Title: Disordered Quantum Wires: Microscopic origins of the DMPK theory
Abstract: We study the electronic transport properties of the Anderson
model on a
strip, modeling a quasi one-dimensional disordered quantum wire.
For the tranfer matrices of the wire, we derive a stochastic
differential equation,
thus relating the random matrix theory of quantum transport to a
microscopic model.
The conductance of the wire is determined by the singular values of the
transfer matrix, which solve the DMPK equation, an SDE with singular
repulsion coefficients.
After verifying the existence of a unique strong solution to this
equation, we are able to proof Ohm's law in the thick-wire limit.
This talk presents joint work with Sven Bachmann and Wojciech De Roeck.