Moment and Continued Fraction Expansions of Time Autocorrelation Functions

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概要

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• Two representations of the Laplace transforms of time autocorrelation functions, namely the moment expansion and Mori's continued fraction representation, are studied from the point of view of their convergence, with the aim of obtaining new general properties of time autocorrelation functions. First, the relation between them is established by using mathematical techniques in the case of a general dynamical variable, and a direct method, useful for applications, in the case of Hermitian variables. The mathematical structure associated to Mori's generalized random forces is investigated and it is shown that these random forces can be obtained by a Schmidt orthogonalization of the sequence of initial time derivatives of the dynamical variable considered. Then, the convergence criteria for both representations are examined and an illustration is given with the exactly solvable case of an isotopic impurity in a linear chain of coupled harmonic oscillators. Finally, the question of knowing whether the continued fraction expansion is convergent for any Hermitian dynamical variable and any system is discussed, with its implications for the general behaviour of time autocorrelation functions.

• 理論物理学刊行会の論文
• 1967-03-25

著者

• Dupuis Marc

  Institute Of Physics College Of General Education University Of Tokyo : Department De Physico-chimie

• Dupuis Marc

  Institute of Physics, College of General Education University of Tokyo : Department de Physico-Chimie, Centre d'Etudes Nucleaires de Saclay

関連論文

• On the Continued Fraction Expansion of Time Correlation Functions
• Moment and Continued Fraction Expansions of Time Autocorrelation Functions

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