Counting defects with the two-point correlator

Abstract

We study how topological defects manifest themselves in the equal-time two-point field correlator. We consider a scalar field with Z_2 symmetry in 1, 2 and 3 spatial dimensions, allowing for kinks, domain lines and domain walls, respectively. Using numerical lattice simulations, we find that in any number of dimensions, the correlator in momentum space is to a very good approximation the product of two factors, one describing the spatial distribution of the defects and the other describing the defect shape. When the defects are produced by the Kibble mechanism, the former has a universal form as a function of k/n, which we determine numerically. This signature makes it possible to determine the kink density from the field correlator without having to resort to the Gaussian approximation. This is essential when studying field dynamics with methods relying only on correlators (Schwinger-Dyson, 2PI).

11 pages, 7 figures.

References in corpus (2)

• O(N) symmetry-breaking quantum quench: Topological defects versus quasiparticles
• Soliton form factors from lattice simulations

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• Non-equilibrium Quantum Spin Dynamics from 2PI Functional Integral Techniques in the Schwinger Boson Representation
• Topological defect formation from 2PI effective action techniques
• The Kibble Zurek Mechanism of Topological Defect Formation in Quantum Field Theory with Matrix Product States
• Bubble nucleation and quantum initial conditions in classical statistical simulations