Mesoscopic Systems With Fixed Number of Electrons

TL;DR

This paper investigates the statistical physics of mesoscopic systems with a fixed number of noninteracting electrons, focusing on the differences between canonical and grand canonical ensembles, especially in disordered systems.

Contribution

It provides a detailed analysis of the canonical ensemble for mesoscopic systems with disorder, highlighting the technical challenges and methods to relate it to the grand canonical ensemble.

Findings

Differences between canonical and grand canonical ensembles are elucidated.

Methods to perform disorder averaging in fixed-electron-number systems are discussed.

The impact of disorder on mesoscopic system statistics is characterized.

Abstract

In this paper, we study the physics of mesoscopic systems with noninteracting, but fixed number of electrons. From a technical point of view, this means a discussion of the differences between the canonical and the grand canonical ensemble (fixed versus fluctuating number of particles). Such a discussion is not trivial since the grand canonical ensemble is the most convenient basis for the statistics of identical particles and one has to spend labour in order to retrieve the canonical ensemble. Specifically, we are considering ensembles of mesoscopic systems with disorder, either by atomic defects or by fluctuations in their geometric definitions and we discuss various forms of disorder averages.