## Abstract / Description of output

A general framework is proposed for the numerical approximation of Feynman-Kac path integrals in the context of quantum statistical mechanics. Each infinite-dimensional path integral is approximated by a Riemann integral over a finite-dimensional Sobolev space by restricting the integrand to a subspace of all admissible paths. Through this process, a wide class of methods is derived, with each method corresponding to a different choice for the approximating subspace. It is shown that the traditional "short-time" approximation and "Fourier discretization" can be recovered by using linear and spectral basis functions, respectively. As an illustration of the flexibility afforded by the subspace approach, a novel method is formulated using cubic elements and is shown to have improved convergence properties when applied to model problems.

Original language | English |
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Pages (from-to) | 472-483 |

Number of pages | 12 |

Journal | Journal of Computational Physics |

Volume | 185 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Mar 2003 |

## Keywords / Materials (for Non-textual outputs)

- Feynman-Kac path integrals
- Functional integration
- Path integral methods
- Quantum statistical mechanics