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Analytically solvable model of a driven system with quenched dichotomous disorder
S I Denisov1, M Kostur, E S Denisova
1Institut für Physik, Universität Augsburg, Universitätsstrasse 1, D-86135 Augsburg, Germany.
Summary
We studied driven particle dynamics in random potentials. The probability density evolves from a delta-singularity at short times to a Gaussian form at long times.
Area of Science:
- Statistical physics
- Condensed matter physics
- Nonlinear dynamics
Background:
- Understanding particle dynamics in disordered systems is crucial for various fields.
- Random potentials and forces introduce complex behaviors in physical systems.
Purpose of the Study:
- To investigate the time-dependent dynamics of overdamped particles in a 1D random potential.
- To analytically study the probability density function (PDF) evolution over time.
Main Methods:
- Derivation of the path integral representation for the PDF.
- Transformation of the PDF into a Fourier integral for analytical treatment.
- Analysis of the PDF's behavior at short and long time scales.
Main Results:
- The PDF exhibits a delta-singular contribution dominant at short times.
- A regular part of the PDF governs the behavior at large evolution times.
- The PDF shows a slow approach towards a limiting Gaussian form as time tends to infinity.
Conclusions:
- The study provides analytical insights into the finite-time evolution of particle probability density.
- The findings elucidate the transition from short-time to long-time dynamics in disordered systems.
- The research contributes to the understanding of statistical properties of driven systems with quenched disorder.
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