Solvable model of multichannel localization

A model of the disordered conductor with a fixed number of conducting channels, N, is suggested. A longitudinal motion of electrons is accompanied by random transverse hoppings. This scheme is characterized by the same tunneling probability from any channel into another one. Thus, the metallic properties in the transverse direction are postulated and a longitudinal localization becomes an object of investigation. The following results are obtained. Far from the edges of the conductivity band, where disorder can be regarded as a weak one, the following values are calculated: the density of states ν(ɛ), the correlator of densities in the infinitely remotest moments of time $p_{\infty }$(x), and the probability function W(scrR) for the participation ratio scrR=FdV ${\psi }^4$/( F dV ${\psi }^2$ ${)}^2$ . The density of states per unit length ν(ɛ)=N/π$v_F$ depends additively on a number of channels. The functions $p_{\infty }$(x),W(scrR) which describe localization are expressed in terms of the universal equations, where N manifests itself only in the combinations ν(ɛ) and $l_c$=l(N+1)/2. .AE