Nonequilibrium quantum dynamics of second order phase transitions - art. no. 125020

We use the so-called Liouville-von Neumann (LvN) approach to study the none quilibrium quantum dynamics of time-dependent second order phase transition s. The LvN approach is a canonical method that unifies the functional Schro dinger equation for the quantum evolution of pure states and the LvN equati on for the quantum description of mixed states of either equilibrium or non equilibrium. As nonequilibrium quantum mechanical systems we study a time-d ependent harmonic and an anharmonic oscillator and find the exact Fock spac e and density operator for the harmonic oscillator and the nonperturbative Gaussian Fock space and density operator for the anharmonic oscillator. The density matrix and the coherent, thermal, and coherent-thermal states are found in terms of their classical solutions, for which the effective Hamilt onians and equations of motion are derived. The LvN approach is further ext ended to quantum fields undergoing time-dependent second order phase transi tions. We study an exactly solvable model with a finite smooth quench and f ind the two-point correlation functions. Because of the spinodal instabilit y of long wavelength modes, the two-point correlation functions lead to the t(1/4)-scaling relation during the quench and the Cahn-Allen scaling relat ion t(1/2) after completion of the quench. Further, after the finite quench the domain formation shows a time-lag behavior at the cubic power of the q uench period. Finally we study the time-dependent phase transition of a sel f-interacting scalar field.