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We consider the large-N $\Phi^4$ theory with spontaneously broken symmetry atfinite temperature. We study, in the large-N limit, quantum states which arecharacterized by a time dependent, spatially homogenous expectation value ofone of the field components, $\phi_N(t)$, and by quantum fluctuations of theother $N-1$ components, that evolve in the background of the classical field.Investigating such systems out of equilibrium has recently been shown todisplay several interesting features. We extend here this type ofinvestigations to finite temperature systems. Essentially the novel featuresobserved at T=0 carry over to finite temperature. This is not unexpected, asthe main mechanisms that determine the late-time behavior remain the same. Weextend two empirical - presumably exact - relations for the late-time behaviorto finite temperature and use them to define the boundaries between the regionof different asymptotic regimes. This results in a phase diagram with thetemperature and the initial value of the classical field as parameters, thephases being characterized by spontaneous symmetry breaking resp. symmetryrestoration. The time evolution is computed numerically and agrees very wellwith the expectations.Comment: 21 pages, 13 Figures, LaTeX, some typos correcte

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Nonequilibrium evolution and symmetry structure of the large-<i>N</i><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>Φ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>model at finite temperature

Nonequilibrium evolution and symmetry structure of the large-NΦ4model at finite temperature