Real time dynamics from quantum Monte Carlo data: A genetic algorithm approach

The intriguing task of evaluating, in a Quantum Monte Carlo simulation, the dynamic structure factor of a condensed matter sample, hence gaining informations about the elementry excitations which may be observed in a thermal neutrons scattering experiment, is yet a very delicate one. The difficulties arise because, in a simulation, dynamics takes place in the imaginary time domain, and analystic continuation is requied to translate the resutls into real time dynamical correlations functions. This is far from trivial since one has to care for the role of statistical noise, which, if not properly taken into account, may lead to uncontrolled incertaininties and only qualitatively interesting results. We suggest a new analystic continuation technique, relying on genetic optimization algorithms, and assuming the first few momenta as the only prior knolwedge about the spectral function. As an example, we show the results of the method when applied to the study of a sample of He-4 atoms at zero-temperature in the liquid phase.