An alternative to the conventional micro-canonical ensemble

TL;DR

This paper explores the Quantum Micro-Canonical (QMC) ensemble as an alternative to the traditional micro-canonical ensemble in quantum statistical physics, analyzing its properties, finite-size effects, and potential realizability in small quantum systems.

Contribution

It introduces the QMC ensemble as a conceptual and practical alternative, providing numerical and analytical insights into its properties and differences from Boltzmann-Gibbs equilibrium.

Findings

QMC ensemble agrees with analytical results for large systems

Finite-size corrections improve analytical-numerical agreement

Variance of energy fluctuations distinguishes QMC from BG equilibrium

Abstract

Usual approach to the foundations of quantum statistical physics is based on conventional micro-canonical ensemble as a starting point for deriving Boltzmann-Gibbs (BG) equilibrium. It leaves, however, a number of conceptual and practical questions unanswered. Here we discuss these questions, thereby motivating the study of a natural alternative known as Quantum Micro-Canonical (QMC) ensemble. We present a detailed numerical study of the properties of the QMC ensemble for finite quantum systems revealing a good agreement with the existing analytical results for large quantum systems. We also propose the way to introduce analytical corrections accounting for finite-size effects. With the above corrections, the agreement between the analytical and the numerical results becomes very accurate. The QMC ensemble leads to an unconventional kind of equilibrium, which may be realizable after strong perturbations in small isolated quantum systems having large number of levels. We demonstrate that the variance of energy fluctuations can be used to discriminate the QMC equilibrium from the BG equilibrium. We further suggest that the reason, why BG equilibrium commonly occurs in nature rather than the QMC-type equilibrium, has something to do with the notion of quantum collapse.