Ponente
Descripción
We study the time-evolution from an initial state to an equilibrium state for a 2D-Dyson gas of $N$ charged particles interacting through a 2D-logarithmic Coulomb potential surrounded by a thermal bath at a reduced temperature $\beta=q^2_0/(k_BT)$, with $q_0$ the charge per particle, $T$ the temperature of the bath and $k_B$ the Boltzmann's constant, for $\beta$ in range $[0.1,4.0]$. We analyze the standard deviation of two-particle distances using a standard growth model in logarithmic independent variable, and the spacing distribution between nearest neighbors using a generalized Wigner’s distribution model from which we can know the standard deviation to compare with the initial analysis. We show how a logrithmic-time-law scale governs the time-evolution of this process and prove the validity of Wigner's Surmise for $\beta\geq1.0$ compared with those values used in Gaussian ensembles for times greater than relaxation time $\tau\gg\tau_{\text{Eq}}$, i.e., when the system has reached the thermal equilibrium.
