A test on analytic continuation of thermal imaginary-time data

A test on analytic continuation of thermal imaginary-time data,10.1140/epjc/s10052-011-1619-0,European Physical Journal C,Y. Burnier,M. Laine,L. Methe

A test on analytic continuation of thermal imaginary-time data   (Citations: 2)
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Some time ago, Cuniberti et al. have proposed a novel method for analytically continuing thermal imaginary-time correlators to real time, which requires no model input and should be applicable with finite-precision data as well. Given that these assertions go against common wisdom, we report on a naive test of the method with an idealized example. We do encounter two problems, which we spell out in detail; this implies that systematic errors are difficult to quantify. On a more positive note, the method is simple to implement and allows for an empirical recipe by which a reasonable qualitative estimate for some transport coefficient may be obtained, if statistical errors of an ultraviolet-subtracted imaginary-time measurement can be reduced to roughly below the per mille level.
Journal: European Physical Journal C - EUR PHYS J C , vol. 71, no. 4, pp. 1-7, 2011
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    • ...Fig. 33. The complex planes, basic functions and analytic structures (figure from [182])...
    • ...It was recently reviewed and tested in a realistic example by Burnier et al. [182]...
    • ...The practical recipe that the result (312) suggests is to truncate the sum (311) at some � = � max [182]...
    • ...physical condition put forward in [182] is to require that G(t) t→∞ → 0 [35], which is equivalent to � N =1 a� =0 . We...
    • ...The analysis of [182], where the narrowest feature of the (resummed perturbative) spectral function has width ≈ πT , then shows that one needs a relative error at least as small as 10 −3 on the UV-subtracted Euclidean correlator and Nt = 24 to reconstruct semi-quantitatively the spectral function...

    Harvey B. Meyer. Transport properties of the quark-gluon plasma

    • ...The inherent uncertainties related to analytic continuation from Euclidean numerical data have also been looked into, and it appears that it might be feasible to carry through the program at least on the qualitative level [20]...

    M. Laine. Heavy flavour kinetic equilibration in the confined phase

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