Distribution of scattering resonances for generic Schrodinger operators

2017/09/19 by Dinh, Tien-Cuong, Nguyen, Viet-Anh
#35P25 #47A40 #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1709.06375

Abstract

Let -Delta+V be the Schrodinger operator acting on L²(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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