Typical equilibrium state of an embedded quantum system

TL;DR

This paper derives an analytical partition function for the long-time equilibrium state of a quantum system embedded in an environment, revealing a new thermodynamical ensemble that generalizes microcanonical and canonical ensembles.

Contribution

It introduces a novel partition function based on eigenvector overlaps, extending thermodynamic descriptions of embedded quantum systems.

Findings

Derived an analytical expression for the equilibrium partition function.

Validated predictions through numerical simulations.

Unified microcanonical and canonical ensembles within a new thermodynamic framework.

Abstract

We consider an arbitrary quantum system coupled non perturbatively to a large arbitrary and fully quantum environment. In [G. Ithier and F. Benaych-Georges, Phys. Rev. A 96, 012108 (2017)] the typicality of the dynamics of such an embedded quantum system was established for several classes of random interactions. In other words, the time evolution of its quantum state does not depend on the microscopic details of the interaction. Focusing at the long time regime, we use this property to calculate analytically a new partition function characterizing the stationary state and involving the overlaps between eigenvectors of a bare and a dressed Hamiltonian. This partition function provides a new thermodynamical ensemble which includes the microcanonical and canonical ensembles as particular cases. We check our predictions with numerical simulations.