Resonances for large one-dimensional "ergodic" systems

TL;DR

This paper investigates the distribution of quantum resonances in large one-dimensional ergodic systems, analyzing how the spectral properties of the limit operator affect resonance behavior.

Contribution

It provides a detailed analysis of resonance distributions in large ergodic quantum systems, linking spectral theory of the limit operator to resonance behavior.

Findings

Resonance distributions depend on the spectral properties of the limit operator.

Periodic and random potentials influence resonance patterns differently.

As the system size increases, resonance behavior converges to a limit described by the spectral theory.

Abstract

The present paper is devoted to the study of resonances for one-dimensional quantum systems with a potential that is the restriction to some large box of an ergodic potential. For discrete models both on a half-line and on the whole line, we study the distributions of the resonances in the limit when the size of the box where the potential does not vanish goes to infinity. For periodic and random potentials, we analyze how the spectral theory of the limit operator influences the distribution of the resonances.