  We first review the problem of a rigorous justification of Kubo's formula for
transport coefficients in gapped extended Hamiltonian quantum systems at zero
temperature. In particular, the theoretical understanding of the quantum Hall
effect rests on the validity of Kubo's formula for such systems, a connection
that we review briefly as well. We then highlight an approach to linear
response theory based on non-equilibrium almost-stationary states (NEASS) and
on a corresponding adiabatic theorem for such systems that was recently
proposed and worked out by one of us in [51] for interacting fermionic systems
on finite lattices. In the second part of our paper we show how to lift the
results of [51] to infinite systems by taking a thermodynamic limit.
