Infrared Catastrophe in Fermi Gases with Local Scattering Potentials

We prove that the ground state of a system of $N$ fermions is orthogonal to the ground state in the presence of a finite range scattering potential, as $N\to \infty$. This implies that the response to application of such a potential involves only emission of excitations into the continuum, and that certain processes in Fermi gases may be blocked by orthogonality in a low-$T$, low-energy limit.