Simulations of Classical Three-Body Thermalization in One Dimension
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910519278960640 |
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| author | Eltohfa, M. Wang, Xinghan Griffin, Colton M. Robicheaux, F. |
| author_facet | Eltohfa, M. Wang, Xinghan Griffin, Colton M. Robicheaux, F. |
| contents | One-dimensional systems, such as nanowires or electrons moving along strong magnetic field lines, have peculiar thermalization physics. The binary collision of point-like particles, typically the dominant process for reaching thermal equilibrium in higher dimensional systems, cannot thermalize a 1D system. We study how dilute classical 1D gases thermalize through three-body collisions. We consider a system of identical classical point particles with pairwise repulsive inverse power-law potential $V_{ij} \propto 1/|x_i-x_j|^n$ or the pairwise Lennard-Jones potential. Using Monte Carlo methods, we compute a collision kernel and use it in the Boltzmann equation to evolve a perturbed thermal state with temperature $T$ toward equilibrium. We explain the shape of the kernel and its dependence on the system parameters. Additionally, we implement molecular dynamics simulations of a many-body gas and show agreement with the Boltzmann evolution in the low density limit. For the inverse power-law potential, the rate of thermalization is proportional to $ρ^2 T^{\frac{1}{2}-\frac{1}{n}}$ where $ρ$ is the number density. The corresponding proportionality constant decreases with increasing $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00089 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simulations of Classical Three-Body Thermalization in One Dimension Eltohfa, M. Wang, Xinghan Griffin, Colton M. Robicheaux, F. Atomic Physics Statistical Mechanics Classical Physics One-dimensional systems, such as nanowires or electrons moving along strong magnetic field lines, have peculiar thermalization physics. The binary collision of point-like particles, typically the dominant process for reaching thermal equilibrium in higher dimensional systems, cannot thermalize a 1D system. We study how dilute classical 1D gases thermalize through three-body collisions. We consider a system of identical classical point particles with pairwise repulsive inverse power-law potential $V_{ij} \propto 1/|x_i-x_j|^n$ or the pairwise Lennard-Jones potential. Using Monte Carlo methods, we compute a collision kernel and use it in the Boltzmann equation to evolve a perturbed thermal state with temperature $T$ toward equilibrium. We explain the shape of the kernel and its dependence on the system parameters. Additionally, we implement molecular dynamics simulations of a many-body gas and show agreement with the Boltzmann evolution in the low density limit. For the inverse power-law potential, the rate of thermalization is proportional to $ρ^2 T^{\frac{1}{2}-\frac{1}{n}}$ where $ρ$ is the number density. The corresponding proportionality constant decreases with increasing $n$. |
| title | Simulations of Classical Three-Body Thermalization in One Dimension |
| topic | Atomic Physics Statistical Mechanics Classical Physics |
| url | https://arxiv.org/abs/2403.00089 |