The canonical heat capacity of normal mesoscopic fermion systems: the temperature evolution and particle number oscillations

TL;DR

This paper investigates the temperature-dependent behavior of heat capacity in mesoscopic fermion systems, revealing four distinct stages and oscillations related to particle number and level spacings near the Fermi energy.

Contribution

It provides a detailed analysis of heat capacity evolution in mesoscopic fermion systems across various temperatures and particle numbers, highlighting resonance effects and oscillations.

Findings

Heat capacity exhibits four temperature stages with characteristic behaviors.

Oscillations in heat capacity as a function of particle number reveal level density variations.

For large N, heat capacity follows a T-linear law with N-dependent modifications.

Abstract

The heat capacity (C) of a mesoscopic nonsuperconducting fermion system treated as a canonical ensemble of independent particles is studied in a wide range of particle numbers and temperatures which vary from values close to zero up to the Fermi energy. The temperature evolution of C is naturally divided into four stages. On the first one the heat capacity exponentially increases with temperature and at a resonance temperature reaches either a local maximum or an irregularity in its growth. This resonance temperature being measured can give information concerning the level spacings in the immediate proximity of the Fermi energy. On the second stage the progressive suppression of the level density oscillations takes place. During this stage oscillations of C v.s. particle number N can be distinctly observed. These oscillations give the N-variations of the temperature averaged level density. The growth of C on the third stage of the evolution is governed by the T-linear law if the particle number is large enough (N>1000). It is found that the Sommerfeld factor in the linear law for such small systems shows more complicated N-dependence as compared with large systems where C is strictly proportional to N. For temperatures tending to the Fermi energy the deviations from the T-linearity are evident and at T larger than the Fermi energy (the fourth stage of the evolution) any system attains to the classic Boltzmann-Maxwell limit irrespective of the particle