Showing papers by "Fred Cooper published in 1980"

Effective Potential for a Renormalized d -Dimensional g ϕ 4 Field Theory in the Limit g → ∞

Abstract: The first four coefficients in the effective potential ${V}_{\mathrm{eff}}({\ensuremath{\phi}}_{R})=\ensuremath{\Sigma}{n=1}^{\ensuremath{\infty}} {V}_{2n}{{\ensuremath{\phi}}_{R}}^{2n}$ are calculated for a mass- and wave-function-renormalized $g{\ensuremath{\phi}}^{4}$ field theory in $d$ space-time dimensions in the limit where the unrenormalized coupling $g\ensuremath{\rightarrow}\ensuremath{\infty}$ with the renormalized mass $M$ held fixed. The accuracy of these numerical results is verified by exact analytical calculations of the effective potential performed in 0 and 1 space-time dimensions.

Strong coupling expansion for classical statistical dynamics

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 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 Pade approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.