Semiclassical evaluation of quantum fidelity

Abstract

We present a numerically feasible semiclassical (SC) method to evaluate quantum fidelity decay (Loschmidt echo, FD) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a uniform SC expression not only is tractable but it gives remarkably accurate numerical results for the standard map in both the Fermi-golden-rule and Lyapunov regimes. Because it allows Monte Carlo evaluation, the uniform expression is accurate at times when there are 10^70 semiclassical contributions. Remarkably, it also explicitly contains the ``building blocks'' of analytical theories of recent literature, and thus permits a direct test of the approximations made by other authors in these regimes, rather than an a posteriori comparison with numerical results. We explain in more detail the extended validity of the classical perturbation approximation (CPA) and show that within this approximation, the so-called ``diagonal approximation'' is automatic and does not require ensemble averaging.

Added references, small textual improvements

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Cited by in corpus (59)

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• Stability of Quantum Motion: Beyond Fermi-golden-rule and Lyapunov decay
• Relation of exact Gaussian basis methods to the dephasing representation: Theory and application to time-resolved electronic spectra
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• Quantum Reversibility and Echoes in Interacting Systems
• Hyperfine Spectroscopy of Optically Trapped Atoms
• Mesoscopic Fluctuations of the Loschmidt Echo
• Engineering fidelity echoes in Bose-Hubbard Hamiltonians
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• Classical versus quantum errors in quantum computation of dynamical systems
• Loschmidt echoes in two-body random matrix ensembles
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