Generalized moments of spectral functions from short-time correlation functions

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dc.creatorPredescu, Cristian
dc.date2006-02-12
dc.date2006-02-26
dc.date.accessioned2026-07-07T07:02:58Z
dc.date.available2026-07-07T07:02:58Z
dc.descriptionWe present an integral transformation capable of extracting moments of arbitrary Paley-Wiener entire functions against a given spectral distribution based solely on short-time values of the correlation function in a small open disk about the origin. The integral is proven to converge absolutely to the expected result for those correlation functions that can be extended analytically to the entire complex plane, with the possible exception of two branch cuts on the imaginary axis. It is only the existence of an analytic continuation that is required and not the actual values away from the small disk about the origin. If the analytic continuation exists only for a strip |Im(z)| < τ_0, then the integral transformation remains valid for all Paley-Wiener functions obtained by Fourier-Laplace transforming a compactly supported distribution, with the support included in the interval (-2τ_0, 2τ_0). Finally, if the support of the distribution is contained in the interval $(-τ_0, τ_0)$, then the generalized moment can be evaluated from the short-time values of the correlation function exponentially fast
dc.description13 pages; several typos have been removed; a new section (V) has been added; it deals with the numerical implementation of the formula
dc.identifierhttps://arxiv.org/abs/math-ph/0602027
dc.identifierhttp://arxiv.org/abs/math-ph/0602027
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/108797
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectChemical Physics
dc.titleGeneralized moments of spectral functions from short-time correlation functions
dc.typetext

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