Intensity distribution of non-linear scattering states

TL;DR

This paper explores how non-linear interactions, quantum chaos, and wave coherence influence the intensity distribution of scattering states in Bose-Einstein condensates, extending linear wave theories with a semiclassical approach.

Contribution

It introduces a local Gaussian model with a position-dependent variance for non-linear scattering states and proposes a semiclassical method to account for deviations from Gaussianity.

Findings

The intensity distribution is well described by a local Gaussian with position-dependent variance.

A semiclassical approach based on classical paths explains deviations from Gaussian distribution.

Rare events like rogue waves do not significantly impact the statistical results.

Abstract

We investigate the interplay between coherent effects characteristic of the propagation of linear waves, the non-linear effects due to interactions, and the quantum manifestations of classical chaos due to geometrical confinement, as they arise in the context of the transport of Bose-Einstein condensates. We specifically show that, extending standard methods for non-interacting systems, the body of the statistical distribution of intensities for scattering states solving the Gross-Pitaevskii equation is very well described by a local Gaussian ansatz with a position-dependent variance. We propose a semiclassical approach based on interfering classical paths to fix the single parameter describing the universal deviations from a global Gaussian distribution. Being tail effects, rare events like rogue waves characteristic of non-linear field equations do not affect our results.