Journal of Statistical Physics

, Volume 24, Issue 1, pp 39–44 | Cite as

On the brownian motion of a frequencymodulated oscillator

  • Robert M. Mazo


The Langevin equations for a harmonically bound particle, where the force constant is a given function of time, is solved. The mean and mean-square properties of the solution are determined. The analysis is then specialized to the case of a force constant periodic in time. It is shown that the mean fluctuations remain bounded in time precisely when the mean motion is stable (remains bounded).

Key words

Langevin equations Brownian motion fluctuations Hill's equation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. C. Wang Chang and G. E. Uhlenbeck,Rev. Mod. Phys. 17:323 (1945).CrossRefADSGoogle Scholar
  2. 2.
    S. Chandrasekhar,Rev. Mod. Phys. 15:1 (1943).MATHCrossRefMathSciNetADSGoogle Scholar
  3. 3.
    S. Adelman,J. Chem. Phys. 64:124 (1976).CrossRefMathSciNetADSGoogle Scholar
  4. 4.
    R. J. P. Grappin,Physica 88A:435 (1977).MathSciNetADSGoogle Scholar
  5. 5.
    N. W. McLachlan,Theory and Application of Mathieu Functions (Oxford, 1947).Google Scholar
  6. 6.
    E. T. Whittaker and G. N. Watson,A Course of Modem Analysis, 4th ed., (Cambridge, 1952), Chapter XIX.Google Scholar

Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • Robert M. Mazo
    • 1
  1. 1.Institute of Theoretical Science and Department of ChemistryUniversity of OregonEuge⊙e

Personalised recommendations