Title: Nonequilibrium transport in classical and quantum low dimensional
systems

Abstract:  The  understanding of  the  underlying  dynamical mechanisms  which
determine  the macroscopic laws  of transport  is a  long standing  problem of
nonequilibrium statistical mechanics.  Given a particular classical, many-body
Hamiltonian system, neither  phenomenological nor fundamental transport theory
can predict whether  or not this specific Hamiltonian  system yields an energy
transport governed  by the Fourier's law  of heat conduction. In  this talk we
will discuss the relation between  the microscopic dynamics properties and the
onset of  macroscopic transport.  At the  classical side, we  will analyze the
heat and particle transport in open ergodic billiards connected to two or more
thermal  particle  reservoirs  and  show  that in  the  Knudsen  limit,  exact
expressions for all the linear transport coefficients can be obtained in terms
of  the billiard  properties. When  the  interaction is  weak, an  approximate
description of  cross transport is yet  possible. At the quantum  side we will
study  the problem  of  heat conduction  in  quantum spin  chains and  discuss
evidence, linking the onset of Fourier's law with that of quantum chaos.