Vol. 2, No. 4, 2020

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Resonances and viscosity limit for the Wigner–von Neumann-type Hamiltonian

Kentaro Kameoka and Shu Nakamura

Vol. 2 (2020), No. 4, 861–873
Abstract

The resonances for the Wigner–von Neumann-type Hamiltonian are defined by the periodic complex distortion in the Fourier space. Also, following Zworski, we characterize resonances as the limit points of discrete eigenvalues of the Hamiltonian with a quadratic complex-absorbing potential in the viscosity-type limit.

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Keywords
quantum resonances, Wigner–von Neumann potential, semiclassical analysis, viscosity limit
Mathematical Subject Classification
Primary: 35J10
Secondary: 35P25
Milestones
Received: 25 March 2020
Revised: 3 September 2020
Accepted: 3 November 2020
Published: 25 February 2021
Authors
Kentaro Kameoka
Graduate School of Mathematical Sciences
University of Tokyo
Tokyo
Japan
Shu Nakamura
Department of Mathematics
Faculty of Sciences
Gakushuin University
Tokyo
Japan