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arXiv · 1707.00814

Unusual equilibration of a particle in a potential with a thermal wall

Deepak Bhat·Sanjib Sabhapandit·Anupam Kundu·Abhishek Dhar
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Abstract

We consider a particle in a one-dimensional box of length $L$ with a Maxwell bath at one end and a reflecting wall at the other end. Using a renewal approach, as well as directly solving the master equation, we show that the system exhibits a slow power law relaxation with a logarithmic correction towards the final equilibrium state. We extend the renewal approach to a class of confining potentials of the form $U(x) \propto x^\alpha$, $x>0$, where we find that the relaxation is $\sim t^{-(\alpha+2)/(\alpha-2)}$ for $\alpha >2$, with a logarithmic correction when $(\alpha+2)/(\alpha-2)$ is an integer. For $\alpha <2$ the relaxation is exponential. Interestingly for $\alpha=2$ (harmonic potential) the localised bath can not equilibrate the particle.

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Deepak Bhat, Sanjib Sabhapandit, Anupam Kundu, Abhishek Dhar. 2017-07-04. Unusual equilibration of a particle in a potential with a thermal wall. https://doi.org/10.1088/1742-5468/aa9683

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