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Dynamical transition on the periodic Lorentz gas: Stochastic and deterministic approaches
Rafael Mateus Feliczaki1, Eduardo Vicentini1, Pedro Pablo González-Borrero1
1Departamento de Física, Universidade Estadual do Centro-Oeste, Simeão Camargo Varela de Sá 3, 85040-080 Guarapuava PR, Brazil.
Physical Review. E
|January 20, 2018
Summary
This study examines how the periodic Lorentz gas
Area of Science:
- Physics
- Statistical Mechanics
- Dynamical Systems
Background:
- The periodic Lorentz gas is a model system for studying transport properties in disordered media.
- Understanding the relationship between geometric structure and dynamical properties is crucial for various physical phenomena.
Purpose of the Study:
- To investigate the impact of geometric transitions in periodic Lorentz gases on dynamical properties.
- To analyze the autocorrelation function and diffusion coefficient in systems with varying horizon properties.
Main Methods:
- Numerical simulations using a double square lattice to isolate and study different corridor types.
- Comparison of simulation results with a stochastic model based on escape-rate formalism.
Main Results:
- The study reveals the sensitivity of the diffusion coefficient to geometric changes.
- Identified the significant role of open corridors in driving dynamical transitions.
Conclusions:
- Geometric transitions in periodic Lorentz gases profoundly influence transport properties.
- The escape-rate formalism provides a valuable framework for understanding these dynamical transitions.
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