Rogue waves in discrete-time quantum walks

TL;DR

This paper investigates the emergence of rogue waves in discrete-time quantum walks with random phase modulation, revealing their statistical properties and distribution, which follow the Gumbel extreme value distribution.

Contribution

It introduces a novel analysis of rogue waves in quantum walks, demonstrating their statistical behavior and dependence on randomness, expanding understanding of extreme events in quantum systems.

Findings

Rogue waves exhibit long-tailed statistics in quantum walks.

Their distribution follows the Gumbel extreme value distribution.

The degree of randomness influences rogue wave occurrence.

Abstract

Rogue waves are rapid and unpredictable events of exceptional amplitude reported in various fields, such as oceanography and optics, with much of the interest being targeted towards their physical origins and likelihood of occurrence. Here, we use the all-round framework of discrete-time quantum walks to study the onset of those events due to a random phase modulation, unveiling its long-tailed statistics, distribution profile, and dependence upon the degree of randomness. We find that those rogue waves belong the Gumbel family of extreme value distributions.