Domain Formation: Decided Before, or After the Transition?

Abstract

There is increasing evidence that causality provides useful bounds in determining the domain structure after a continuous transition. In devising their scaling laws for domain size after such a transition, Zurek and Kibble presented arguments in which causality is important both before and after the time at which the transition begins to be implemented. Using numerical simulations of kinks in 1+1 dimensions, we explain how the domain structure is determined exclusively by what happens after the transition, even though the correlation length freezes in before the transition.

6 pages, 3 figs, final extended version published in PRD

References in corpus (17)

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• Big bang simulation in superfluid 3He-B -- Vortex nucleation in neutron-irradiated superflow
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• Observation of Magnetic Flux Generated Spontaneously During a Rapid Quench of Superconducting Films
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• Dynamics of defect formation
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Cited by in corpus (26)

• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Kibble-Zurek mechanism in colloidal monolayers
• Causality and non-equilibrium second-order phase transitions in inhomogeneous systems
• Quench dynamics of the 2d XY model
• Full Counting Statistics of Topological Defects After Crossing a Phase Transition
• Adiabatic quenches through an extended quantum critical region
• Universal breakdown of Kibble-Zurek scaling in fast quenches across a phase transition
• Global formation of topological defects in the multiferroic hexagonal manganites
• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
• Kibble-Zurek scaling in the Yang-Lee edge singularity
• Phase Transition in Space: How Far Does a Symmetry Bend Before It Breaks?
• New Experiments for Spontaneous Vortex Formation in Josephson Tunnel Junctions
• Causality and defect formation in the dynamics of an engineered quantum phase transition in a coupled binary Bose-Einstein condensate
• Spontaneous Fluxon Production in Annular Josephson Tunnel Junctions in the Presence of a Magnetic Field
• Looking for defects in the 2PI correlator
• Hybridized Kibble-Zurek scaling in the driven critical dynamics across an overlapping critical region
• Kibble-Zurek scaling in one-dimensional localization transitions
• Nonequilibrium critical dynamics in the quantum chiral clock model
• Scaling in driven dynamics starting in the vicinity of a quantum critical point
• Structural phase transition and its critical dynamics from holography
• Gaussianity revisited: Exploring the Kibble-Zurek mechanism with superconducting rings
• Colloidal test bed for universal dynamics of phase transitions
• Spontaneous Vortex Production in Driven Condensates with Narrow Feshbach Resonances
• Separation of the Kibble-Zurek Mechanism from Quantum Criticality
• Pattern formation in individual-based systems with time-varying parameters
• Continuous Dimer Angles on the Silicon Surface: Critical Properties and the Kibble-Zurek Mechanism