\"odinger operator with complex periodic potential
Sbornik. Mathematics, Tome 208 (2017) no. 10, pp. 1535-1556

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SM_2017_208_10_a6,
     author = {D. V. Nekhaev and A. I. Shafarevich},
     title = {A~quasiclassical limit of the spectrum of {a~Schr\"odinger} operator with complex periodic potential},
     journal = {Sbornik. Mathematics},
     pages = {1535--1556},
     publisher = {mathdoc},
     volume = {208},
     number = {10},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2017_208_10_a6/}
}
TY  - JOUR
AU  - D. V. Nekhaev
AU  - A. I. Shafarevich
TI  - A~quasiclassical limit of the spectrum of a~Schr\"odinger operator with complex periodic potential
JO  - Sbornik. Mathematics
PY  - 2017
SP  - 1535
EP  - 1556
VL  - 208
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2017_208_10_a6/
LA  - en
ID  - SM_2017_208_10_a6
ER  - 
%0 Journal Article
%A D. V. Nekhaev
%A A. I. Shafarevich
%T A~quasiclassical limit of the spectrum of a~Schr\"odinger operator with complex periodic potential
%J Sbornik. Mathematics
%D 2017
%P 1535-1556
%V 208
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2017_208_10_a6/
%G en
%F SM_2017_208_10_a6
D. V. Nekhaev; A. I. Shafarevich. A~quasiclassical limit of the spectrum of a~Schr\"odinger operator with complex periodic potential. Sbornik. Mathematics, Tome 208 (2017) no. 10, pp. 1535-1556. http://geodesic.mathdoc.fr/item/SM_2017_208_10_a6/