Statistics of the work distribution for a quenched Fermi gas

The local quench of a Fermi gas, giving rise to the Fermi edge singularity and the Anderson orthogonality catastrophe, is an analytically tractable out of equilibrium problem in condensed matter. It describes the generic physics which occurs when a localized scattering potential is suddenly introduced in a Fermi sea leading to a brutal disturbance of its quantum state. It has recently been proposed that the effect could be efficiently simulated in a controlled manner using the tunability of ultra-cold atoms. In this work, we analyze the quench problem in a gas of trapped ultra-cold fermions from a thermodynamic perspective using the full statistics of the so called work distribution. The statistics of work are shown to provide an accurate insight into the fundamental physics of the process.