Quantum Formation of Topological Defects

Abstract

We consider quantum phase transitions with global symmetry breakings that result in the formation of topological defects. We evaluate the number densities of kinks, vortices, and monopoles that are produced in $d=1,2,3$ spatial dimensions respectively and find that they scale as $t^{-d/2}$ and evolve towards attractor solutions that are independent of the quench timescale. For $d=1$ our results apply in the region of parameters $\lambda \tau /m\ll 1$ where $\lambda$ is the quartic self-interaction of the order parameter, $\tau$ is the quench timescale, and $m$ the mass parameter.

arXiv comment20 pages, 16 figures, published version

References in corpus (24)

• Cosmological Experiments in Condensed Matter Systems
• Dynamics of a Quantum Phase Transition
• Big bang simulation in superfluid 3He-B -- Vortex nucleation in neutron-irradiated superflow
• The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals
• Density of kinks after a quench: When symmetry breaks, how big are the pieces?
• Observation of Magnetic Flux Generated Spontaneously During a Rapid Quench of Superconducting Films
• Structural defects in ion crystals by quenching the external potential: the inhomogeneous Kibble-Zurek mechanism
• Zurek-Kibble domain structures: The Dynamics of Spontaneous Vortex formation in Annular Josephson Tunnel Junctions
• Non-Appearance of Vortices in Fast Mechanical Expansions of Liquid 4He Through the Lambda Transition
• Vortex String Formation in a 3D U(1) Temperature Quench
• Vortex formation in two dimensions: When symmetry breaks, how big are the pieces?
• Defect formation and local gauge invariance
• Zurek-Kibble Mechanism for the Spontaneous Vortex Formation in $Nb-Al/A{l}_{ox}/Nb$ Josephson Tunnel Junctions: New Theory and Experiment
• Exploring the Kibble-Zurek mechanism with homogeneous Bose gases
• Search for Spontaneous Nucleation of Magnetic Flux During Rapid Cooling of YBCO films Through Tc
• Defect Formation and Critical Dynamics in the Early Universe
• Initial Vortex Densities after a Temperature Quench
• New Experiments for Spontaneous Vortex Formation in Josephson Tunnel Junctions
• Classical-Quantum Correspondence for Fields
• Quantum Spinodal Decomposition
• Counting defects in an instantaneous quench
• Spontaneous vortex formation on a superconductor film
• Rolling with quantum fields
• Emergence of classical structures from the quantum vacuum

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• Canonical description of cosmological backreaction
• Domain wall annihilation -- a QFT perspective
• Kibble mechanism for electroweak magnetic monopoles and magnetic fields
• Holographic Lifshitz flows
• Cosmological scaling of precursor domain walls
• Evolution of a kink-antikink ensemble in a quantum vacuum