Quantum Formation of Topological Defects

TL;DR

This paper investigates quantum phase transitions with symmetry breaking, analyzing how topological defects like kinks, vortices, and monopoles form and scale in different dimensions, revealing attractor solutions independent of quench timescales.

Contribution

It provides a detailed analysis of defect formation in quantum phase transitions across various dimensions, including scaling laws and conditions for attractor solutions.

Findings

Defect densities scale as t^{-d/2} in d dimensions.

Defect formation reaches attractor solutions independent of quench timescale.

Results are applicable in specific parameter regimes for d=1.

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.