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We compute analytically the distribution function P(E) for the energy Eacquired by a Fermi gas after being subjected to an arbitrary time-dependentexternal potential (switching event). We relate the distribution function to asolution of a matrix Riemann-Hilbert problem and present explicit formulae forthe low order cumulants of P(E). These general results are used to find thedistribution of dissipated energy in a biased quantum point contact.Comment: 17 pages LaTeX2e,2 real postscript figures and 12 auxilary files:  output from feynmp. Needs feynmp.sty to draw Feynman diagram

Fermi gas response to the nonadiabatic switching of an external potential