caa a22 4500 46791088X CHVBK 20180406152849.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s11232-006-0100-y doi (NATIONALLICENCE)springer-10.1007/s11232-006-0100-y Quantized Riemann surfaces and semiclassical spectral series for a non-self-adjoint Schrödinger operator with periodic coefficients [Elektronische Daten] [S. Galtsev, A. Shafarevich] We consider a non-self-adjoint Schrödinger operator describing the motion of a particle in a one-dimensional space with an analytic potential iV (x) that is periodic with a real period T and is purely imaginary on the real axis. We study the spectrum of this operator in the semiclassical limit and show that the points of its spectrum asymptotically belong to the so-called spectral graph. We construct the spectral graph and evaluate the asymptotic form of the spectrum. A Riemann surface of the particle energy-conservation equation can be constructed in the phase space. We show that both the spectral graph and the asymptotic form of the spectrum can be evaluated in terms of integrals of the pdx form (where x ∈31 ℂ/Tℤ and p ∈, ℂ are the particle coordinate and momentum) taken along basis cycles on this Riemann surface. We use the technique of Stokes lines to construct the asymptotic form of the spectrum. Springer Science+Business Media, Inc., 2006 spectrum nationallicence spectral graph nationallicence non-self-adjoint operator nationallicence Schrödinger operator nationallicence Stokes lines nationallicence Galtsev S. Moscow State University, Moscow, Russia aut Shafarevich A. Moscow State University, Moscow, Russia aut Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 148/2(2006-08-01), 1049-1066 0040-5779 148:2<1049 2006 148 11232 https://doi.org/10.1007/s11232-006-0100-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11232-006-0100-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Galtsev S. Moscow State University, Moscow, Russia aut NATIONALLICENCE 700 1- Shafarevich A. Moscow State University, Moscow, Russia aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 148/2(2006-08-01), 1049-1066 0040-5779 148:2<1049 2006 148 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer