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On a Schrödinger operator with a purely imaginary potential in the semiclassical limit

Banff International Research Station for Mathematical Innovation and Discovery

We consider the operator ${\mathcal A}_h=-h^2\Delta+iV$ in the semi-classical limit $h\rightarrow0$, where $V$ is a smooth real potential with no critical points. We obtain both the left margin of the spectrum, as well as resolvent estimates on the left side of this margin. We extend here previous results obtained for the Dirichlet realization of ${\mathcal A}_h$ by removing significant limitations that were formerly imposed on $V$. In addition, we apply our techniques to the more general Robin boundary condition and to a transmission problem which is of significant interest in physical applications.

Mathematics; Partial differential equations; Statistical mechanics, structure of matter

video/mp4

Author affiliation: Louisiana State University

2017-10-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63477

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/