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05:20
Characterization of Thermal Transport in One-dimensional Solid Materials
Published on: January 26, 2014
Anomalous transport in a one-dimensional Lorentz gas model.
1Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, D-48149 Münster, Germany. yeahhart@uni-muenster.de
The Journal of Chemical Physics
|December 3, 2008
Summary
This study derives a kinetic equation for a random kick model using a generalized master equation, revealing a connection to Levy walks and stochastic Lorentz gases. The research analyzes long-time behavior and moment relations for annealed disorder systems.
Area of Science:
- Statistical Physics
- Non-equilibrium Thermodynamics
- Kinetic Theory
Background:
- Generalized master equations provide a framework for describing complex stochastic processes.
- Understanding kinetic equations is crucial for modeling particle dynamics in disordered systems.
Purpose of the Study:
- To derive a kinetic equation for a random kick model using a generalized master equation.
- To explore the connection between this model and Levy walks.
- To analyze a one-dimensional stochastic Lorentz gas with annealed disorder.
Main Methods:
- Employing the generalized master equation framework.
- Deriving a fractional master equation for a specific time evolution kernel.
- Applying the model to a one-dimensional stochastic Lorentz gas.
- Obtaining exact moment relations in Laplace space.
Main Results:
- A kinetic equation for the random kick model was successfully derived.
- A fractional master equation, relatable to Levy walks, was obtained.
- Exact moment relations were derived for the stochastic Lorentz gas.
- The long-time behavior of moments was analyzed.
Conclusions:
- The generalized master equation offers a versatile tool for deriving kinetic equations.
- The derived model provides insights into stochastic processes in disordered media.
- The connection to Levy walks highlights potential applications in anomalous transport phenomena.
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