  Many problems in quantum dynamics can be cast as the decay of a single
quantum state into a continuum. The time-dependent overlap with the initial
state, called the fidelity, characterizes this decay. We derive an analytic
expression for the fidelity after a quench to an ergodic Hamiltonian. The
expression is valid for both weak and strong quenches, and timescales before
finiteness of the Hilbert space limits the fidelity. It reproduces initial
quadratic decay and asymptotic exponential decay with a rate which, for strong
quenches, differs from Fermi's golden rule. The analysis relies on the
statistical Jacobi approximation (SJA), which was originally applied in nearly
localized systems, and which we here adapt to well-thermalizing systems. Our
results demonstrate that the SJA is predictive in disparate regimes of quantum
dynamics.
