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

TL;DR

This paper investigates the resonances of a Wigner-von Neumann type Hamiltonian using complex distortion and absorption potential methods, providing a new characterization of resonances in the viscosity limit.

Contribution

It introduces a novel approach to define and analyze resonances via complex distortion and absorption potentials in the viscosity limit for this class of Hamiltonians.

Findings

Resonances are characterized as limit points of eigenvalues with complex absorbing potentials.

The method connects complex distortion techniques with the viscosity limit approach.

Provides a new framework for understanding resonances in quantum Hamiltonians.

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.