Existence of a unique strong solution to the DMPK equation

Maximilian Butz

Published 2012-05-15, updated 2013-01-08Version 2

For the transmission of electrons in a weakly disordered strip of material Dorokhov, Mello, Pereyra and Kumar (DMPK) proposed a diffusion process for the transfer matrices. The correspoding transmission eigenvalues satisfy the DMPK stochastic differential equations, like Dyson Brownian motion in the context of GOE/GUE random matrices. We control the singular repulsion terms of this SDE with a stopping-time argument, and its degenerate initial condition by an approximation procedure, and thereby establish the DMPK equation to be well posed.