Loschmidt echoes in two-body random matrix ensembles

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.