Neutral and Charged Anyon Fluids

TL;DR

This paper reviews the properties of neutral and charged anyon fluids, focusing on their potential superconductivity and the limitations of traditional approximation methods, suggesting the need for more advanced theories.

Contribution

It provides a comprehensive comparison of neutral and charged anyon fluids and discusses the necessity of beyond-RPA approaches for accurate physical descriptions.

Findings

Charged anyon fluids may exhibit superconductivity at finite temperatures.

Traditional RPA and SCF methods are equivalent but insufficient for certain phenomena.

Advanced theories beyond Hartree-Fock are needed for flux quantization and vortex formation.

Abstract

(Review) Properties of neutral and charged anyon fluids are examined, with the main focus on the question whether or not a charged anyon fluid exhibits a superconductivity at zero and finite temperature. Quantum mechanics of anyon fluids is precisely described by Chern-Simons gauge theory. The random phase approximation (RPA), the linearized self-consistent field method (SCF), and the hydrodynamic approach employed in the early analysis of anyon fluids are all equivalent. Relations and differences between neutral and charged anyon fluids are discussed. It is necessary to go beyond RPA and the linearized SCF, and possively beyond the Hartree-Fock approximation, to correctly describe various phenomena such as the flux quantization, vortex formation, and phase transition. Topics includes: Anyons, Aharonov-Bohm effect, Chern-Simons gauge theory, Hartree-Fock ground state, RPA and SCF, Path integral representation, RPA = linearized SCF, Response functions, Phonons and plasmons, Hydrodynamic description, Effective theory, Meissner effect at zero and finite temperature, de Haas - van Alphen effect in SCF, Thermodynamic potential in inhomogeneous fields, T_c, Other important issues. (To appear in Int. J. Mod. Phys. B)