Spreading for the generalized nonlinear Schroedinger equation with disorder

TL;DR

This study investigates the short- and long-term dynamics of wavepackets in a generalized nonlinear Schrödinger equation with disorder, revealing subdiffusive behavior and challenging previous assumptions about critical phenomena related to the nonlinearity parameter.

Contribution

It provides the first detailed numerical analysis of wavepacket spreading for arbitrary nonlinearity in disordered systems, including long-time behavior and the absence of criticality as a function of p.

Findings

Wavepacket exhibits subdiffusive spreading with <m_{2}>~t^a.

No evidence of critical behavior as a function of nonlinearity parameter p.

Long-time numerical results support the robustness of subdiffusive dynamics.

Abstract

The dynamics of an initially localized wavepacket is studied for the generalized nonlinear Schroedinger Equation with a random potential, where the nonlinearity term is |\psi|^p*\psi and "p" is arbitrary. Mainly short times for which the numerical calculations can be performed accurately are considered. Long time calculations are presented as well. In particular the subdiffusive behavior where the average second moment of the wavepacket is of the form <m_{2}>~t^a is computed. Contrary to former heuristic arguments, no evidence for any critical behavior as function of "p" is found. The properties of \alpha(t) are explored.