Relaxation in Luttinger liquids: Bose-Fermi duality

We explore the lifetime of excitations in a dispersive Luttinger liquid. We perform a bosonization supplemented by a sequence of unitary transformations that allows us to treat the problem in terms of weakly interacting quasiparticles. The relaxation described by the resulting Hamiltonian is analyzed by bosonic and (after a refermionization) by fermionic perturbation theory. We show that the fermionic and bosonic formulations of the problem exhibit a remarkable strong-weak coupling duality. Specifically, the fermionic theory is characterized by a dimensionless coupling constant λ=m∗l2T and the bosonic theory by λ-1, where 1/m∗ and l characterize the curvature of the fermionic and bosonic spectra, respectively, and T is the temperature.