Abstract
The usual approach to the foundations of quantum statistical physics is based on the conventional micro-canonical ensemble as a starting point for deriving the 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 the quantum micro-canonical (QMC) ensemble. We present a detailed numerical study of the properties of the QMC ensemble for finite quantum systems, revealing 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. We demonstrate that the variance of energy fluctuations can be used to discriminate the QMC equilibrium from the BG equilibrium.
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