Zero-bias anomaly in disordered wires

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