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Updated: Jun 14, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Subdiffusion in the nonlinear Schrödinger equation with disorder.

Alexander Iomin¹

¹Department of Physics, Technion, Haifa, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 7, 2010

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.

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Last Updated: Jun 14, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

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Published on: September 26, 2016

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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.