N ov 2 00 3 A random matrix formulation of fidelity decay

We propose to study echo dynamics in a random matrix framework, where we assume that the perturbation is time independent, random and orthogonally invariant. This allows to use a basis in which the unperturbed Hamiltonian is diagonal and its properties are thus largely determined by its spectral statistics. We concentrate on the effect of spectral correlations usually associated to chaos and disregard secular variations in spectral density. We obtain analytic results for the fidelity decay in the linear response regime. To extend the domain of validity, we heuristically exponentiate the linear response result. The exponentiation, exact in the perturbative limit, agrees well with chaotic dynamical systems even in the transition region between the " Fermi golden rule " and the perturbative regimes. In general, we find that spectral stiffness enhances fidelity.