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

Murdoch, A.I. and Bedeaux, D. (2001) Characterization of microstates for confined systems and associated scale-dependent continuum fields via Fourier coefficients. Journal of Physics A: Mathematical and Theoretical, 34 (33). pp. 6495-6508. ISSN 0305-4470

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Abstract

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.