One of the most straightforward ways to study thermal properties beyond linear
response is to monitor the relaxation of an arbitrarily large left-right
temperature gradient TL−TR. In one-dimensional systems which support ballistic
thermal transport, the local energy currents ⟨j(t)⟩ acquire a nonzero value at
long times, and it was recently investigated whether or not this steady state
fulfills a simple additive relation ⟨j(t→∞)⟩=f(TL)−f(TR) in integrable models.
In this paper, we probe the nonequilibrium dynamics of the Hubbard chain using
density matrix renormalization group (DMRG) numerics. We show that the above
form provides an effective description of thermal transport in this model;
violations are below the finite-time accuracy of the DMRG. As a second setup,
we study how an initially equilibrated system radiates into different
nonthermal states (such as the vacuum)
