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Many problems in quantum dynamics can be cast as the decay of a singlequantum state into a continuum. The time-dependent overlap with the initialstate, called the fidelity, characterizes this decay. We derive an analyticexpression for the fidelity after a quench to an ergodic Hamiltonian. Theexpression is valid for both weak and strong quenches, and timescales beforefiniteness of the Hilbert space limits the fidelity. It reproduces initialquadratic decay and asymptotic exponential decay with a rate which, for strongquenches, differs from Fermi's golden rule. The analysis relies on thestatistical Jacobi approximation (SJA), which was originally applied in nearlylocalized systems, and which we here adapt to well-thermalizing systems. Ourresults demonstrate that the SJA is predictive in disparate regimes of quantumdynamics.

Beyond Fermi's golden rule with the statistical Jacobi approximation