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Title: Peristaltic modes of a single vortex in the Abelian Higgs model

Abstract

Using the Abelian Higgs model, we study the radial excitations of single vortex and their propagation modes along the vortex line. We call such beyond-stringy modes peristaltic modes of single vortex. With the profile of the static vortex, we derive the vortex-induced potential, i.e., single-particle potential for the Higgs and the photon field fluctuations around the static vortex, and investigate the coherently propagating fluctuations which correspond to the vibration of the vortex. We derive, analyze, and numerically solve the field equations of the Higgs and the photon field fluctuations around the static vortex with various Ginzburg-Landau parameter {kappa} and topological charge n. Around the Bogomol'nyi-Prasad-Sommerfield value or critical coupling {kappa}{sup 2}=1/2, there appears a significant correlation between the Higgs and the photon field fluctuations mediated by the static vortex. As a result, for {kappa}{sup 2}=1/2, we find the characteristic new-type discrete pole of the peristaltic mode corresponding to the quasibound state of coherently fluctuating fields and the static vortex. We investigate its excitation energy, correlation energy of coherent fluctuations, spatial distributions, and the resulting magnetic flux behavior in detail. Our investigation covers not only usual type-II vortices with n=1 but also type-I and type-II vortices with n set-membership sign Zmore » for the application to various general systems where the vortexlike objects behave as the essential degrees of freedom.« less

Authors:
; ;  [1]
  1. Department of Physics, Kyoto University, Kyoto 606-8502 (Japan)
Publication Date:
OSTI Identifier:
20935272
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.75.105015; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; DEGREES OF FREEDOM; ELECTRON CORRELATION; EXCITATION; FIELD EQUATIONS; GINZBURG-LANDAU THEORY; HIGGS MODEL; MAGNETIC FLUX; PHOTONS; POTENTIALS; QUASIBOUND STATE; SPATIAL DISTRIBUTION; TOPOLOGY

Citation Formats

Kojo, Toru, Suganuma, Hideo, and Tsumura, Kyosuke. Peristaltic modes of a single vortex in the Abelian Higgs model. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.105015.
Kojo, Toru, Suganuma, Hideo, & Tsumura, Kyosuke. Peristaltic modes of a single vortex in the Abelian Higgs model. United States. doi:10.1103/PHYSREVD.75.105015.
Kojo, Toru, Suganuma, Hideo, and Tsumura, Kyosuke. Tue . "Peristaltic modes of a single vortex in the Abelian Higgs model". United States. doi:10.1103/PHYSREVD.75.105015.
@article{osti_20935272,
title = {Peristaltic modes of a single vortex in the Abelian Higgs model},
author = {Kojo, Toru and Suganuma, Hideo and Tsumura, Kyosuke},
abstractNote = {Using the Abelian Higgs model, we study the radial excitations of single vortex and their propagation modes along the vortex line. We call such beyond-stringy modes peristaltic modes of single vortex. With the profile of the static vortex, we derive the vortex-induced potential, i.e., single-particle potential for the Higgs and the photon field fluctuations around the static vortex, and investigate the coherently propagating fluctuations which correspond to the vibration of the vortex. We derive, analyze, and numerically solve the field equations of the Higgs and the photon field fluctuations around the static vortex with various Ginzburg-Landau parameter {kappa} and topological charge n. Around the Bogomol'nyi-Prasad-Sommerfield value or critical coupling {kappa}{sup 2}=1/2, there appears a significant correlation between the Higgs and the photon field fluctuations mediated by the static vortex. As a result, for {kappa}{sup 2}=1/2, we find the characteristic new-type discrete pole of the peristaltic mode corresponding to the quasibound state of coherently fluctuating fields and the static vortex. We investigate its excitation energy, correlation energy of coherent fluctuations, spatial distributions, and the resulting magnetic flux behavior in detail. Our investigation covers not only usual type-II vortices with n=1 but also type-I and type-II vortices with n set-membership sign Z for the application to various general systems where the vortexlike objects behave as the essential degrees of freedom.},
doi = {10.1103/PHYSREVD.75.105015},
journal = {Physical Review. D, Particles Fields},
number = 10,
volume = 75,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}
  • Treating the flux of the magnetic field penetrating the vortex as a dynamical variable, we consider the question of the stability of the quantum state of the vortex against the decay to the excitations which are present in the Abelian Higgs model. Specifically, the partial widths of the decay to a pair of the scalar field excitations possessing the Bogolyubov spectrum and to such a pair plus the quantum of the electromagnetic field with the finite radius of propagation implied by the finite London penetration depth are evaluated.
  • An excited vortex in the Abelian Higgs model is investigated with the help of a polynomial approximation. The excitation consists of the longitudinal component of a vector field trapped by the vortex. The energy and profile of the excitation as well as its back reaction on the vortex are found in the case of small {kappa}. It turns out that the width of the excited vortex oscillates in time. Moreover, the vector field has a radiative long range component. Also, an upper bound on the amplitude of the excitation is found. {copyright} {ital 1996 The American Physical Society.}
  • An exact vortex solution for the Abelian Higgs model is found when a particular relation between the coupling constants is satisfied. For this case (in which the masses of the scalar and vector bosons are the same), we decouple the classical field equations and solve them. We obtain power-series expansions and asymptotic expressions for the solution. The values of the fields are explicitly calculated for a one-quantum-of-flux solution, and bounds are established for the n-quanta case. Finally, we discuss the field form factors. (AIP)
  • The confining and topological properties of the compact Abelian Higgs model with doubly-charged Higgs field in three space-time dimensions are studied. We consider the London limit of the model. We show that the monopoles are forming chainlike structures (kept together by Abrikosov-Nielsen-Olesen vortices), the presence of which is essential for getting simultaneously permanent confinement of singly-charged particles and breaking of the string spanned between doubly-charged particles. In the confinement phase, the chains are forming percolating clusters, while in the deconfinement (Higgs) phase, the chains are of finite size. The described picture is in close analogy with the synthesis of themore » Abelian monopole and the center vortex pictures in confining non-Abelian gauge models. The screening properties of the vacuum are studied by means of the photon propagator in the Landau gauge.« less
  • We present an exact numerical computation of the one-loop correction of the string tension for the Nielsen-Olesen vortex in the Abelian Higgs model. The computation proceeds via the computation of the Euclidean Green's function for the gauge, Higgs, and Faddeev-Popov fields using mode functions, and taking the appropriate trace. Renormalization is an essential part of this computation. It is done by removing leading order contributions from the numerical results so as to make these finite, and to add the divergent parts back, after suitable regularization and renormalization. We encounter and solve some problems which are specific to gauge theories andmore » topological solutions. The corrections to the energy are found to be sizable, but still smaller than the classical energy as long as g{sup 2} is smaller than unity.« less