Anomalous transport in low-dimensional many-body systems: Condensed matter meets ultracold atomic gases

Transport in quasi-one dimensional strongly-correlated electron systems can be strongly inhibited not only because of reduced phase space for scattering but also due to the existence of nontrivial conservation laws. These can fully prevent intrinsic scattering mechanisms from relaxing currents, resulting in divergent conductivities. Theoretical research in this field is strongly motivated by the experimental observation of surprisingly large thermal conductivities in many quasi-1D quantum magnets. In this talk, I will discuss transport properties of several models that are relevant in the context of such experiments, for which we apply exact numerical methods to compute transport coefficients. More recent experimental progress gives access to real-time resolved heat-imaging in quantum magnets, which we model by means of time-dependent numerical simulations. The fundamental theoretical question of ballistic versus diffusive dynamics in strongly interacting many-body systems can be addressed in non-equilibrium experiments with ultra-cold atomic gases as well. Our numerical results are in excellent agreement with experimental data, both unambiguously showing that even systems with infinitely strong interactions can exhibit ballistic dynamics, protected by non-trivial conservation laws.