Universality of the Long Time Tail in Hamiltonian Dynamics

An Approach to the f−1 Noise of Quartz Oscillators
  • Y. Aizawa
  • K. Tanaka
Conference paper
Part of the Research Reports in Physics book series (RESREPORTS)


A universal law of the long time tail in nearly integrable systems is discussed and the onset mechanism of ”non-stationary” and ”f v fluctuation” is briefly reviewed using a lattice vibration model. The mechanism of f −1 fluctuations in quartz crystals is numerically pursued and compared with several experimental observations such as phase noises, phonon number fluctuations and dissipation coefficients.


Dielectric Loss Phase Noise Quartz Crystal Lattice Vibration Resonant Mode 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Y. Aizawa
    • 1
  • K. Tanaka
    • 1
  1. 1.Department of Applied MathematicsWaseda University169 Shinjuku, TokyoJapan

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