# Dario Poletti: From conserved quantities to the emergence of slow relaxation and steady currents

The understanding of the relaxation of large quantum systems has received an important boost from the point of view of pure state quantum statistical mechanics, and in particular from the eigenstate thermalization hypothesis. At the same time, the dynamics of quantum systems has been investigated by out of time ordered correlators. Interestingly it was shown, using hydrodynamic theory, that such correlators relax algebraically in the presence of conserved quantities. Here we show how such slow relaxation can be expected from the eigenstate thermalization hypothesis.

At the same time, conserved quantities can lead to the phenomenon of pre-thermalization. Here we show that considering two large non-integrable systems weakly coupled to each other, one can show that in the thermodynamic limit a steady current between the two will emerge, and that this current is typical.