Topological phase transitions in the 1D multichannel Dirac equation with random mass and a random matrix model

We establish the connection between a multichannel disordered model --the 1D Dirac equation with $N\times N$ matricial random mass-- and a random matrix model corresponding to a deformation of the Laguerre ensemble. This allows us to derive exact determinantal representations for the density of states and identify its low energy ($\epsilon \to 0$) behaviour $\rho (\epsilon )\sim \mathrm{\mid }\epsilon {\mathrm{\mid }}^{\alpha -1}$. The vanishing of the exponent $\alpha$ for $N$ specific values of the averaged mass over disorder ratio corresponds to $N$ phase transitions of topological nature characterised by the change of a quantum number (Witten index) which is deduced straightforwardly in the matrix model.