# Destruction of Anderson localization in quantum nonlinear Schr\"odinger lattices

## TL;DR

This paper demonstrates that quantum nonlinear interactions can eliminate Anderson localization, causing unlimited, threshold-free wave spreading with subdiffusive dynamics, providing new insights into relaxation processes in disordered quantum systems.

## Contribution

It reveals that four-wave interactions in quantum nonlinear Schrödinger lattices destroy Anderson localization without thresholds, leading to subdiffusive spreading.

## Key findings

- Localization is destroyed by quantum nonlinear interactions.
- Wave spreading follows a subdiffusive law with exponent 1/2.
- The process is threshold-free in the quantum domain.

## Abstract

The four-wave interaction in quantum nonlinear Schr\"odinger lattices with disorder is shown to destroy the Anderson localization of waves, giving rise to unlimited spreading of the nonlinear field to large distances. Moreover, the process is not thresholded in the quantum domain, contrary to its "classical" counterpart, and leads to an accelerated spreading of the subdiffusive type, with the dispersion $\langle(\Delta n)^2\rangle \sim t^{1/2}$ for $t\rightarrow+\infty$. The results, presented here, shed new light on the origin of subdiffusion in systems with a broad distribution of relaxation times.