Quantum Boltzmann equation of composite fermions interacting with a gauge field

Abstract

We derive the quantum Boltzmann equation (QBE) of composite fermions at/near the $ν= 1/2$ state using the non-equilibrium Green's function technique. The lowest order perturbative correction to the self-energy due to the strong gauge field fluctuations suggests that there is no well defined Landau-quasi-particle. Therefore, we cannot assume the existence of the Landau-quasi-particles {\it a priori} in the derivation of the QBE. Using an alternative formulation, we derive the QBE for the generalized Fermi surface displacement which corresponds to the local variation of the chemical potential in momentum space. {}From this QBE, one can understand in a unified fashion the Fermi-liquid behaviors of the density-density and the current-current correlation functions at $ν= 1/2$ (in the long wave length and the low frequency limits) and the singular behavior of the energy gap obtained from the finite temperature activation behavior of the compressibility near $ν= 1/2$. Implications of these results to the recent experiments are also discussed.