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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.18581 |
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| _version_ | 1866912741663440896 |
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| author | de Souza, Lucas G. B. da Luz, M. G. E. Raposo, E. P. Curado, Evaldo M. F. Viswanathan, G. M. |
| author_facet | de Souza, Lucas G. B. da Luz, M. G. E. Raposo, E. P. Curado, Evaldo M. F. Viswanathan, G. M. |
| contents | We study sums of independent and identically distributed random velocities in special relativity. We show that the resulting one-dimensional velocity distributions are not only stable under relativistic velocity addition but define a genuinely new class of stochastic processes--relativistic Lévy processes. Given a system, this allows identifying distinct relativistic regimes in terms of the distribution's concavity at the origin and the probability of measuring relativistic velocities. These features provide a protocol to assess the relevance of stochastic relativistic effects in actual experiments. As supporting evidence, we find agreement with previous results about heavy-ion diffusion and show that our findings are consistent with the distribution of momentum deviations observed in measurements of antiproton cooling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18581 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relativistic Lévy processes de Souza, Lucas G. B. da Luz, M. G. E. Raposo, E. P. Curado, Evaldo M. F. Viswanathan, G. M. Statistical Mechanics Mathematical Physics We study sums of independent and identically distributed random velocities in special relativity. We show that the resulting one-dimensional velocity distributions are not only stable under relativistic velocity addition but define a genuinely new class of stochastic processes--relativistic Lévy processes. Given a system, this allows identifying distinct relativistic regimes in terms of the distribution's concavity at the origin and the probability of measuring relativistic velocities. These features provide a protocol to assess the relevance of stochastic relativistic effects in actual experiments. As supporting evidence, we find agreement with previous results about heavy-ion diffusion and show that our findings are consistent with the distribution of momentum deviations observed in measurements of antiproton cooling. |
| title | Relativistic Lévy processes |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2412.18581 |