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Semiclassical approach to the quantum Loschmidt echo in deep quantum regions: from validity to breakdown

Semiclassical results are usually expected to be valid in the semiclassical regime. An interesting question is, in models in which appropriate effective Planck constants can be introduced, to what extent will a semiclassical prediction stay valid when the effective Planck constant is increased? In this paper, we numerically study this problem, focusing on semiclassical predictions for the decay of the quantum Loschmidt echo in deep quantum regions. Our numerical simulations, carried out in the chaotic regime in the sawtooth model and in the kicked rotator model and also in the critical region of a 1D Ising chain in transverse field, show that the semiclassical predictions may work even in deep quantum regions, in particularly, for perturbation strength in the so-called Fermi-Golden-rule regime.