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Nonequilibrium dynamics in quantum field theory has been studied extensivelyusing truncations of the 2PI effective action. Both 1/N and loop expansionsbeyond leading order show remarkable improvement when compared to mean-fieldapproximations. However, in truncations used so far, only the leading-orderparts of the self energy responsible for memory loss, damping and equilibrationare included, which makes it difficult to discuss convergence systematically.For that reason we derive the real and causal evolution equations for an O(N)model to next-to-next-to-leading order in the 2PI-1/N expansion. Due to theappearance of internal vertices the resulting equations appear intractable fora full-fledged 3+1 dimensional field theory. Instead, we solve the closelyrelated three-loop approximation in the auxiliary-field formalism numericallyin 0+1 dimensions (quantum mechanics) and compare to previous approximationsand the exact numerical solution of the Schroedinger equation.

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

Nonequilibrium dynamics in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>model to next-to-next-to-leading order in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>N</mml:mi></mml:math>expansion

Nonequilibrium dynamics in theO(N)model to next-to-next-to-leading order in the1/Nexpansion