Dynamical thermalization in isolated quantum dots and black holes

Abstract

We study numerically a model of quantum dot with interacting fermions. At strong interactions with small conductance the model is reduced to the Sachdev-Ye-Kitaev black hole model while at weak interactions and large conductance it describes a Landau Fermi liquid in a regime of quantum chaos. We show that above the Aberg threshold for interactions there is an onset of dynamical themalization with the Fermi-Dirac distribution describing the eigenstates of isolated dot. At strong interactions in the isolated black hole regime there is also onset of dynamical thermalization with the entropy described by the quantum Gibbs distribution. This dynamical thermalization takes place in an isolated system without any contact with thermostat. We discuss possible realization of these regimes with quantum dots of 2D electrons and cold ions in optical lattices.