Spreading of wave packets in disordered systems with tunable nonlinearity

TL;DR

This paper investigates how wave packets spread in disordered one-dimensional Klein-Gordon chains with tunable nonlinearity, revealing subdiffusive behavior and the destruction of Anderson localization depending on the nonlinearity strength.

Contribution

It provides a comprehensive numerical and theoretical analysis of wave packet spreading in disordered nonlinear systems with variable nonlinearity exponent.

Findings

Subdiffusive spreading with growth as t^α observed

Exponent α matches theoretical predictions for σ ≥ 2

Evidence of strong chaos regime and localization destruction for small σ

Abstract

We study the spreading of single-site excitations in one-dimensional disordered Klein-Gordon chains with tunable nonlinearity $|u_{l}|^{\sigma} u_{l}$ for different values of $\sigma$. We perform extensive numerical simulations where wave packets are evolved a) without and, b) with dephasing in normal mode space. Subdiffusive spreading is observed with the second moment of wave packets growing as $t^{\alpha}$. The dependence of the numerically computed exponent $\alpha$ on $\sigma$ is in very good agreement with our theoretical predictions both for the evolution of the wave packet with and without dephasing (for $\sigma \geq 2$ in the latter case). We discuss evidence of the existence of a regime of strong chaos, and observe destruction of Anderson localization in the packet tails for small values of $\sigma$.