Resistivity of a one-dimensional interacting quantum fluid

The frequency and temperature dependence of the conductivity of a one-dimensional fermion system with attractive interactions is studied by using a renormalization-group technique. At half filling the real part of the conductivity has both a {δ}({ω}) part and a divergent frequency behavior ω^-ν at finite frequencies, where {ν} is a nonuniversal exponent depending on the interactoins. For the particular case of the attractive Hubbard model, logarithmic corrections appear and the conductivity behaves as 1/[{ω} log₁₀²({ω})], plus a {δ}({ω}) part. Away from half filling the conductivity has a {δ}({ω}) part and a gap up to a critical frequency ωc, where ωc is proportional to the doping with a prefactor depending on the interactions. The results obtained for the fermion model can be straightforwardly extended to the conductivity of an interacting one-dimensional boson model.