Subdiffusion in the Nonlinear Schroedinger Equation with Disorder

TL;DR

This paper investigates how wave packets spread slowly over time in a disordered nonlinear Schrödinger system, explaining subdiffusion through a probabilistic model and deriving a specific transport exponent.

Contribution

It introduces a probabilistic framework for understanding subdiffusive spreading in the nonlinear Schrödinger equation with disorder and calculates the transport exponent as 2/5.

Findings

Wave packet exhibits subdiffusive spreading with exponent 2/5

Probabilistic model explains subdiffusion dynamics

Provides a new theoretical approach to disordered nonlinear systems

Abstract

The nonlinear Schroedinger equation in the presence of disorder is considered. The dynamics of an initially localized wave packet is studied. A subdiffusive spreading of the wave packet is explained in the framework of a continuous time random walk. A probabilistic description of subdiffusion is suggested and a transport exponent of subdiffusion is obtained to be 2/5.