Haldane Exclusion Statistics and the Boltzmann Equation

TL;DR

This paper extends the Boltzmann equation to include Haldane exclusion statistics, deriving a generalized collision term, and applies it to calculate response functions and relaxation times in quantum systems.

Contribution

It introduces a generalized collision term in the Boltzmann equation for particles obeying Haldane exclusion statistics, enabling new calculations in quantum transport.

Findings

Derived the golden rule factor for quantum transitions with Haldane statistics

Calculated the density response function of a 1D electron gas with new statistics

Estimated nuclear spin relaxation times using the modified golden rule

Abstract

We generalize the collision term in the one-dimensional Boltzmann-Nordheim transport equation for quasiparticles that obey the Haldane exclusion statistics. For the equilibrium situation, this leads to the ``golden rule'' factor for quantum transitions. As an application of this, we calculate the density response function of a one-dimensional electron gas in a periodic potential, assuming that the particle-hole excitations are quasiparticles obeying the new statistics. We also calculate the relaxation time of a nuclear spin in a metal using the modified golden rule.