Characterization of microstates for confined systems and associated scale-dependent continuum fields via Fourier coefficients

A.I. Murdoch, D. Bedeaux

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    The phase space description of a system of N point masses confined to a rectangular box is shown to be equivalent to knowledge of a minimal set of 6N complex Fourier coefficients associated with the discrete distributions of matter and momentum. The corresponding real-valued truncated Fourier series yield continuum densities of particle number and momentum at a specific length scale, min . Continuum descriptions at any scale >min correspond to further truncation of these series. Attention is drawn to the relevance of the results to recent investigations of reproducible macroscopic behaviour, at a given pair and - of length time scales, using projection operator methodology.
    Original languageEnglish
    Pages (from-to)6495-6508
    Number of pages13
    JournalJournal of Physics A: Mathematical and Theoretical
    Issue number33
    Publication statusPublished - 10 Aug 2001



    • Fourier coefficients
    • reproducible macroscopic behaviour
    • projection operator methodology
    • physics

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