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Numerical Investigation of the Cumulant Expansion for Fourier Path Integrals

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7134)

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.

Keywords

  • path integral
  • Monte Carlo
  • cumulant expansion

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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

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28144-0

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