Loschmidt echoes in two-body random matrix ensembles

Abstract

Fidelity decay is studied for quantum many-body systems with a dominant independent particle Hamiltonian resulting, e.g., from a mean field theory with a weak two-body interaction. The diagonal terms of the interaction are included in the unperturbed Hamiltonian, while the off-diagonal terms constitute the perturbation that distorts the echo. We give the linear response solution for this problem in a random matrix framework. While the ensemble average shows no surprising behavior, we find that the typical ensemble member as represented by the median displays a very slow fidelity decay known as ``freeze.'' Numerical calculations confirm this result and show that the ground state even on average displays the freeze. This may contribute to explanation of the ``unreasonable'' success of mean field theories.