Related papers: Formation, Interaction and Observation of Topologi…
Structure formation with topological defects is described. The main differences from inflationary models are highlighted. The results are compared with recent observations. It is concluded that all the defect models studied so far are in…
We study the nonequilibrium dynamics leading to the formation of topological defects in a symmetry-breaking phase transition of a quantum scalar field with \lambda\Phi^4 self-interaction in a spatially flat, radiation-dominated…
Cosmological inflation and topological defects have been considered for a long time, either in disagreement or in competition. On the one hand an inflationary era is required to solve the shortcomings of the hot big bang model, while on the…
Periodic boundary conditions are a common theoretical and computational tool used to emulate effectively infinite domains. However, two-dimensional periodic domains are topologically distinct from the infinite plane, eliciting the question:…
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…
In this work, we develop a universal picture from topology in the thermodynamic parameters space to describe first order phase transitions of black holes. By employing an off-shell internal energy, we find two types of topological defects.…
When a symmetry gets spontaneously broken in a phase transition, topological defects are typically formed. The theoretical picture of how this happens in a breakdown of a global symmetry, the Kibble-Zurek mechanism, is well established and…
These lecture notes discuss several topics in the physics of cosmic structure formation starting from the evolution of small-amplitude fluctuations in the radiation-dominated era. The topics include relativistic cosmological perturbation…
We consider a perfectly homogeneous and isotropic universe which undergoes a sudden phase transition. If the transition produces topological defects, which we assume, perturbations in the geometry and the cosmic fluid also suddenly appear.…
We study the behaviour of cosmic string networks in contracting universes, and discuss some of their possible consequences. We note that there is a fundamental time asymmetry between defect network evolution for an expanding universe and a…
In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely…
This is a survey article for the Encyclopedia of Mathematical Physics, 2nd Edition. Topological defects are described in the context of the 2-dimensional Ising model on the lattice, in 2-dimensional quantum field theory, in topological…
How topological defects affect the dynamics of particles hopping between lattice sites of a distorted, two-dimensional crystal is addressed. Perturbation theory and numerical simulations show that weak, short-ranged topological disorder…
Contact defects are time-periodic patterns in one space dimension that resemble spatially homogeneous oscillations with an embedded defect in their core region. For theoretical and numerical purposes, it is important to understand whether…
An introduction to modern theories for the origin of structure in the Universe is given. After a brief review of the growth of cosmological perturbations in an expanding Universe and a summary of some important observational results, the…
The status quo in our understanding of defect formation during a rapid transition into the broken symmetry state in condensed matter and cosmology is discussed. An observation of vortex nucleation in neutron absorption experiments in…
In studying the formation of topological defects, it is conventional to assume the ``geodesic rule'' which is equivalent to minimizing gradients of the order parameter. This assumption has been called into question in field-theoretic…
Cosmic strings are one-dimensional topological defects which could have been formed in the early stages of our Universe. They triggered a lot of interest, mainly for their cosmological implications: they could offer an alternative to…
In supersymmetric theories, topological defects can have nontrivial behaviors determined purely by whether or not supersymmetry is restored in the defect core. A well-known example of this is that some supersymmetric cosmic strings are…
We study the topology of smectic defects in two and three dimensions. We give a topological classification of smectic point defects and disclination lines in three dimensions. In addition we describe the combination rules for smectic point…