Title: Microscopic Conductivity of Lattice Fermions at Equilibrium - Part II: Interacting Particles,
Abstract: We apply Lieb-Robinson bounds for multi-commutators we recently derived to
study the (possibly non-linear) response of interacting fermions at thermal
equilibrium to perturbations of the external electromagnetic field. This
analysis leads to an extension of the results for quasi-free fermions of
\cite{OhmI,OhmII} to fermion systems on the lattice with short-range
interactions. More precisely, we investigate entropy production and charge
transport properties of non-autonomous $C^{\ast }$-dynamical systems associated
with interacting lattice fermions within bounded static potentials and in
presence of an electric field that is time- and space-dependent. We verify the
1st law of thermodynamics for the heat production of the system under
consideration. In linear response theory, the latter is related with Ohm and
Joule's laws. These laws are proven here to hold at the microscopic scale,
uniformly with respect to the size of the (microscopic) region where the
electric field is applied. An important outcome is the extension of the notion
of conductivity measures to interacting fermions.