Existence of a unique strong solution to the DMPK equation

2012/05/15 by Butz, Maximilian
#60B20 #60H10 #60K35 #82D77 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1205.3396

Abstract

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.

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