Spectral Properties of the Quantum Random Energy Model

Simone Warzel
Technische Universitaet Muenchen
October 23, 2013

The quantum random energy model is a random matrix of Schroedinger type: a Laplacian on the hypercube plus a random potential. It features in various contexts from mathematical biology to quantum information theory as well as an effective description of (de)localization in many particle systems. Among its interesting properties is a first-order phase transition of the ground-state depending on the strength of the disorder.

Diffusion from deterministic dynamics

Antti Kupiainen
University of Helsinki; Member, School of Mathematics
October 24, 2013

I discuss a renormalization group method to derive diffusion from time reversible quantum or classical microscopic dynamics. I start with the problem of return to equilibrium and derivation of Brownian motion for a quantum particle interacting with a field of phonons or photons and then discuss how the method could be extended to classical coupled maps or coupled Hamiltonian systems.