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Field-dependent collision frequency of the two-dimensional driven random Lorentz gas
C Dellago1, H Beijeren, D Panja
1Department of Chemistry, University of Rochester, Rochester, New York 14627, USA. dellago@chem.rochester.edu
Summary
Collision frequency in a Lorentz gas rises with applied magnetic fields because of long-time correlations. Computer simulations confirm kinetic theory predictions of nonanalytic field dependence in collision rates.
Area of Science:
- Physics
- Statistical Mechanics
- Computational Physics
Background:
- The Lorentz gas model describes non-interacting particles in a fixed background of scatterers.
- Applied fields can introduce complex dynamics and correlations in such systems.
- Kinetic theory predicts specific behaviors for collision rates under external influences.
Purpose of the Study:
- To investigate the effect of applied magnetic fields on collision frequency in a thermostated Lorentz gas.
- To confirm the presence of nonanalytic terms in the field dependence of collision rates.
- To validate predictions from kinetic theory using computational methods.
Main Methods:
- Computer simulations of the field-driven, thermostated Lorentz gas.
- Analysis of collision frequency as a function of applied field magnitude.
- Comparison of simulation results with theoretical predictions from kinetic theory.
Main Results:
- Observed an increase in collision frequency with increasing magnetic field strength.
- Confirmed the presence of nonanalytic terms in the collision rate's field dependence.
- Simulation data showed strong agreement with kinetic theory predictions.
Conclusions:
- Long-time correlations are responsible for the field-dependent increase in collision frequency.
- The study validates the theoretical framework of kinetic theory for the Lorentz gas under external fields.
- Computational simulations are a powerful tool for studying complex physical phenomena.