Zero-bias anomaly in disordered wires

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