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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.08130 |
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| _version_ | 1866908929724776448 |
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| author | Xiong, Zhongqiang Komura, Shigeyuki Doi, Masao |
| author_facet | Xiong, Zhongqiang Komura, Shigeyuki Doi, Masao |
| contents | We study the Brownian motion of a rigid rod threading through a small fixed ring while the ring can freely rotate. We derive the distribution function for the sliding displacement and the unit vector along the rod both at equilibrium and non-equilibrium. The equilibrium distribution is quadratic in the sliding displacement and is controlled by the moment of inertia (mass distribution). Applying the Onsager variational principle, we derive a Smoluchowski equation in which sliding and rotational diffusion are coupled. The mean square displacement (MSD) of sliding shows a metastable plateau in a certain time range before it approaches the final equilibrium value. The longest sliding relaxation time scales as $α^{-1/2}$, where $α$ is the dimensionless moment of inertia of the rod. The rotational relaxation time obtained from the orientational correlation function is longer than that of a rod with its center fixed but faster than a rod with one end fixed. These results may be useful in understanding the dynamics of polymers connected by sliding rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08130 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Brownian motion of a rod threading through a ring with fixed ring-center Xiong, Zhongqiang Komura, Shigeyuki Doi, Masao Soft Condensed Matter We study the Brownian motion of a rigid rod threading through a small fixed ring while the ring can freely rotate. We derive the distribution function for the sliding displacement and the unit vector along the rod both at equilibrium and non-equilibrium. The equilibrium distribution is quadratic in the sliding displacement and is controlled by the moment of inertia (mass distribution). Applying the Onsager variational principle, we derive a Smoluchowski equation in which sliding and rotational diffusion are coupled. The mean square displacement (MSD) of sliding shows a metastable plateau in a certain time range before it approaches the final equilibrium value. The longest sliding relaxation time scales as $α^{-1/2}$, where $α$ is the dimensionless moment of inertia of the rod. The rotational relaxation time obtained from the orientational correlation function is longer than that of a rod with its center fixed but faster than a rod with one end fixed. These results may be useful in understanding the dynamics of polymers connected by sliding rings. |
| title | Brownian motion of a rod threading through a ring with fixed ring-center |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2601.08130 |