Time Correlation Calculation Method Based on Delayed Coordinates

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Abstract

An approximate calculation method of time correlations by use of delayed coordinate is proposed. For a solvable piecewise linear hyperbolic chaotic map, this approximation is compared with the exact calculation, and an exponential convergence for the maximum time delay M is found. By use of this exponential convergence, the exact result for M → ∞ is extrapolated from this approximation for the first few values of M. This extrapolation is shown to be much better than direct numerical simulations based on the definition of the time correlation function. As an application, the irregular dependence of diffusion coefficients similar to Takagi or Weierstrass functions is obtained from this approximation, which is indistinguishable from the exact result only at M = 2. The method is also applied to the dissipative Lozi and Hénon maps and the conservative standard map in order to show wide applicability.

Journal

  • Progress of Theoretical Physics

    Progress of Theoretical Physics 121(6), 1143-1156, 2009-06-25

    Oxford University Press (OUP)

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Codes

  • NII Article ID (NAID)
    110007339433
  • NII NACSIS-CAT ID (NCID)
    AA00791455
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    0033068X
  • NDL Article ID
    10261156
  • NDL Source Classification
    ZM35(科学技術--物理学)
  • NDL Call No.
    Z53-A468
  • DOI
    10.1143/PTP.121.1143
  • Data Source
    CJP  NDL  NII-ELS  IR  Crossref 
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