SEMINAIRE MERCREDI 7 JUIN 2006
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Jean Bellissard
Georgia Institute of Technology, School of
Mathematics and School of Physics, Atlanta GA, USA

Title: On Quantum Transport Theory for Solids

Abstract: Transport theory is a complex subject due to the interplay between several
scales in time, length and/or energy. Few striking effects in Solids will
be used as a motivation. We will review the heuristic leading to various
approximations and to the formalism used in such a situation: the local
equilibrium approximation, the Markov approximation, the adiabatic
approximation. We will also give the heuristic derivation of the
Green-Kubo formula for transport coefficients within the linear response
theory. Then we will discuss various rigorous problem to be investigated
and various results already obtained: existence of Markov semigroups for a
large class of realistic models describing electrons on a lattice,
one-to-one correspondence with XY-type quantum spin systems,
classification of Markov semigroups on various types of C*-algebras.
(work with R. Rebolledo, D. Spehner)