Density of states in coupled chains with off-diagonal disorder

We compute the density of states rho(varepsilon) in N coupled chains with random hopping. At zero energy, rho(varepsilon) shows a singularity that strongly depends on the parity of N. For odd N, rho(varepsilon) approximately 1/|varepsilonln (3)varepsilon|, with and without time-reversal symmetry. For even N, rho(varepsilon) approximately |lnvarepsilon| in the presence of time-reversal symmetry, while there is a pseudogap, rho(varepsilon) approximately |varepsilonlnvarepsilon|, in the absence of time-reversal symmetry.