We study the dynamics and thermalization of strongly correlated fermions in finite one-dimensional lattices after a quantum quench. Our calculations are performed using exact diagonalization. We focus on one- and two-body observables such as the momentum distribution function
[n(k)] and the density-density structure factor
[N(k)], respectively, and study the effects of approaching an integrable point. We show that while the relaxation dynamics and thermalization of
N(k) for fermions is very similar to the one of hardcore bosons, the behavior of
n(k) is distinctively different. The latter observable exhibits a slower relaxation dynamics in fermionic systems. We identify the origin of this behavior, which is related to the off-diagonal matrix elements of
n(k) in the basis of the eigenstates of the Hamiltonian. More generally, we find that thermalization occurs far away from integrability and that it breaks down as one approaches the integrable point.
Two conducting quantum systems coupled only via interactions can exhibit the phenomenon of Coulomb drag, in which a current passed through one layer can pull a current along in the other. However, in systems with particle-hole symmetry-for instance, the half filled Hubbard model or graphene near the Dirac point-the Coulomb drag effect vanishes to leading order in the interaction. Its thermal analog, whereby a thermal current in one layer pulls a thermal current in the other, does not vanish and is indeed the dominant form of drag in particle-hole symmetric systems. By studying a quantum quench, we show that thermal drag, unlike charge drag, displays a non-Fermi's golden rule growth at short times due to a logarithmic scattering singularity generic to one dimension. Exploiting the integrability of the Hubbard model, we obtain the long-time limit of the quench for weak interactions. Finally, we comment on thermal drag effects in higher dimensional systems.