Ergodic properties of occupation times in heterogeneous media
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914158425931776 |
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| author | Méndez, Vicenç Flaquer-Galmés, Rosa |
| author_facet | Méndez, Vicenç Flaquer-Galmés, Rosa |
| contents | We investigate the ergodic properties of Brownian motion in heterogeneous media through the statistics of occupation times. Using the Feynman-Kac formalism, we derive analytical expressions for the distributions, moments, and ergodicity breaking parameters of occupation times in two models with spatially varying diffusion coefficient: a piecewise-constant profile and a power-law profile. In the piecewise model, the half occupation time and the occupation time within an interval follow asymmetric arcsine and half-Gaussian distributions, respectively, indicating non-ergodic behavior. For the power-law case, the corresponding distributions are the Lamperti and Mittag-Leffler. In both models, we identify a transition from non-ergodic to ergodic dynamics as the exponent vary. Numerical simulations fully corroborate the analytical results, demonstrating the effectiveness of the Feynman-Kac approach for quantifying ergodicity in heterogeneous diffusion processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11099 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ergodic properties of occupation times in heterogeneous media Méndez, Vicenç Flaquer-Galmés, Rosa Statistical Mechanics We investigate the ergodic properties of Brownian motion in heterogeneous media through the statistics of occupation times. Using the Feynman-Kac formalism, we derive analytical expressions for the distributions, moments, and ergodicity breaking parameters of occupation times in two models with spatially varying diffusion coefficient: a piecewise-constant profile and a power-law profile. In the piecewise model, the half occupation time and the occupation time within an interval follow asymmetric arcsine and half-Gaussian distributions, respectively, indicating non-ergodic behavior. For the power-law case, the corresponding distributions are the Lamperti and Mittag-Leffler. In both models, we identify a transition from non-ergodic to ergodic dynamics as the exponent vary. Numerical simulations fully corroborate the analytical results, demonstrating the effectiveness of the Feynman-Kac approach for quantifying ergodicity in heterogeneous diffusion processes. |
| title | Ergodic properties of occupation times in heterogeneous media |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2511.11099 |