  Integrable models such as the spin-1/2 Heisenberg chain, the Lieb-Liniger or
the one-dimensional Hubbard model are known to avoid thermalization, which was
also demonstrated in several quantum-quench experiments. Another dramatic
consequence of integrability is the zero-frequency anomaly in transport
coefficients, which results in ballistic finite-temperature transport, despite
the presence of strong interactions. While this aspect of nonergodic dynamics
has been known for a long time, there has so far not been any unambiguous
experimental realization thereof. We make a concrete proposal for the
observation ballistic transport via local quantum quench experiments in
fermionic quantum-gas microscopes. Such an experiment would also unveil the
coexistence of ballistic and diffusive transport channels in one and the same
system and provide a means of measuring finite-temperature Drude weights. The
connection between local quenches and linear-response functions is established
via time-dependent Einstein relations.
