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.