The Fermi liquid theory with fractional exclusion statistics

TL;DR

This paper develops a generalized Fermi liquid theory where quasiparticle energies are redefined to match the total system energy, enabling the description of thermodynamics using fractional exclusion statistics.

Contribution

It introduces a novel approach to Fermi liquid theory by incorporating fractional exclusion statistics through a redefinition of quasiparticle energies.

Findings

Quasiparticle energies can be redefined to match total system energy.

Thermodynamics of interacting systems can be described by fractional exclusion statistics.

The approach unifies Fermi liquid theory with fractional exclusion statistics.

Abstract

The Fermi liquid theory may provide a good description of the thermodynamic properties of an interacting particle system when the interaction between the particles contributes to the total energy of the system with a quantity which may depend on the total particle number, but does not depend on the temperature. In such a situation, the ideal part of the Hamiltonian, i.e. the energy of the system without the interaction energy, also provides a good description of the system's thermodynamics. If the total interaction energy of the system, being a complicated function of the particle populations, is temperature dependent, then the Landau's quasiparticle gas cannot describe accurately the thermodynamics of the system. A general solution to this problem is presented in this paper, in which the quasiparticle energies are redefined in such a way that the total energy of the system is identical to the sum of the energies of the quasiparticles. This implies also that the thermodynamic properties of the system and those of the quasiparticle gas are identical. By choosing a perspective in which the quasiparticle energies are fixed while the density of states along the quasiparticle axis vary, we transform our quasiparticle system into an ideal gas which obey fractional exclusion statistics.