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• W2553415643 abstract "In this paper, we describe the leftmost eigenvalue of the non-selfadjoint operator $mathcal{A}_h = -h^2Delta+iV(x)$ with Dirichlet boundary conditions on a smooth bounded domain $Omegasubsetmathbb{R}^n,$, as $hrightarrow0,$. $V$ is assumed to be a Morse function without critical point at the boundary of $Omega,$. More precisely, we compare $infResigma(mathcal{A}_h)$ with the minimum of the spectrum's real part for some model operator. In the case where $V$ has no critical point, the spectrum is determined by the boundary points where $nabla V$ is orthogonal, and the model operator involves a $1$-dimensional complex Airy operator in $mathbb{R}^+,$. If $V$ is a Morse function with critical points in $Omega,$, the behavior of the operator near the critical points prevails, and the model operator is a complex harmonic oscillator. This question is related to the decay of associated semigroups. In particular, it allows to recover, in a simplified setting, some stability results by Almog in superconductivity theory." @default.
• W2553415643 created "2016-11-30" @default.
• W2553415643 creator A5083032761 @default.
• W2553415643 date "2014-05-23" @default.
• W2553415643 modified "2023-09-27" @default.
• W2553415643 title "On the semi-classical analysis of Schrödinger operators with purely imaginary electric potentials in a bounded domain" @default.
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