Abstract
Recent developments associated with the cumulant expansion of the Fourier path integral Monte Carlo method are illustrated numerically using a simple one-dimensional model of a quantum fluid. By calculating the Helmholtz free energy of the model we demonstrate that 1) recently derived approximate asymptotic expressions for the cumulants requiring only one-dimensional quadrature are both accurate and viable, 2) expressions through third-cumulant order are significantly more rapidly convergent than either the primitive Fourier method or the partial average method, and 3) the derived cumulant convergence orders can be verified numerically.
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Plattner, N., Kunikeev, S., Freeman, D.L., Doll, J.D. (2012). Numerical Investigation of the Cumulant Expansion for Fourier Path Integrals. In: Jónasson, K. (eds) Applied Parallel and Scientific Computing. PARA 2010. Lecture Notes in Computer Science, vol 7134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28145-7_2
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DOI: https://doi.org/10.1007/978-3-642-28145-7_2
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