Scaling invariance for the diffusion coefficient in a billiard system
Abstract
We investigated the unbounded diffusion observed in a time-dependent oval-shaped billiard and its suppression owing to inelastic collisions with the boundary. The main focus is on the behavior of the diffusion coefficient, which plays a key role in describing the scaling invariance characteristic of this transition. For short times, the low-action regime is characterized by a constant diffusion coefficient, which begins to decay after a crossover iteration, thereby suppressing the unlimited growth of velocity. We demonstrate that this behavior is scaling-invariant concerning the control parameters and can be described by a homogeneous generalized function and its associated scaling laws. The critical exponents are determined both phenomenologically and analytically, including the decay exponent beta = -1, previously identified in the diffusion coefficient of the dissipative standard map.
Cite
@article{arxiv.2507.06395,
title = {Scaling invariance for the diffusion coefficient in a billiard system},
author = {Anne Kétri P. da Fonseca and Diego F. M. Oliveira and Edson D. Leonel},
journal= {arXiv preprint arXiv:2507.06395},
year = {2025}
}
Comments
Accepted for publication at Discontinuity, Nonlinearity, and Complexity in 05/12/2025