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Diffusion in a rough potential.

¹University of Maryland, College Park, MD 20742.

Proceedings of the National Academy of Sciences of the United States of America

|April 1, 1988

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This study analyzes diffusion in rough 1D potentials using mean first passage time. Results show the effective diffusion coefficient can significantly decrease at low temperatures.

Area of Science:

Physics
Physical Chemistry
Statistical Mechanics

Background:

Diffusion is a fundamental physical process crucial for understanding transport phenomena.
Spatially varying potentials introduce complexities in diffusion dynamics.
Mean first passage time is a key metric for analyzing diffusion processes.

Purpose of the Study:

To investigate diffusion in a one-dimensional potential with spatial roughness.
To derive a general expression for the effective diffusion coefficient under these conditions.
To explore the temperature dependence of diffusion.

Main Methods:

Analysis of the mean first passage time.
Theoretical treatment of diffusion in a disordered potential landscape.

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Main Results:

A general expression for the effective diffusion coefficient was derived.
The effective diffusion coefficient was found to be strongly dependent on temperature.
A significant reduction in diffusion was observed at low temperatures.

Conclusions:

The spatial roughness of a one-dimensional potential critically impacts diffusion.
Low temperatures exacerbate the reduction in diffusion, leading to very small effective diffusion coefficients.
This work provides a theoretical framework for understanding anomalous diffusion in disordered systems.