Nonequilibrium Bose-Einstein condensates, dynamical scaling, and symmetricevolution in the large N Phi(4) theory - art. no. 125009

We analyze the nonequilibrium dynamics of the O(N) Phi(4) model in the larg e N limit with a broken symmetry tree level potential and for states of lar ge energy density. The dynamics is dramatically different when the energy d ensity is above the top of the tree level potential V-0 than when it is bel ow it. When the energy density is below V-0, we find that nonperturbative p article production through spinodal instabilities provides a dynamical mech anism for the Maxwell construction. The asymptotic values of the order para meter only depend on the initial energy density and all values between the minima of the tree level potential are available; the asymptotic dynamical "effective potential" is flat between the minima. When the energy density i s larger than V-0, the evolution samples ergodically the broken symmetry st ates, as a consequence of nonperturbative particle production via parametri c amplification. Furthermore, we examine the quantum dynamics of phase orde ring into the broken symmetry phase and find a novel scaling behavior of th e correlation function. There is a crossover in the dynamical correlation l ength at a time scale t(s)approximate to ln(1/lambda). For t<t(s) the dynam ical correlation length xi(t) proportional to root t and the evolution is d ominated by linear instabilities and spinodal decomposition, whereas for t> t(s) the evolution is nonlinear and dominated by the onset of nonequilibriu m Bose-Einstein condensation of long-wavelength Goldstone bosons. In this r egime a true scaling solution emerges with a nonperturbative anomalous scal ing length dimension z=1/2 and a dynamical correlation length xi(t)proporti onal to(t-t(s)). The equal time correlation function in this scaling regime vanishes for r>2(t-t(s)) by causality. For t>t(s) phase ordering proceeds by the formation of domains that grow at the speed of light, with nonpertur bative condensates of Goldstone bosons and the equal time correlation funct ion falls of as 1/r. A semiclassical but stochastic description emerges for time scales t>t(s). Our results are compared to phase ordering in classica l stochastic descriptions in condensed matter and cosmology. [S0556-2821(99 )00412-9].