Analytic continuation and incomplete data tomography

Analytic Continuation of QMC Data

2 Formalism 3 2.1 Green’s functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Bayesian statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Prior probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Likelihood function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.5 Details of the ...

Green currents and analytic continuation

On Effective Analytic Continuation

Until now, the area of symbolic computation has mainly focused on the manipulation of algebraic expressions. It would be interesting to apply a similar spirit of “exact computations” to the field of mathematical analysis. One important step for such a project is the ability to compute with computable complex numbers and computable analytic functions. Such computations include effective analytic...

Maximum Entropy Analytic Continuation of Quantum Monte Carlo Data

We present a pedagogical discussion of the Maximum Entropy Method which is a precise and systematic way of analytically continuing Euclidean-time quantum Monte Carlo results to real frequencies. Here, Bayesian statistics are used to determine which of the infinite number of real-frequency spectra are consistent with the QMC data is most probable. Bayesian inference is also used to qualify the s...

Image Reconstruction from Incomplete Data