ISSN:
1572-9613
Keywords:
Strong coupling expansion
;
damped
;
randomly driven anharmonic oscillator
;
large-Reynolds-number expansion
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract 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 Hamiltonianp 2/2 +m 2 x 2/2 +vx 4 +λx 6/2, we evaluate the path integral on a lattice by assuming that theλx 6 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01013934
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