Spectral semi-classical analysis of a complex Schrödinger operator in exterior domains

Abstract

Generalizing previous results obtained for the spectrum of the Dirichlet and Neumann realizations in a bounded domain of a Schrödinger operator with a purely imaginary potential $h^2\Delta +iV$ in the semiclassical limit $h\to 0$ 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.

References in corpus (4)

• Diffusion MRI/NMR at high gradients: challenges and perspectives
• On spectral properties of the Bloch-Torrey operator in two dimensions
• The complex Airy operator with a semi-permeable barrier
• On the semi-classical analysis of Schrödinger operators with purely imaginary electric potentials in a bounded domain

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• Spectral properties of the Bloch-Torrey operator in three dimensions