Statistical Ensembles and Spectral Correlations in Mesoscopic Systems

TL;DR

This paper explores how different statistical ensembles affect physical observable averages in mesoscopic systems, linking these differences to spectral correlations and identifying conditions for thermodynamic limit realization.

Contribution

It introduces a systematic diagrammatic approach to analyze ensemble differences and their relation to spectral correlations in mesoscopic systems.

Findings

Ensemble differences depend on disorder and temperature.

Spectral correlations influence observable averages.

Conditions for thermodynamic limit are identified.

Abstract

Employing different statistical ensembles may lead to qualitatively different results concerning averages of physical observables on the mesoscopic scale. Here we discuss differences between the canonical and the grandcanonical ensembles due to both quenched disorder and thermodynamical effects. We show how these differences are related to spectral correlations of the system at hand, and evaluate the conditions (temperature, system's size) when the thermodynamic limit is achieved. We demonstrate our approach by evaluating the heat capacity, persistent currents and the occupation probability of single electron states, employing a systematic diagrammatic approach.