Jiři Vaniček: Dephasing representation of quantum fidelity
Due to the Heisenberg uncertainty principle, various classical systems differing only on the scale smaller than Planck's cell correspond to the same quantum system. This fact is used to find a unique semiclassical representation without the Van Vleck determinant, applicable to a large class of correlation functions expressible as quantum fidelity (Loschmidt echo). As in the Feynman path integral formulation of quantum mechanics, all contributing trajectories have the same amplitude and differ only in their phase: that is why it is denoted the ``dephasing representation.'' Counterintuitively, all of fidelity decay is due to destructive interference and none due to the decay of classical overlaps. By relating the present approach to the problem of existence of true trajectories near numerically-computed chaotic trajectories, the approximation is justified for any system in which the shadowing theorem holds. However, numerical implementation only requires computing actions along the unperturbed trajectories and not finding the shadowing trajectories. Dephasing representation appears to be an efficient and accurate method to compute quantum fidelity in nonuniversal regimes of fidelity decay, in mixed dynamical systems, for local and nonlocal pure or mixed initial quantum states, and in systems with many degrees of freedom where exact quantum calculations are impossible.
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