Stochastically perturbed billiards: fingerprints of chaos and universality classes
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917484537315328 |
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| author | Artuso, Roberto Burlo, Matteo |
| author_facet | Artuso, Roberto Burlo, Matteo |
| contents | Billiards tables - a minimal model for particles moving in a confined region - are known to present classical (and quantum) different features according to their shape, ranging from strongly chaotic to integrable dynamics. Here we consider the role of a stochastic perturbation of the elastic reflection law, and show that while chaotic billiards maintain their key statistical feature, the behaviour for integrable billiard tables is completely different: it can be linked, for tiny perturbations, to Evans stochastic billiard, where at each collision the reflected angle is a uniformly distributed stochastic variable on $(-π/2,π/2$). The resulting spatial stationary measure has peculiar aspects, like being typically non uniform along the boundary, differently from any chaotic billiard table. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11849 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastically perturbed billiards: fingerprints of chaos and universality classes Artuso, Roberto Burlo, Matteo Chaotic Dynamics Mathematical Physics Billiards tables - a minimal model for particles moving in a confined region - are known to present classical (and quantum) different features according to their shape, ranging from strongly chaotic to integrable dynamics. Here we consider the role of a stochastic perturbation of the elastic reflection law, and show that while chaotic billiards maintain their key statistical feature, the behaviour for integrable billiard tables is completely different: it can be linked, for tiny perturbations, to Evans stochastic billiard, where at each collision the reflected angle is a uniformly distributed stochastic variable on $(-π/2,π/2$). The resulting spatial stationary measure has peculiar aspects, like being typically non uniform along the boundary, differently from any chaotic billiard table. |
| title | Stochastically perturbed billiards: fingerprints of chaos and universality classes |
| topic | Chaotic Dynamics Mathematical Physics |
| url | https://arxiv.org/abs/2605.11849 |