Non-Equilibrium Dynamics of a Quench-Induced Phase Transition and Topological Defect Formation

Abstract

We study the full out-of-thermal-equilibrium dynamics of a relativistic classical scalar field through a symmetry breaking phase transition. In these circumstances we determine the evolution of the ensemble averages of the correlation length and topological defect densities. This clarifies many aspects of the non-perturbative dynamics of fields in symmetry breaking phase transitions and allows us to comment on a quantitative basis on the canonical pictures for topological defect formation and evolution. We also compare these results to those obtained from the field evolution in the Hartree approximation or using the linearized theory. By doing so we conclude about the regimes of validity of these approximations.

35 pages, 16 figures, RevTeX, available through anonymous ftp from ftp://euclid.tp.ph.ic.ac.uk/papers/ or on WWW at http://euclid.tp.ph.ic.ac.uk/Papers/

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• Non-Equilibrium Quantum Fields in the Large N Expansion
• Phase Transitions out of Equilibrium: domain formation and growth
• Quantum Rolling Down out of Equilibrium
• Statistical Mechanics of Kinks in (1+1)-Dimensions: Numerical Simulations and Double Gaussian Approximation
• The Dynamics Of Vortex And Monopole Production By Quench Induced Phase Separation
• Nonlinear Noise in Cosmology
• Winding Number Correlation Functions and Cosmic String Formation

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• Dynamics of defect formation
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• Unraveling critical dynamics: The formation and evolution of topological textures
• Properties of the Langevin and Fokker-Planck equations for scalar fields and their application to the dynamics of second order phase transitions
• Quantum Dynamics in Classical Time Evolution of Correlation Functions
• How to Count Kinks: From the Continuum to the Lattice and Back
• Stochastic Production Of Kink-Antikink Pairs In The Presence Of An Oscillating Background
• Counting defects with the two-point correlator
• Additive and Multiplicative Noise Driven Systems in 1+1 Dimensions: Waiting Time Extraction of Nucleation Rates
• The formation of vortex loops (strings) in continuous phase transitions
• Density of Topological Defects After a Quench