Rogue waves in quantum lattices with correlated disorder

TL;DR

This paper explores how correlated disorder in quantum lattices can lead to rogue wave phenomena, highlighting the interplay between localization and mobility, and demonstrating the impact of disorder correlation length on extreme wave amplitudes.

Contribution

It reveals the role of correlated disorder in inducing rogue waves in quantum lattices, a novel insight into disorder's influence on wavefunction extremes.

Findings

Correlated disorder enhances rogue wave occurrence in quantum lattices.

Disorder correlation length critically affects wave amplitude extremes.

Findings applicable to a broad class of one-dimensional systems.

Abstract

We investigate the outbreak of anomalous quantum wavefunction amplitudes in a one-dimensional tight-binding lattice featuring correlated diagonal disorder. Such rogue-wave-like behavior is fostered by a competition between localization and mobility. The effective correlation length of the disorder is ultimately responsible for bringing the local disorder strength to a minimum, fuelling the occurrence of extreme events of much higher amplitudes, specially when compared to the case of uncorrelated disorder. Our findings are valid for a class of discrete one-dimensional systems and reveal profound aspects of the role of randomness in rogue-wave generation.