# Aspects of diffusion in the stadium billiard.

@article{Lozej2018AspectsOD, title={Aspects of diffusion in the stadium billiard.}, author={{\vC}rt Lozej and Marko Robnik}, journal={Physical review. E}, year={2018}, volume={97 1-1}, pages={ 012206 } }

We perform a detailed numerical study of diffusion in the ɛ stadium of Bunimovich, and propose an empirical model of the local and global diffusion for various values of ɛ with the following conclusions: (i) the diffusion is normal for all values of ɛ (≤0.3) and all initial conditions, (ii) the diffusion constant is a parabolic function of the momentum (i.e., we have inhomogeneous diffusion), (iii) the model describes the diffusion very well including the boundary effects, (iv) the approach to…

## 5 Citations

### Spectral form factors and dynamical localization

- Physics
- 2023

: Quantum dynamical localization occurs when quantum interference stops the diffusion of wave packets in momentum space. The expectation is that dynamical localization will occur when the typical…

### Diffusion phenomena in a mixed phase space.

- PhysicsChaos
- 2020

We show that, in strongly chaotic dynamical systems, the average particle velocity can be calculated analytically by consideration of Brownian dynamics in a phase space, the method of images, and the…

### Structure, size, and statistical properties of chaotic components in a mixed-type Hamiltonian system.

- PhysicsPhysical review. E
- 2018

A detailed study of the chaotic component in mixed-type Hamiltonian systems on the example of a family of billiards finds the standard deviation of cell recurrence time is found to be a good quantifier of stickiness on a global scale.

### Statistical properties of the localization measure of chaotic eigenstates and the spectral statistics in a mixed-type billiard.

- PhysicsPhysical review. E
- 2019

The quantum localization in the chaotic eigenstates of a billiard with mixed-type phase space is studied, and it is shown that A is linearly related to normalized inverse participation ratio, similar to the quantum kicked rotator and the stadium billiard.

## References

SHOWING 1-10 OF 43 REFERENCES

### New universal aspects of diffusion in strongly chaotic systems

- Mathematics
- 1997

We study some new universal aspects of diffusion in chaotic systems, especially those having very large Lyapunov coefficients on the chaotic (indecomposable, topologically transitive) component. We…

### Survey on the role of accelerator modes for anomalous diffusion: the case of the standard map.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014

We perform an extensive and detailed analysis of the generalized diffusion processes in deterministic area preserving maps with noncompact phase space, exemplified by the standard map, with the…

### Classical dynamics of a family of billiards with analytic boundaries

- Physics
- 1983

The classical dynamics of a billiard which is a quadratic conformal image of the unit disc is investigated. The author gives the stability analysis of major periodic orbits, present the Poincare…

### State-dependent diffusion: Thermodynamic consistency and its path integral formulation.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

This work shows that the requirement that a particle's distribution function approach the Boltzmann distribution at long times dictates that a drift term must be added to the Langevin equation, and derives a path integral representation for arbitrary interpretation of the noise.

### Statistical properties of the localization measure in a finite-dimensional model of the quantum kicked rotator.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

A more refined theory of the localization length in the quantum kicked rotator and in similar Floquet systems is called for, where not only the mean value of the inverse of the localized length L but also its (Gaussian) distribution is predicted, in particular the variance.

### Diffusion and Localization in Chaotic Billiards.

- PhysicsPhysical review letters
- 1996

The classical diffusive process which takes place in a chaotic billiard is studied analytically and numerically to estimate the conditions under which the statistical properties of eigenvalues and eigenfunctions can be described by Random Matrix Theory.

### Power-law behavior of Lyapunov exponents in some conservative dynamical systems

- Mathematics, Physics
- 1984

### Semiempirical theory of level spacing distribution beyond the Berry–Robnik regime: modeling the localization and the tunneling effects

- Physics
- 2010

In this work we study the level spacing distribution in the classically mixed-type quantum systems (which are generic), exhibiting regular motion on invariant tori for some initial conditions and…