Dynamical thermalization in isolated quantum dots and black holes

TL;DR

This paper investigates how isolated quantum dots and black holes exhibit dynamical thermalization through numerical modeling, revealing transitions from quantum chaos to thermal states without external contact.

Contribution

It demonstrates the onset of dynamical thermalization in a quantum dot model, connecting the black hole and Fermi liquid regimes through numerical analysis.

Findings

Dynamical thermalization occurs above the Aberg threshold.

Eigenstates follow Fermi-Dirac distribution in the Fermi liquid regime.

Entropy aligns with quantum Gibbs distribution in the black hole regime.

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.