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Aspects of diffusion in the stadium billiard.
1CAMTP - Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia, European Union.
Physical Review. E
|February 17, 2018
Summary
Diffusion in the Bunimovich stadium is normal for all epsilon values and initial conditions. The diffusion constant follows a parabolic function of momentum, indicating inhomogeneous diffusion, and is well-modeled including boundary effects.
Area of Science:
- Physics
- Statistical Mechanics
- Quantum Chaos
Background:
- The Bunimovich stadium is a classic model in dynamical systems and quantum chaos.
- Understanding diffusion properties is crucial for characterizing particle transport in such systems.
Purpose of the Study:
- To conduct a detailed numerical study of diffusion in the Bunimovich stadium for various epsilon values.
- To develop an empirical model for local and global diffusion.
- To determine the classical transport time, a key parameter in quantum chaos.
Main Methods:
- Detailed numerical simulations of diffusion.
- Development and validation of an empirical diffusion model.
- Analysis of diffusion constant dependence on momentum and boundary effects.
Main Results:
- Normal diffusion observed for all epsilon values (<=0.3) and initial conditions.
- Diffusion constant exhibits a parabolic dependence on momentum, signifying inhomogeneous diffusion.
- The proposed model accurately describes diffusion, including boundary effects.
- Exponential approach to the asymptotic equilibrium steady state.
- Excellent agreement with the random model (Robnik et al., 1997).
- Consistency between diffusion constants derived from momentum space distribution and second moment.
Conclusions:
- The study provides a robust model for diffusion in the Bunimovich stadium.
- Inhomogeneous diffusion is confirmed, with the diffusion constant being momentum-dependent.
- The classical transport time can be reliably determined from these findings.
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