Fermi gas response to non-adiabatic switching of external potential

Abstract

We compute analytically the distribution function P(E) for the energy E acquired by a Fermi gas after being subjected to an arbitrary time-dependent external potential (switching event). We relate the distribution function to a solution of a matrix Riemann-Hilbert problem and present explicit formulae for the low order cumulants of P(E). These general results are used to find the distribution of dissipated energy in a biased quantum point contact.