Stability of Quantum Systems beyond Canonical Typicality

TL;DR

This paper investigates the stability of quantum system distributions when strongly coupled with a heat bath, revealing that stability depends on the system's response function and refining canonical statistical theory for small systems.

Contribution

It introduces a criterion based on the response function for the stability of quantum distributions and analyzes this in the context of non-interacting bosonic impurity systems.

Findings

System distribution stability depends on the response function at zero frequency.

Proposed a stability criterion:  ilde ext{chi}( ext{0+}) > 0.

Refined the theoretical framework of canonical statistics for small-scale quantum systems.

Abstract

Involvement of the environment is indispensable for establishing the statistical distribution of system. We analyze the statistical distribution of a quantum system coupled strongly with a heat bath. This distribution is determined by tracing over the bath's degrees of freedom for the equilibrium system-plus-bath composite. The stability of system distribution is largely affected by the system--bath interaction strength. We propose that the quantum system exhibits a stable distribution only when its system response function in the frequency domain satisfies $\tilde\chi(\omega = 0+)>0$. We show our results by investigating the non-interacting bosonic impurity system from both the thermodynamic and dynamic perspectives. Our study refines the theoretical framework of canonical statistics, offering insights into thermodynamic phenomena in small-scale systems.