Correlation functions are of interest due to their explanation of how many-bodied systems interact, specifically how a measureable at a given time relates to its initial value.  Ultimately, correlation functions can be related to physical observables such as diffusion coefficients for a given substance. Therefore, proposing a method for the evaluation correlation functions that maintains accuracy yet is computationally efficient becomes quite beneficial. This work acts as a proof of concept which implements a Monte Carlo approach to correlation function calculations of model systems brought into favorable forms through the utilization of cyclic invariance.  To avoid the famous 'sign problem', the current formulation dampens the oscillations that are normally present in said functions while avoiding the  insertion of multiple sets of continuous states, thereby keeping the computational cost reasonable.  A statistical analysis and justification of the new method is shown for harmonic and anharmonic model systems.

Analysis of correlation functions using cyclic invariance

247th National Meeting (2014)

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