Heating and cooling of quantum gas by eigenstate Joule expansion

We investigate the Joule expansion of an interacting quantum gas in an energy eigenstate. The Joule expansion occurs when two subsystems of different particle density are allowed to exchange particles. We demonstrate numerically that the subsystems in their energy eigenstates evolves unitarily into the global equilibrium state in accordance with the eigenstate thermalization hypothesis. We find that the quantum gas changes its temperature after the Joule expansion with a characteristic inversion temperature T_{I}. The gas cools down (heats up) when the initial temperature is higher (lower) than T_{I}, implying that T_{I} is a stable fixed point, which is contrasted to the behavior of classical gases. Our work exemplifies that transport phenomena can be studied at the level of energy eigenstates.