Scaling invariance for the diffusion coefficient in a billiard system
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918239465897984 |
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| author | da Fonseca, Anne Kétri P. Oliveira, Diego F. M. Leonel, Edson D. |
| author_facet | da Fonseca, Anne Kétri P. Oliveira, Diego F. M. Leonel, Edson D. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06395 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scaling invariance for the diffusion coefficient in a billiard system da Fonseca, Anne Kétri P. Oliveira, Diego F. M. Leonel, Edson D. Chaotic Dynamics 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. |
| title | Scaling invariance for the diffusion coefficient in a billiard system |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2507.06395 |