Nonequilibrium thermal transport and its relation to linear response

We study the real-time dynamics of spin chains driven out of thermal\nequilibrium by an initial temperature gradient T_L \\neq T_R using density\nmatrix renormalization group methods. We demonstrate that the nonequilibrium\nenergy current saturates fast to a finite value if the linear-response thermal\nconductivity is infinite, i.e. if the Drude weight D is nonzero. Our data\nsuggests that a nonintegrable dimerized chain might support such\ndissipationless transport (D>0). We show that the steady-state value J_E of the\ncurrent for arbitrary T_L \\neq T_R is of the functional form J_E=f(T_L)-f(T_R),\ni.e. it is completely determined by the linear conductance. We argue for this\nfunctional form, which is essentially a Stefan-Boltzmann law in this integrable\nmodel; for the XXX ferromagnet, f can be computed via thermodynamic Bethe\nansatz in good agreement with the numerics. Inhomogeneous systems exhibiting\ndifferent bulk parameters as well as Luttinger liquid boundary physics induced\nby single impurities are discussed briefly.\n