On the relaxation properties of stochastic Ginzburg–Landau type models

Considering the project of studying the basic properties of commonly used stochastic nonlinear dynamical systems, we investigate and present new properties of the relaxation to equilibrium of stochastic Ginzburg–Landau type models with polynomial interaction with nonlocal nonlinear terms. In our approach, we map the initial stochastic model on a imaginary-time quantum field theory. We show that (with a suitable nonlocality) a two-particle bound state appears below the two-particle threshold even if all the coefficients in the polynomial interaction are positive. The existence of such a bound state changes the relaxation rate to equilibrium, and so, it is an experimentally observable effect of physical interest. Moreover, we show that the bound state masses are sensitive to changes in the rate of nonlocality, which may favor other phenomena related to the low-lying spectrum of the dynamics generator. Our results involve a perturbative analysis (supported by previous rigorous results): in the computation of the bound state mass we use a Bethe–Salpeter equation in the ladder approximation.