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

2017/03/22 by Almog, Yaniv, Grebenkov, Denis, Helffer, Bernard · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1703.07733

Abstract

We consider the operator \mathcal A_h=-Δ+iV in the semi-classical h→ 0, 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.

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• Generalized boundary triples for adjoint pairs with applications to non-self-adjoint Schrödinger operators

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