Journal of Statistical Physics

, Volume 22, Issue 6, pp 647–660 | Cite as

Strong coupling expansion for classical statistical dynamics

  • Carl M. Bender
  • Fred Cooper
  • Gerald Guralnik
  • Harvey A. Rose
  • David H. Sharp


We discuss the simple, randomly driven systemdx/dt = −Μx −γx3 +f(t), wheref(t) is a Gaussian random function or stirring force with 〈f(t)f(t′)〉 = ℱ δ(t − t′). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's functions as power series in (1/R)n, whereR is the internal Reynolds number (ℱγ)1/2/Μ, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonianp2/2 +m2x2/2 +vx4 +λx6/2, we evaluate the path integral on a lattice by assuming that theλx6 term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(λa)1/3, wherea is the lattice spacing. Using Padé approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.

Key words

Strong coupling expansion damped randomly driven anharmonic oscillator large-Reynolds-number expansion 


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Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • Carl M. Bender
    • 1
  • Fred Cooper
    • 1
  • Gerald Guralnik
    • 1
  • Harvey A. Rose
    • 1
  • David H. Sharp
    • 1
  1. 1.Theoretical Division, Los Alamos Scientific LaboratoryUniversity of CaliforniaLos Alamos

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