Statistics of work and orthogonality catastrophe in discrete level systems: an application to fullerene molecules and ultra-cold trapped Fermi gases.

The sudden introduction of a local impurity in a Fermi sea leads to an anomalous disturbance of its quantum state that represents a local quench, leaving the system out of equilibrium and giving rise to the Anderson orthogonality catastrophe. The statistics of the work done describe the energy fluctuations produced by the quench, providing an accurate and detailed insight into the fundamental physics of the process. We present here a numerical approach to the non-equilibrium work distribution, supported by applications to phenomena occurring at very diverse energy ranges.