Dispersion Relations for Waves propagating in Composite Fermion Gases

TL;DR

This paper investigates wave propagation in composite fermion gases at filling factor 1/2 using linearized Uehling-Uhlenbeck equations, revealing how magnetic fields influence dispersion relations in quantum gases.

Contribution

It introduces a novel analysis of dispersion relations in composite fermion gases considering magnetic field effects and Pauli-blocking parameters.

Findings

Magnetic fields induce anomalous dispersion relations.

Dispersion relations vary with particle statistics (Bose, Boltzmann, Fermi).

Linearized Uehling-Uhlenbeck equations effectively model wave propagation.

Abstract

The discrete Uehling-Uhlenbeck equations are solved to study the propagation of plane (sound) waves in a system of composite fermionic particles with hard-sphere interactions and the filling factor ($\nu$) being 1/2. The Uehling-Uhlenbeck collision sum, as it is highly nonlinear, is linearized firstly and then decomposed by using the plane wave assumption. We compare the dispersion relations thus obtained by the relevant Pauli-blocking parameter $B$ which describes the different-statistics particles for the quantum analog of the discrete Boltzmann system when $B$ is positive (Bose gases), zero (Boltzmann gases), and negative (Fermi Gases). We found, as the effective magnetic field being zero ($\nu$=1/2 using the composite fermion formulation), the electric and fluctuating (induced) magnetic fields effect will induce anomalous dispersion relations.