Federico Bonetto – Georgia Institute of Technology
Date/Time/Location
Thursday, March 5, 2026, 12:10 pm; Hill Center 705
Approach to equilibrium for a particle interacting with a harmonic thermal bath
We study the long time evolution of the position-position correlation function $C_{alpha,N}(s,t)$ for a harmonic oscillator (the {it probe}) interacting via a coupling $alpha$ with a large chain of $N$ coupled oscillators (the {it heat bath}). At $t=0$ the probe and the bath are in equilibrium at temperature $T_P$ and $T_B$, respectively. We show that for times $t$ and $s$ of the order of $N$,$C_{alpha,N}(s,t)$ is very well approximated by its limit $C_{alpha}(s,t)$ as $Ntoinfty$. We find that, if the frequency $Omega$ of the probe is in the spectrum of the bath, the system appears to thermalize, at least at lower order in $alpha$, while, at higher order in $alpha$, $C_{alpha}(s,t)$ contains terms that oscillate or vanish as a power law in $|t-s|$. That is, even when the bath is very large, it cannot be thought of as an ideal stochastic thermostat. This is a work in collaboration with Alberto Maiocchi