Logarithmic Subdiffusion from a Damped Bath Model

Fuente: arXiv
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Main Authors: Guff, Thomas, Rocco, Andrea
Format: Preprint
Published: 2024
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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