A new class of solutions of the Dorokhov–Mello–Pereyra–Kumar equation

Abstract

We introduce and discuss a new class of solutions of the Dorokhov–Mello–Pereyra–Kumar(DMPK) equation in which some of the eigenvalues are grouped into clusters which areconserved in the asymptotic large distance limit (i.e. as the length of the wireincreases). We give an explicit expression for the asymptotic expansion of thesesolutions and suggest some possible applications. In particular, these new solutionscould be useful for avoiding the quasi-one-dimensional constraint in the DMPKequation and for studying the crossover between the metallic and insulating phases.