English

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 h2Δ+iVh^2\Delta+iV in the semiclassical limit h0h\to 0 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}
}