Nonequilibrium Bose-Einstein condensates, dynamical scaling, and symmetric evolution in the large {ital N} {Phi}{sup 4} theory
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 (United States)
- LPTHE, Universite Pierre et Marie Curie (Paris VI) et Denis Diderot (Paris VII), Tour 16, 1er. etage, 4, Place Jussieu F-75252 Paris, Cedex 05 (France)
- Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 (United States)
We analyze the nonequilibrium dynamics of the O(N) {Phi}{sup 4} model in the large {ital N} limit with a broken symmetry tree level potential and for states of large energy density. The dynamics is dramatically different when the energy density is above the top of the tree level potential V{sub 0} than when it is below it. When the energy density is below V{sub 0}, we find that nonperturbative particle production through spinodal instabilities provides a dynamical mechanism for the Maxwell construction. The asymptotic values of the order parameter only depend on the initial energy density and all values between the minima of the tree level potential are available; the asymptotic {ital dynamical} {open_quotes}effective potential{close_quotes} is flat between the minima. When the energy density is larger than V{sub 0}, the evolution samples ergodically the broken symmetry states, as a consequence of nonperturbative particle production via parametric amplification. Furthermore, we examine the quantum dynamics of phase ordering into the broken symmetry phase and find a novel scaling behavior of the correlation function. There is a crossover in the dynamical correlation length at a time scale t{sub s}{approx}ln(1/{lambda}). For t{lt}t{sub s} the dynamical correlation length {xi}(t){proportional_to}{radical} (t) and the evolution is dominated by linear instabilities and spinodal decomposition, whereas for t{gt}t{sub s} the evolution is nonlinear and dominated by the onset of nonequilibrium Bose-Einstein condensation of long-wavelength Goldstone bosons. In this regime a true scaling solution emerges with a nonperturbative anomalous scaling length dimension z=1/2 and a dynamical correlation length {xi}(t){proportional_to}(t{minus}t{sub s}). The equal time correlation function in this scaling regime vanishes for r{gt}2(t{minus}t{sub s}) by causality. For t{gt}t{sub s} phase ordering proceeds by the formation of domains that grow at the speed of light, with nonperturbative condensates of Goldstone bosons and the equal time correlation function falls of as 1/r. A semiclassical but stochastic description emerges for time scales t{gt}t{sub s}. Our results are compared to phase ordering in {ital classical} stochastic descriptions in condensed matter and cosmology. {copyright} {ital 1999} {ital The American Physical Society}
- OSTI ID:
- 341452
- Journal Information:
- Physical Review, D, Vol. 59, Issue 12; Other Information: PBD: Jun 1999
- Country of Publication:
- United States
- Language:
- English
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