Local persistence exponent and its log-periodic oscillations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908446636376064 |
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| author | Ye, Yilin Grebenkov, Denis S. |
| author_facet | Ye, Yilin Grebenkov, Denis S. |
| contents | We investigate the local persistence exponent of the survival probability of a particle diffusing near an absorbing self-similar boundary. We show by extensive Monte Carlo simulations that the local persistence exponent exhibits log-periodic oscillations over a broad range of timescales. We determine the period and mean value of these oscillations in a family of Koch snowflakes of different fractal dimensions. The effect of the starting point and its local environment on this behavior is analyzed in depth by a simple yet intuitive model. This analysis uncovers how spatial self-similarity of the boundary affects the diffusive dynamics and its temporal characteristics in complex systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08628 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local persistence exponent and its log-periodic oscillations Ye, Yilin Grebenkov, Denis S. Statistical Mechanics Chemical Physics We investigate the local persistence exponent of the survival probability of a particle diffusing near an absorbing self-similar boundary. We show by extensive Monte Carlo simulations that the local persistence exponent exhibits log-periodic oscillations over a broad range of timescales. We determine the period and mean value of these oscillations in a family of Koch snowflakes of different fractal dimensions. The effect of the starting point and its local environment on this behavior is analyzed in depth by a simple yet intuitive model. This analysis uncovers how spatial self-similarity of the boundary affects the diffusive dynamics and its temporal characteristics in complex systems. |
| title | Local persistence exponent and its log-periodic oscillations |
| topic | Statistical Mechanics Chemical Physics |
| url | https://arxiv.org/abs/2507.08628 |