Dynamics of a tracer trapped in a correlated medium in the presence of a wall
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917106587533312 |
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| author | Pruszczyk, Marcin Piotr Gambassi, Andrea |
| author_facet | Pruszczyk, Marcin Piotr Gambassi, Andrea |
| contents | We describe the random motion of a particle immersed in a thermally fluctuating medium and harmonically trapped at a certain distance from a wall. The medium, modeled by a Gaussian field with a tunable correlation length $ξ$, is linearly coupled to the particle and evolves according to dissipative relaxational dynamics. Dirichlet boundary conditions imposed on the field at the wall give rise to a repulsive fluctuation-induced force acting on the particle, causing a shift in its average position and a renormalization of the strength of the harmonic trap. We describe the effective overdamped dynamics of the particle, which features a nonlinear memory term depending on the wall-particle separation. We show that the two-time correlation function of the particle position features a memory-induced term that depends on the distance of the particle from the wall. At the critical point, this term decays algebraically upon increasing time and it displays a crossover from the behavior observed in the bulk to that corresponding to having the particle at the wall. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21436 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics of a tracer trapped in a correlated medium in the presence of a wall Pruszczyk, Marcin Piotr Gambassi, Andrea Statistical Mechanics Soft Condensed Matter We describe the random motion of a particle immersed in a thermally fluctuating medium and harmonically trapped at a certain distance from a wall. The medium, modeled by a Gaussian field with a tunable correlation length $ξ$, is linearly coupled to the particle and evolves according to dissipative relaxational dynamics. Dirichlet boundary conditions imposed on the field at the wall give rise to a repulsive fluctuation-induced force acting on the particle, causing a shift in its average position and a renormalization of the strength of the harmonic trap. We describe the effective overdamped dynamics of the particle, which features a nonlinear memory term depending on the wall-particle separation. We show that the two-time correlation function of the particle position features a memory-induced term that depends on the distance of the particle from the wall. At the critical point, this term decays algebraically upon increasing time and it displays a crossover from the behavior observed in the bulk to that corresponding to having the particle at the wall. |
| title | Dynamics of a tracer trapped in a correlated medium in the presence of a wall |
| topic | Statistical Mechanics Soft Condensed Matter |
| url | https://arxiv.org/abs/2511.21436 |