Dynamics of stochastic oscillator chains with harmonic and FPUT potentials
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| Format: | Preprint |
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2025
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| _version_ | 1866911419204632576 |
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| author | Cirillo, Emilio N. M. Colangeli, Matteo Giberti, Claudio Rondoni, Lamberto |
| author_facet | Cirillo, Emilio N. M. Colangeli, Matteo Giberti, Claudio Rondoni, Lamberto |
| contents | Inspired by recent studies on deterministic oscillator models, we introduce a stochastic one-dimensional model for a chain of interacting particles. The model consists of $N$ oscillators performing continuous-time random walks on the integer lattice $\mathbb{Z}$ with exponentially distributed waiting times. The oscillators are bound by confining forces to two particles that do not move, placed at positions $x_0$ and $x_{N+1}$, respectively, and they feel the presence of baths with given inverse temperatures: $β_L$ to the left, $β_B$ in the middle, and $β_R$ to the right. Each particle has an index and interacts with its nearest neighbors in index space through either a quadratic potential or a Fermi-Pasta-Ulam-Tsingou type coupling. This local interaction in index space can give rise to effective long-range interactions on the spatial lattice, depending on the instantaneous configuration. Particle hopping rates are governed either by the Metropolis rule or by a modified version that breaks detailed balance at the interfaces between regions with different baths. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_26820 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics of stochastic oscillator chains with harmonic and FPUT potentials Cirillo, Emilio N. M. Colangeli, Matteo Giberti, Claudio Rondoni, Lamberto Statistical Mechanics Mathematical Physics Probability Inspired by recent studies on deterministic oscillator models, we introduce a stochastic one-dimensional model for a chain of interacting particles. The model consists of $N$ oscillators performing continuous-time random walks on the integer lattice $\mathbb{Z}$ with exponentially distributed waiting times. The oscillators are bound by confining forces to two particles that do not move, placed at positions $x_0$ and $x_{N+1}$, respectively, and they feel the presence of baths with given inverse temperatures: $β_L$ to the left, $β_B$ in the middle, and $β_R$ to the right. Each particle has an index and interacts with its nearest neighbors in index space through either a quadratic potential or a Fermi-Pasta-Ulam-Tsingou type coupling. This local interaction in index space can give rise to effective long-range interactions on the spatial lattice, depending on the instantaneous configuration. Particle hopping rates are governed either by the Metropolis rule or by a modified version that breaks detailed balance at the interfaces between regions with different baths. |
| title | Dynamics of stochastic oscillator chains with harmonic and FPUT potentials |
| topic | Statistical Mechanics Mathematical Physics Probability |
| url | https://arxiv.org/abs/2510.26820 |