Vortex Densities and Correlations at Phase Transitions (original) (raw)

Vortex Production in Non-Relativistic and Relativistic Media

We examine string (vortex) formation at a quench for a weakly-coupled global U(1) theory when the excitation spectrum is non-relativistic. It is so similar to vortex production in the corresponding relativistic plasma as to reinforce arguments for the similarity of vortex production in the early universe and in low-temperature many-body physics.

The Onset of Phase Transitions in Condensed Matter and Relativistic QFT

Condensed Matter Physics, 2000

Zurek have provided a unifying causal picture for the appearance of topological defects like cosmic strings or vortices at the onset of phase transitions in relativistic QFT and condensed matter systems respectively. There is no direct experimental evidence in QFT, but in condensed matter the predictions are largely, but not wholly, supported in superfluid experiments on liquid helium. We provide an alternative picture for the initial appearance of strings/vortices that is commensurate with all the experimental evidence from condensed matter and consider some of its implications for QFT.

Non-abelian charged vortices as cosmic strings

Physics Letters B, 1986

We study vortex solutions in non-abelian gauge theories with spontaneous symmetry breaking. We construct string configurations with electric charge showing that they necessarily have infinite energy per unit length. Although this prevents its application in problems like catalysis of proton decay, we show, by analyzing the cosmological evolution of the strings, that they can produce density fluctuations leading to galaxy formation.

Dynamical interactions of cosmic strings and flux vortices in superconductors

Physics Letters B, 1988

We perform a numerIca simulation of the dynanwal mteractlons of vortex excltatlons m the abehan Hlggs model These structures can be Interpreted as cross sections of cosmic strings or of magnetic flux tubes trapped m a superconductor Although at a critical value of the coupling constant the mteractlon energy between static vortices vamshes, colhdmg vortices interact nontrlwally by scattering at 90" m a head-on colhsion, and are therefore not sohtons We also observe 90" scattenng at non-cntlcal values of the couphng constant In a superconducting matenal magnetic field lmes -which are normally excluded from the material by the Melssner effect -can become trapped m quantized flux tubes which are known as "vortices " These vortices are localized obJects that behave much hke particles m two dimensions More recently it has been found that similar vortex-hke structures, called cosmic strings, can be produced m the early stages of the evolution of the Universe [ 1,2] Flux vortices m superconductors and the simplest prototypes of cosmic strings share a common field theoretical background -they are both described by the abehan Hlggs (or Gmzburg-Landau) model The general nature of the mteractlons between vortices in the abehan Hlggs model has been known [ 3 ] for some time A critical value of the couplmg constant 2 separates two domains For values less than the critIca coupling (correspondmg to a type I super-conductor) vortices attract each other, while for values greater than the critical coupling (correspondmg to a type II superconductor) they repel At the cntlcal coupling it was shown [ 41 that the interaction energy of two isolated vortices IS zero, which suggested to some that m a colhslon crltlcally coupled vortices might behave like sohtons and simply pass through each other The results we report here show, however, that this 1s not the case crltlcally coupled vortices interact non-tnvlally (in a head-on collision they scatter at 90"'), and are therefore not sohtlons Slmliar results have been reported recently by Matzner [ 5 ] and by Shellard [ 6 ] We also find that this short range non-trivial interaction is present at non-critical values of the couplmg, m addition to the longer range attractive or repulsive forces Vortices in the abehan Hlggs model, or m the Gmzburg-Landau theory, [ 7,, are stable topologl-

Statistical mechanics of vortices from field theory

Nuclear Physics B - NUCL PHYS B, 1999

We study with lattice Monte Carlo simulations the interactions and macroscopic behavior of a large number of vortices in the three-dimensional U(1) gauge + Higgs field theory, in an external magnetic field. We determine non-perturbatively the (attractive or repelling) interaction energy between two or more vortices, as well as the critical field strength Hc, the thermodynamical discontinuities, and the surface tension related to the boundary between the Meissner phase and the Coulomb phase in the type I region. We also investigate the emergence of vortex lattice and vortex liquid phases in the type II region. For the type I region the results obtained are in qualitative agreement with mean field theory, except for small values of Hc, while in the type II region there are significant discrepancies. These findings are relevant for superconductors and some models of cosmic strings, as well as for the electroweak phase transition in a magnetic field.

Collapsing vortex filaments and the spectrum of quantum turbulence

Low Temperature Physics, 2017

The method of correlation functions and the method of quantum vortex configurations are used to calculate the energy spectrum of a three-dimensional velocity field that is induced by collapsing (immediately before reconnection) vortex filaments. The formulation of this problem is motivated by the idea of modeling classical turbulence by a set of chaotic quantized vortex filaments. Among the various arguments that support the idea of quasi-classical behavior for quantum turbulence, the most persuasive is probably the resulting Kolmogorov energy spectrum resembling EðkÞ / k À5=3 that was obtained in a number of numerical studies. Another goal is associated with an important and intensely studied theme that relates to the role of hydrodynamic collapse in the formation of turbulence spectra. Calculations have demonstrated that vortex filaments create a velocity field at the moment of contact, which has a singularity. This configuration of vortex filaments generates the spectrum E(k), which bears the resemblance to the Kolmogorov law. A possible cause for this observation is discussed, as well as the likely reasons behind any deviations. The obtained results are discussed from the perspective of both classical and quantum turbulence.

Vortices in equilibrium scalar electrodynamics

1998

Scalar electrodynamics can be used to investigate the formation of cosmic strings in the early universe. We present the results of lattice Monte Carlo simulations of an effective three-dimensional U(1)+Higgs theory that describes the equilibrium properties of finite-temperature scalar electrodynamics near the transition. A gauge-invariant criterion for the existence of a vortex is used in measuring the properties of the vortex network in the equilibrium state both in the Coulomb and in the Higgs phase of the system. The naive definition of the vortex density becomes meaningless in the continuum limit and special care is needed in extracting physical quantities. Numerical evidence for a physical discontinuity in the vortex density is given.

Applications of the Abelian Vortex Model to Cosmic Strings and the Universe Evolution

New Ideas Concerning Black Holes and the Evolution of the Universe [Working Title], 2019

Due to the wide range of applications and effects of the Abelian vortex model of Nielsen and Olesen in the many areas of physics, ranging from condensed matter to astrophysical effects, some work in the literature is necessary to approach this topic in a succinct form that the undergraduate student in both physics and related areas has the possibility to know and understand. The mechanisms associated with this vortex model indicate him as a strong candidate for the source for the topological defects proposed by Vilenkin.

Inhomogeneous vortex matter

We present a generalization of the continuum theory of vortex matter for non-uniform superfluid density. This theory explains the striking regularity of vortex lattices observed in Bose-Einstein condensates, and predicts the frequencies of long-wavelength lattice excitations.