  Electronic transport properties in a disordered quantum wire are very well
described by the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation, which describes
the evolution of the transmission eigenvalues as a function of the length of a
multichannel conductor. However, the DMPK equation is restricted to quasi one
dimensional systems only. We derive a generalized DMPK equation for higher
dimensions, containing dependence on the dimensionality through the properties
of the transmission eigenvectors, by making certain statistical assumptions
about the transfer matrix. An earlier phenomenological generalization is
obtained as a special case.
