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.
This talk is based on joint work with P. Otte and W. Spitzer.
