Zero-Bias Anomaly in Disordered Wires

We calculate the low-energy tunneling density of states ν(ɛ,T) of an N-channel disordered wire, taking into account the electron-electron interaction nonperturbatively. The finite scattering rate 1/τ results in a crossover from the Luttinger liquid behavior at higher energies, ν~ɛ^α, to the exponential dependence ν(ɛ,T = 0)~exp(-ɛ^*/ɛ) at low energies, where ɛ^*~1/(Nτ). At finite temperature T, the tunneling density of states depends on the energy through the dimensionless variable ɛ/(ɛ^*T). At the Fermi level ν(ɛ = 0,T)~exp(-(ɛ^*/T) ).