Multiple-scale analysis and renormalization of quenched second order phasetransitions - art. no. 105026

A quenched second order phase transition is modeled by an effective Phi (4) theory with a time-dependent Hamiltonian (H) over cap (t), whose symmetry is broken spontaneously in time. The quantum field evolves out of equilibri um (nonequilibrium) during the phase transition as the density operator sig nificantly deviates from <(<rho>)over cap>(t) = e (-beta(H) over cap (t))/Z (H). The recently developed Liouville-von Neumann method provides various q uantum states for the phase transition in terms of a complex solution to th e mean-field equation, which is equivalent to the Gaussian effective potent ial in the static case and to the time-dependent Hartree-Fock equation in t he nonequilibrium case. Using multiple-scale perturbation theory we solve t he mean-field equation analytically to the first order of the coupling cons tant and find the quantum states during the quenched second order phase tra nsition. We propose a renormalization scheme during the process of phase tr ansition to regularize the divergences, which originate from the mode coupl ing between hard and hard modes or between soft and hard modes. The effect of mode coupling is discussed.