Ultrafast dynamics of cold Fermi gas after a local quench

We consider energy dynamics of two initially independent reservoirs A and B filled with a cold Fermi gas coupled and decoupled by two quantum quenches following one another. The energy change in the system adds up the heat transferred between A and B and the work done by the quench to uncouple the reservoirs. In case when A and B interact for a short time, we find an energy increase in both reservoirs upon decoupling. This energy gain results from the quenches' work and does not depend on the initial temperature imbalance between the reservoirs. We relate the quenches' work to the mutual correlations of A and B expressed through their von Neumann entropies. Utilizing this relation, we show that once A and B become coupled, their von Neumann entropies grow (on a timescale of the Fermi time) faster than thermal transport within the system. For a metallic setup, this implies the characteristic timescale of correlations' growth τ to be in the femtosecond range, while for the ultracold atoms, we expect τ ~ 0.1 ms.