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While there is still no complete consensus on the interpretation of these experimental results they triggered a number of theoretical and even more numerical investigations. We shall brieflylist just the most important ones, first regarding quantum fidelity. Using the semiclassical expansion of the quantum propagator Jalabert and Pastawski [7] derived a perturbation independent quantum fidelity decay for localized initial states and chaotic dynamics, also called “Lyapunov decay” due to its dependence on the Lyapunov exponent.
1. Linear response regime for Lipschitz continuous initial density . . . . . . . . . . . . . . . . . . . . . . . . . 2. Linear response regime for discontinuous initial density . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. General (multi-)Lyapunov decay for chaotic few body systems . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Asymptotic long time decay for chaotic dynamics . . . .
1. Limit of weak coupling, diagonal S-matrix elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Rescaled Breit–Wigner approximation and the perturbative regime . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Rescaled Breit–Wigner approximation and linear response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .