On the approximation of Feynman-Kac path integrals for quantum statistical mechanics

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dc.creatorBond, Stephen D.
dc.creatorLaird, Brian B.
dc.creatorLeimkuhler, Benedict J.
dc.date2000-07-06
dc.date.accessioned2026-07-07T02:38:09Z
dc.date.available2026-07-07T02:38:09Z
dc.descriptionDiscretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated by a Riemann integral over a finite-dimensional function space, by restricting the integration to a subspace of all admissible paths. Using this process, a wide class of methods can be derived, with each method corresponding to a different choice for the approximating subspace. The traditional ``short-time'' approximation and ``Fourier discretization'' can be recovered from this approach, using linear and spectral basis functions respectively. As an illustration, a novel method is formulated using cubic elements and is shown to have improved convergence properties when applied to a simple model problem.
dc.description4 pages, 2 figures, submitted to Physical Review Letters
dc.identifierhttps://arxiv.org/abs/cond-mat/0007112
dc.identifierhttp://arxiv.org/abs/cond-mat/0007112
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/16562
dc.subjectStatistical Mechanics
dc.titleOn the approximation of Feynman-Kac path integrals for quantum statistical mechanics
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