# Orthogonality catastrophe induced by a magnetic perturbation

Anderson’s orthogonality catastrophe (AOC) is a phenomenon appearing in  perturbed Fermi gases. P. W. Anderson in 1967 found that the ground  state of a free Fermi gas in the thermodynamic limit is orthogonal to  the ground state of the system with an external potential. He gave the  leading asymptotics of the overlap of the two ground states which is of  order $N^{-\gamma}$ . Here $N$ is the particle number and $\gamma$ a  constant which depends on scattering parameters of the potential.
30  years later I. Affleck stated that the exponent $\gamma$ in AOC, up to  multiples of $\pi$, is equal to the finite size energy (FSE), the  coefficient of the $1/N$-term of the asymptotic expansion of  the difference of the ground state energies of the free and the  perturbed system. However, a mathematically rigorous study of AOC and  FSE has not been carried out until recently, where Anderson’s asymptotic  expansion has been verified for certain systems by groups in München and  Hagen. In this talk we will present some new mathematical results on AOC  and the energy  difference.