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

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 , , where we find that the relaxation is for , with a logarithmic correction when is an integer. For the relaxation is exponential. Interestingly for (harmonic potential) the localised bath cannot equilibrate the particle.