Statistical description of small quantum systems beyond weak-coupling limit

TL;DR

This paper derives a canonical statistical description for small quantum systems weakly coupled to parts of their environment, incorporating interaction effects through a renormalized Hamiltonian, extending beyond mean-field approximations.

Contribution

It provides an explicit, generalized expression for the statistical state of small quantum systems that accounts for interaction effects beyond traditional weak-coupling assumptions.

Findings

The derived expression has a canonical form with a renormalized Hamiltonian.

In systems with narrow spectra and large environments, the modification is mean-field-like.

Beyond mean-field cases are also addressed, capturing more complex interactions.

Abstract

An explicit expression is derived for the statistical description of small quantum systems, which are relatively-weakly and directly coupled to only small parts of their environments. The derived expression has a canonical form, but is given by a renormalized self-Hamiltonian of the studied system, which appropriately takes into account the influence of the system-environment interaction. In the case that the system has a narrow spectrum and the environment is sufficiently large, the modification to the self-Hamiltonian usually has a mean-field feature, given by an environmental average of the interaction Hamiltonian. In other cases, the modification may be beyond the mean-field approximation.