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arXiv · 1709.06375

Distribution of scattering resonances for generic Schrodinger operators

Tien-Cuong Dinh·Viet-Anh Nguyen
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Abstract

Let -Delta+V be the Schrodinger operator acting on L^2(R^d,C) with d odd larger than 2. Here V is a bounded real- or complex-valued function vanishing outside the closed ball of center 0 and radius a. If V belongs to the class of potentials introduced by Christiansen, we show that when r goes to infinity, the resonances of -Delta+V, scaled down by the factor r, are asymptotically distributed, with respect to an explicit probability distribution on the closed lower unit half-disc of the complex plane. The rate of convergence is also considered for subclasses of potentials.

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Tien-Cuong Dinh, Viet-Anh Nguyen. 2017-09-19. Distribution of scattering resonances for generic Schrodinger operators. https://arxiv.org/abs/1709.06375

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