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Nonequilibrium dynamics in the ON model to next-to-next-to-leading order in the 1=N expansion
 

Summary: Nonequilibrium dynamics in the ON model to next-to-next-to-leading order
in the 1=N expansion
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)
Nonequilibrium dynamics in quantum field theory has been studied extensively using truncations of the
2PI effective action. Both 1=N and loop expansions beyond leading order show remarkable improvement
when compared to mean-field approximations. However, in truncations used so far, only the leading-order
parts of the self-energy responsible for memory loss, damping and equilibration are included, which
makes it difficult to discuss convergence systematically. For that reason we derive the real and causal
evolution equations for an ON model to next-to-next-to-leading order in the 2PI-1=N expansion.
Because of the appearance of internal vertices the resulting equations appear intractable for a full-fledged
3 1 dimensional field theory. Instead, we solve the closely related three-loop approximation in the
auxiliary-field formalism numerically in 0 1 dimensions (quantum mechanics) and compare to previous
approximations and the exact numerical solution of the Schro¨dinger equation.
DOI: 10.1103/PhysRevD.74.025004 PACS numbers: 11.15.Pg, 05.70.Ln
I. INTRODUCTION

  

Source: Aarts, Gert - Department of Physics, University of Wales Swansea

 

Collections: Physics