Equilibration in a chiral Luttinger liquid

We explore the weak-strong-coupling Bose-Fermi duality in a model of a single-channel integer or fractional quantum Hall edge state with a finite-range interaction. The system is described by a chiral Luttinger liquid with non-linear dispersion of bosonic and fermonic excitations. We use the bosonization, a unitary transformation, and a refermionization to map the system onto that of weakly interacting fermions at low temperature $T$ or weakly interacting bosons at high $T$. We calculate the equilibration rate which is found to scale with temperature as $T^5$ and $T^{14}$ in the high-temperature (“bosonic”) and the low-temperature (“fermonic”) regimes, respectively. The relaxation rate of a hot particle with the momentum $k$ in the fermonic regime scales as $k^7{T}^7$.