Fourier's law and many-body quantum systems

The topic of this article are transport properties of many-body quantum chains accompanying DMRG-type simulations of the Bose–Hubbard model. To set the stage, we first provide a very brief introduction to many-body quantum theory and tensor network approximations. Transport properties are studied via dynamical density correlation functions, in line with linear response theory. We observe diffusive behavior at “infinite temperature” T→∞. Finally, we mention other approaches to study transport, e.g., explicitly imposing a temperature gradient via thermal reservoirs at the boundary.