Discussing a transition from bounded to unbounded energy in a time-dependent billiard
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912473279365120 |
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| author | da Fonseca, Anne Kétri P. Silveira, Felipe Augusto O. Kuwana, Célia M. Oliveira, Diego F. M. Leonel, Edson D. |
| author_facet | da Fonseca, Anne Kétri P. Silveira, Felipe Augusto O. Kuwana, Célia M. Oliveira, Diego F. M. Leonel, Edson D. |
| contents | We revisit a time-dependent, oval-shaped billiard to investigate a phase transition from bounded to unbounded energy growth. In the static case, the phase space exhibits a mixed structure. The chaotic sea in the static scenario leads to average energy growth for a time-dependent boundary. However, inelastic collisions between the particle and the boundary limit this unbounded energy increase. This transition displays properties similar to continuous phase transitions in statistical mechanics, including scale invariance, interrelated critical exponents governed by scaling laws, and an order parameter/susceptibility approaching zero/infinity at the transition. Furthermore, the system exhibits an elementary excitation that promotes particle diffusion and lacks topological defects that provide modifications to the probability distribution function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12928 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Discussing a transition from bounded to unbounded energy in a time-dependent billiard da Fonseca, Anne Kétri P. Silveira, Felipe Augusto O. Kuwana, Célia M. Oliveira, Diego F. M. Leonel, Edson D. Chaotic Dynamics We revisit a time-dependent, oval-shaped billiard to investigate a phase transition from bounded to unbounded energy growth. In the static case, the phase space exhibits a mixed structure. The chaotic sea in the static scenario leads to average energy growth for a time-dependent boundary. However, inelastic collisions between the particle and the boundary limit this unbounded energy increase. This transition displays properties similar to continuous phase transitions in statistical mechanics, including scale invariance, interrelated critical exponents governed by scaling laws, and an order parameter/susceptibility approaching zero/infinity at the transition. Furthermore, the system exhibits an elementary excitation that promotes particle diffusion and lacks topological defects that provide modifications to the probability distribution function. |
| title | Discussing a transition from bounded to unbounded energy in a time-dependent billiard |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2411.12928 |