Physics – Quantum Physics
Scientific paper
2003-02-26
Phys. Rev. E 68, 056208 (2003).
Physics
Quantum Physics
Added references, small textual improvements
Scientific paper
10.1103/PhysRevE.68.056208
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.
Heller Eric J.
Vanicek Jiri
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