Nonequilibrium dynamics in the O(N) model to next-to-next-to-leading order in the 1/N expansion

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Gert Aarts
Department of Physics, University of Wales Swansea, Singleton Park, Swansea, SA2 8PP, United Kingdom

Anders Tranberg
Department of Physics & Astronomy, University of Sussex, Falmer, Brighton, BN1 9QH, United Kingdom
and DAMTP, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, United Kingdom

Received 21 April 2006; published 6 July 2006

Nonequilibriumdynamics in quantum field theory has been studied extensively usingtruncations of the 2PI effective action. Both 1/N and loopexpansions beyond leading order show remarkable improvement when compared tomean-field approximations. However, in truncations used so far, only theleading-order parts of the self-energy responsible for memory loss, dampingand equilibration are included, which makes it difficult to discussconvergence systematically. For that reason we derive the real andcausal evolution equations for an O(N) model to next-to-next-to-leading orderin the 2PI-1/N expansion. Because of the appearance of internalvertices the resulting equations appear intractable for a full-fledged 3+1dimensional field theory. Instead, we solve the closely related three-loopapproximation in the auxiliary-field formalism numerically in 0+1 dimensions (quantummechanics) and compare to previous approximations and the exact numericalsolution of the Schrödinger equation.

URL:	http://link.aps.org/doi/10.1103/PhysRevD.74.025004
DOI:	10.1103/PhysRevD.74.025004
PACS:	11.15.Pg; 05.70.Ln 11.15.Pg Expansions for large numbers of components (e.g., 1/N_cexpansions) in gauge theories 05.70.Ln Nonequilibrium and irreversible thermodynamics YEAR: 2006

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