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Subdiffusion in the nonlinear Schrödinger equation with disorder.
1Department of Physics, Technion, Haifa, Israel.
Summary
Disordered nonlinear Schrödinger equation dynamics reveal subdiffusive wave packet spreading. A continuous time random walk model explains this phenomenon, yielding a transport exponent of 2/5 for subdiffusion.
Area of Science:
- Physics
- Nonlinear Dynamics
- Condensed Matter Physics
Background:
- The nonlinear Schrödinger equation (NLSE) models various wave phenomena.
- Disorder introduces complex behavior in wave packet dynamics.
- Understanding wave packet spreading is crucial in many physical systems.
Purpose of the Study:
- To investigate the dynamics of wave packets in a disordered nonlinear Schrödinger equation.
- To explain the observed subdiffusive spreading mechanism.
- To develop a probabilistic framework for subdiffusion.
Main Methods:
- Analysis of the nonlinear Schrödinger equation with disorder.
- Study of initially localized wave packet evolution.
- Application of the continuous time random walk (CTRW) model.
- Derivation of a probabilistic description for subdiffusion.
Main Results:
- Observed subdiffusive spreading of the wave packet.
- Successful explanation of subdiffusion using the CTRW framework.
- Obtained a transport exponent of 2/5 for subdiffusion.
- Provided a probabilistic model for the spreading dynamics.
Conclusions:
- Subdiffusion is a key characteristic of wave packet dynamics in disordered NLSE.
- The CTRW model effectively describes and predicts this subdiffusive behavior.
- The derived transport exponent offers a quantitative measure of the spreading process.
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