Logarithmic Subdiffusion from a Damped Bath Model
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908971540938752 |
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| author | Guff, Thomas Rocco, Andrea |
| author_facet | Guff, Thomas Rocco, Andrea |
| contents | A damped oscillator heat bath model is a modification of the standard heat bath model, wherein each bath oscillator itself has a Markovian coupling to its own heat bath [1]. We modify such a model to one where the resulting damping of the oscillators is linear in their frequency rather than being a constant. We find that this generates a memory kernel which behaves like $k(t) \sim 1/t$ as $t \to \infty$, which is a boundary case not considered in previous works. As the memory kernel does not have a finite integral, the reduced system is subdiffusive, and we numerically show that diffusion goes as $\langle ΔQ^{2}(t)\rangle \sim t/\log(t)$ as $t \to \infty$. We also numerically calculate the velocity correlation function in the asymptotic regime and use it to confirm the aforementioned subdiffusion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15613 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Logarithmic Subdiffusion from a Damped Bath Model Guff, Thomas Rocco, Andrea Statistical Mechanics Quantum Physics A damped oscillator heat bath model is a modification of the standard heat bath model, wherein each bath oscillator itself has a Markovian coupling to its own heat bath [1]. We modify such a model to one where the resulting damping of the oscillators is linear in their frequency rather than being a constant. We find that this generates a memory kernel which behaves like $k(t) \sim 1/t$ as $t \to \infty$, which is a boundary case not considered in previous works. As the memory kernel does not have a finite integral, the reduced system is subdiffusive, and we numerically show that diffusion goes as $\langle ΔQ^{2}(t)\rangle \sim t/\log(t)$ as $t \to \infty$. We also numerically calculate the velocity correlation function in the asymptotic regime and use it to confirm the aforementioned subdiffusion. |
| title | Logarithmic Subdiffusion from a Damped Bath Model |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2409.15613 |