Energy spread and current-current correlation in quantum systems

We consider energy (heat) transport in quantum systems, and establish a relationship between energy spread and energy current-current correlation function within linear response theory. The energy current-current correlation is related to thermal conductivity by the Green-Kubo formula, and thus this relationship allows us to extract heat conductivity from the energy spread process. As an example, we investigate a spinless fermion model. At high temperatures, we find good agreement between numerical results and theory. At low temperatures and for finite systems, boundary terms however need to be taken into account due to the finite-size effect. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015