Spectral semi-classical analysis of a complex Schr\"odinger operator in exterior domains
Mathematical Physics
2018-05-09 v1 math.MP
Abstract
Generalizing previous results obtained for the spectrum of the Dirichlet and Neumann realizations in a bounded domain of a Schr\"odinger operator with a purely imaginary potential in the semiclassical limit we address the same problem in exterior domains. In particular we obtain the left margin of the spectrum, and the emptiness of the essential part of the spectrum under some additional assumptions.
Keywords
Cite
@article{arxiv.1708.02926,
title = {Spectral semi-classical analysis of a complex Schr\"odinger operator in exterior domains},
author = {Yaniv Almog and Denis Grebenkov and Bernard Helffer},
journal= {arXiv preprint arXiv:1708.02926},
year = {2018}
}