Zero-bias anomaly in disordered wires

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