Loschmidt echo in Fermi-golden-rule regime: M(t) = exp(-sigma^2 delta^2 t^2 / hbar^2)

Loschmidt echo / fidelity decay framework. Setup: prepare |psi>, evolve forward under H_0 for time t, reverse-evolve under H_1 = H_0 + delta*V. The Loschmidt echo M(t) = |<psi|exp(iH_1 t/hbar)exp(-iH_0 t/hbar)|psi>|^2 measures how rapidly…