The long-time average of the Loschmidt echo (or its rate function) shows nonanalytic behavior when the post-quench parameter crosses a phase transition, and its second derivative equals four times the fidelity susceptibility for small quenches.
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Signature of nonequilibrium quantum phase transition in the long time average of Loschmidt echo
The long-time average of the Loschmidt echo (or its rate function) shows nonanalytic behavior when the post-quench parameter crosses a phase transition, and its second derivative equals four times the fidelity susceptibility for small quenches.