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arXiv:1204.4064

The Fermi liquid theory with fractional exclusion statistics

Dragoş-Victor Anghel

Published Apr 18, 2012• 1 citation
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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.

DOI
10.48550/arxiv.1204.4064

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We describe a mean field interacting particle system in any number of dimensions and in a generic external potential as an ideal gas with fractional exclusion statistics (FES). We define the FES quasiparticle energies, we calculate the FES parameters of the system and we deduce the equations for the equilibrium particle populations. The FES gas is "ideal," in the sense that the quasiparticle energies do not depend on the other quasiparticle levels' populations and the sum of the quasiparticle energies is equal to the total energy of the system. We prove that the FES formalism is equivalent to the semiclassical or Thomas Fermi limit of the self-consistent mean-field theory and the FES quasiparticle populations may be calculated from the Landau quasiparticle populations by making the correspondence between the FES and the Landau quasiparticle energies. The FES provides a natural semiclassical ideal gas description of the interacting particle gas.
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U(1)U(1)U(1) Fermi liquid theory - A Fermi liquid state that supports exclusion statistics
We propose in this paper an effective low-energy theory for interacting fermion systems which supports exclusion statistics. The theory can be viewed as an extension of Landau Fermi liquid theory where besides quasi-particle energy ξkξ_{\mathbf{k}}ξk​, the kinetic momentum k\mathbf{k}k of quasi-particles depends also on quasi-particle occupation numbers as a result of momentum (kkk)-dependent current-current interaction. The dependence of kinetic momentum on quasi-particles excitations leads to change in density of states and exclusion statistics. The properties of this new Fermi liquid state is studied where we show that the state (which we call U(1)U(1)U(1)-Fermi liquid state) has Fermi-liquid like properties except that the quasi-particles are {\em not} adiabatically connected to bare fermions in the system and the state may not satisfy Luttinger theorem.