Field Theory of Active Brownian Particles with Dry Friction
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912030929190912 |
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| author | Zhang, Ziluo Yuan, Shurui Komura, Shigeyuki |
| author_facet | Zhang, Ziluo Yuan, Shurui Komura, Shigeyuki |
| contents | We present a field theoretic approach to capture the motion of a particle with dry friction for one- and two-dimensional diffusive particles, and further expand the framework for two-dimensional active Brownian particles. Starting with the Fokker-Planck equation and introducing the Hermite polynomials as the corresponding eigen-functions, we obtain the actions and propagators. Using a perturbation expansion, we calculate the effective diffusion coefficient in the presence of both wet and dry frictions in a perturbative way via the Green-Kubo relation. We further compare the analytical result with the numerical simulation. Our result can be used to estimate the values of dry friction coefficient in experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03817 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Field Theory of Active Brownian Particles with Dry Friction Zhang, Ziluo Yuan, Shurui Komura, Shigeyuki Statistical Mechanics Mathematical Physics We present a field theoretic approach to capture the motion of a particle with dry friction for one- and two-dimensional diffusive particles, and further expand the framework for two-dimensional active Brownian particles. Starting with the Fokker-Planck equation and introducing the Hermite polynomials as the corresponding eigen-functions, we obtain the actions and propagators. Using a perturbation expansion, we calculate the effective diffusion coefficient in the presence of both wet and dry frictions in a perturbative way via the Green-Kubo relation. We further compare the analytical result with the numerical simulation. Our result can be used to estimate the values of dry friction coefficient in experiments. |
| title | Field Theory of Active Brownian Particles with Dry Friction |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2406.03817 |