@article {vanivcek2003semiclassical,
	title = {Semiclassical evaluation of quantum fidelity},
	journal = {Physical Review E},
	volume = {68},
	year = {2003},
	pages = {056208},
	publisher = {APS},
	abstract = {We present a numerically feasible semiclassical (SC) method to evaluate quantum fidelity decay (Loschmidt echo) 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 also 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 1070 semiclassical contributions. Remarkably, it also explicitly contains the {\textquotedblleft}building blocks{\textquotedblright} 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 and show that within this approximation, the so-called {\textquotedblleft}diagonal approximation{\textquotedblright} is automatic and does not require ensemble averaging.},
	url = {https://doi.org/10.1103/PhysRevE.68.056208},
	author = {Van{\'{\i}{\v c}ek, Ji{\v r}{\'{\i} and Heller, EricJ.}
}
