Zero-bias anomaly in disordered wires

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