Wave Decoherence for the Random Schroedinger Equation with Long-Range Correlations

TL;DR

This paper investigates how wave coherence deteriorates over time in a Schrödinger equation with a slowly decaying random potential, revealing anomalous decoherence effects at various scales.

Contribution

It introduces a novel analysis of wave decoherence using a rescaled Wigner transform for Schrödinger equations with long-range correlated randomness.

Findings

Identification of anomalous decoherence effects at multiple scales

Use of rescaled Wigner transform to analyze decoherence

Insights into wave behavior under long-range correlations

Abstract

In this paper, we study the decoherence of a wave described by the solution to a Schroedinger equation with a time-dependent random potential. The random potential is assumed to have slowly decaying correlations. The main tool to analyze the decoherence behaviors is a properly rescaled Wigner transform of the solution of the random Schroedinger equation. We exhibit anomalous wave decoherence effects at different propagation scales.