Speaker
Description
We study the dynamics of a Log-Coulomb gas consisting of N charged particles confined to a unitary circle and coupled to a thermal bath characterized by a dimensionless effective parameter $\beta = q_0^2/(k_BT)$ with $q_0$ the charge per particle, $T$ the bath temperature, and $k_B$ the Boltzmann’s constant. The use of a circular domain eliminates boundary effects and ensures exact rotational invariance, leading to an uniform equilibrium density without external confinement. This geometry isolates universal collective properties and greatly simplifies both static and dynamical analyses of logarithmic Coulomb gases particularly, for $\beta = 2$, the system can be treated as a free-fermion model, for which we can obtain an analytical expression for the two-point correlation function in the simplest case $N = 2$, and then extend our analysis to $N > 2$ both numerically and analytically. By varying $\beta$, we show that a logarithmic time-law scaling governs the time evolution of this process, and we verify the validity of the probability distribution of spacings between consecutive particles (levels), called Wigner’s surmise, for $\beta \geq 1$ by comparison with the corresponding Gaussian ensembles for times larger than the relaxation time, $\tau \geq \tau_{\text{Eq}}$, i.e., once the system has reached thermal equilibrium.
