Velocity-fluctuation-induced anomalous kinetics of theA+A→∅reaction

Abstract

The effect of a random velocity field on the kinetics of the single-species annihilation reaction A+A--> is analyzed near two dimensions with the aid of the perturbative renormalization group. The previously found asymptotic behavior induced by density fluctuations only in the diffusion-limited reaction is shown to be unstable to any velocity fluctuations (including thermal fluctuations near equilibrium) in spatial dimensions d</=d(c)=2. Four different stable long-time asymptotic regimes induced by the combined effect of velocity and density fluctuations are identified and the corresponding decay rates calculated in the leading order.

Effect of compressibility on the annihilation process

“…Note that in contrast to the previous studies [6,18] here we have to deal only with the three-charges' {g, u, λ} theory. Passive character (no backward influence on the advecting field) of the reacting particle manifests itself also in the relations ∂ λ β g = ∂ λ β u = 0 resulting from (9) and (10).…”

“…The only difference with the incompressible case is that now the velocity field has to be renormalized [11]. Following [6,11,18] it is easy to prove that the model under …”

“…The simplest way to find the average number density n(t) = ψ(t) is to calculate it from the stationarity condition of the functional Legendre transform [21] of the generating functional obtained by replacing the unrenormalized action by the renormalized one in the weight functional [6]. This is a convenient way to avoid any summing procedures used [4] to take into account the higher-order terms in n 0 .…”

“…Since the fields ψ and ψ † are not renormalized, the Callan-Symanzik equation for the mean particle number is easily obtained by the standard procedure [6,22] …”

“…A renormalization group treatment was successfully applied for different choices of reactive flow, e.g. time-independent random drift [5], velocity field described by stochastic Navier-Stokes equation [6] or short-range correlated potential disorder [7]. Often large differences are observed in relation to the experiment and their origin can be caused by the presence of large-scale anisotropies, effect of compressibility or parity violation.…”