Thermodynamics of the interacting Fermi-system in the Static Fluctuation Approximation

TL;DR

This paper introduces a new static fluctuation approximation method to calculate equilibrium correlation functions and thermodynamic properties of an interacting Fermi gas, providing analytical expressions at low temperatures and high densities.

Contribution

The authors develop a novel calculation method within the static fluctuation approximation framework for Fermi systems, enabling the derivation of far-distance equations and thermodynamic parameters.

Findings

Derived expressions for mean energy and heat capacity at low temperatures.

Calculated terms up to order r_s^2 for high-density electron gas.

Demonstrated the method's ability to include high-order terms in the decomposition.

Abstract

We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary order for the interacting Fermi-gas model in the frame of the static fluctuation approximation (SFA) method. This method based only on the single and controllable approximation allows to obtain the so-called far-distance equations (FDEs). These equations connecting the quantum states of a Fermi particle with variables of the local field operator contains all necessary information related to calculation of the desired correlation functions and basic thermodynamic parameters of the many-body system considered. The basic expressions for the mean energy and heat capacity for electron gas at low temperatures in the limit of high density were obtained. All expressions are given in the units of r_s,where r_s determines the ratio of a mean distance between electrons to the Bohr radius a_0. In these expressions we calculated the terms of the order r_s and r_s^2, correspondingly. It was shown also that the SFA allows to find the terms related with high orders of the decomposition with respect to the parameter r_s.