Noise strength effects on the relaxation properties of weakly coupled Ginzburg-Landau models

We search for new effects and extend previous investigations on the relaxation properties of weakly coupled stochastic Ginzburg-Landau models under noise with different intensity. We calculate the one-particle mass up to second order in the Ginzburg-Landau potential coupling constant and show that, as previously predicted, it is in fact less sensitive to the noise strength than the two-particle bound state. For d=1 and 2 and a negative quartic term in the potential, we show that the difference between these masses becomes smaller as we increase the noise strength, which indicates the possibility of a crossover for large noise (i.e., the two-particle bound state mass may become smaller than the one-particle mass) or of a phase transition (the masses are going to zero). For d=1 and in the ladder approximation (first order in the coupling constant), we show the absence of resonances in the spectrum close to the two-particle threshold and the existence of one antibound state for a positive quartic term in the potential, which indicates the possibility of some bound state due to changes in the system (e.g., in the noise intensity).