Elsevier

Physics Letters A

Volume 190, Issues 5–6, 1 August 1994, Pages 447-454
Physics Letters A

Probing microscopic chaotic dynamics by observing macroscopic transport processes

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Abstract

We derive the Kramers equation, namely, the Fokker-Planck equation for an oscillator, from a completely deterministic picture. The oscillator is coupled to a “booster”, i.e., a deterministic system in a fully chaotic state, wherein diffusion is derived from the sensitive dependence of chaos on initial conditions and friction is a consequence of the linear response of the booster to the action exerted on it by the oscillator. To deal with the Hamiltonian nature of the system of interest and of its coupling to the booster, we extend the earlier theoretical derivation of macroscopic transport coefficients from deterministic dynamics. We show that the frequency of the oscillator can be tuned to the microscopic frequencies of the booster without affecting the canonical nature of the “macroscopic” statistics. The theoretical predictions are supported by numerical simulations.

References (23)

  • B.V. Chirikov

    Phys. Rev.

    (1979)
  • P. Ullersma

    Physica

    (1966)
    P. Ullersma

    Physica

    (1966)
    P. Ullersma

    Physica

    (1966)
  • P.E. Philipson

    J. Math. Phys.

    (1987)
  • N. van Kampen et al.

    Physica A

    (1986)
  • K. Lindenberg et al.

    The nonequilibrium statistical mechanics of open and closed systems

    (1990)
  • M. Bianucci, R. Mannella, P. Grigolini and B.J. West, 3 papers submitted to Mod....
  • P. Grigolini

    Mol. Phys.

    (1976)
  • A.B. Rechester et al.

    Phys. Rev. Lett.

    (1988)
  • R.V. Jensen

    Phys. Rev. A

    (1984)
  • H. Fujisaka et al.

    Z. Naturforsch

    (1985)
  • G. Trefan et al.

    Phys. Rev. A

    (1992)
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