By using topological current theory we study the inner topological structure of vortices a two-dimensional (2D) XY model and find the topological current relating to the order parameter field. A scalar field, $ψ$ , is introduced through the topological current theory. By solving the scalar field, the interaction energy of vortices in a 2D XY model is revisited. We study the dynamical evolution of vortices and present the branch conditions for generating, annihilating, crossing, splitting and merging of vortices. During the growth or annihilation of vortices, the dynamical scaling law of relevant length in a 2D XY model, $ξ(t)\propto(t-t^*)^{1/z}$ , is obtained in the neighborhood of the limit point, given the dynamic exponent $z=2$ . This dynamical scaling behavior is consistent with renormalization group theory, numerical simulations, and experimental results. Furthermore, it is found that during the crossing, splitting and merging of vortices, the dynamical scaling law of relevant length is $ξ(t)\propto(t-t^*)$ . However, if vortices are at rest during splitting or merging, the dynamical scaling law of relevant length is a constat.By using topological current theory we study the inner topological structure of vortices a two-dimensional (2D) XY model and find the topological current relating to the order parameter field. A scalar field, $ψ$, is introduced through the topological current theory. By solving the scalar field, the interaction energy of vortices in a 2D XY model is revisited. We study the dynamical evolution of vortices and present the branch conditions for generating, annihilating, crossing, splitting and merging of vortices. During the growth or annihilation of vortices, the dynamical scaling law of relevant length in a 2D XY model, $ξ(t)\propto(t-t^*)^{1/z}$, is obtained in the neighborhood of the limit point, given the dynamic exponent $z=2$. This dynamical scaling behavior is consistent with renormalization group theory, numerical simulations, and experimental results. Furthermore, it is found that during the crossing, splitting and merging of vortices, the dynamical scaling law of relevant length is $ξ(t)\propto(t-t^*)$. However, if vortices are at rest during splitting or merging, the dynamical scaling law of relevant length is a constat.

arXiv:0809.0348Sep 2, 20080 citations

Vortices and Rotation

Carlo F. Barenghi, Nick G. Parker

SpringerBriefs in physicsJan 1, 20161 citation

Violation of single-length-scaling dynamics via spin vortices in an isolated spin-1 Bose gas

Christian-Marcel Schmied, Thomas Gasenzer, P. B. Blakie

We consider the phase-ordering dynamics of an isolated quasi-two-dimensional spin-1 Bose gas quenched into an easy-plane ferromagnetic phase. Preparing the initial system in an unmagnetized antiferromagnetic state the subsequent ordering involves both polar core and Mermin-Ho spin vortices, with the ratio between the different vortices controllable by the quench parameter. Ferromagnetic domain growth occurs as these vortices annihilate. The distinct dynamics of the two types of vortices means that the domain growth law is determined by two macroscopic length scales, violating the standard dynamic scaling hypothesis. Nevertheless we find that universality of the ordering process manifests in the decay laws for the spin vortices. To provide a fuller picture of the phase ordering dynamics we also present results for the scaling of the order parameter correlation function and the hydrodynamic decomposition of the system kinetic energy.We consider the phase-ordering dynamics of an isolated quasi-two-dimensional spin-1 Bose gas quenched into an easy-plane ferromagnetic phase. Preparing the initial system in an unmagnetized antiferromagnetic state the subsequent ordering involves both polar core and Mermin-Ho spin vortices, with the ratio between the different vortices controllable by the quench parameter. Ferromagnetic domain growth occurs as these vortices annihilate. The distinct dynamics of the two types of vortices means that the domain growth law is determined by two macroscopic length scales, violating the standard dynamic scaling hypothesis. Nevertheless we find that universality of the ordering process manifests in the decay laws for the spin vortices. To provide a fuller picture of the phase ordering dynamics we also present results for the scaling of the order parameter correlation function and the hydrodynamic decomposition of the system kinetic energy.

arXiv:1904.13222Physical Review ASep 3, 201923 citations

Visions of vortices

Sarah Tomlin

NatureJan 1, 19991 citation

Quantised Vortices

Tapio Simula

Vortices comprising swirling motion of matter are observable in classical systems at all scales ranging from atomic size to the scale of galaxies. In quantum mechanical systems, such vortices are robust entities whose behaviours are governed by the strict rules of topology. The physics of quantum vortices is pivotal to the basic science of quantum turbulence and high-temperature superconductors, and underpins emerging quantum technologies including topological quantum computation. This handbook is aimed at providing a dictionary-style portal to the fascinating quantum world of vortices.Vortices comprising swirling motion of matter are observable in classical systems at all scales ranging from atomic size to the scale of galaxies. In quantum mechanical systems, such vortices are robust entities whose behaviours are governed by the strict rules of topology. The physics of quantum vortices is pivotal to the basic science of quantum turbulence and high-temperature superconductors, and underpins emerging quantum technologies including topological quantum computation. This handbook is aimed at providing a dictionary-style portal to the fascinating quantum world of vortices.

Morgan & Claypool Publishers eBooksJul 1, 20198 citations

Vortices wiggled and dragged

Charles M. Reichhardt

Nature PhysicsJan 1, 200924 citations

ψ

, is introduced through the topological current theory. By solving the scalar field, the interaction energy of vortices in a 2D XY model is revisited. We study the dynamical evolution of vortices and present the branch conditions for generating, annihilating, crossing, splitting and merging of vortices. During the growth or annihilation of vortices, the dynamical scaling law of relevant length in a 2D XY model,

ξ(t)\propto(t-t^*)^{1/z}

, is obtained in the neighborhood of the limit point, given the dynamic exponent

z=2

. This dynamical scaling behavior is consistent with renormalization group theory, numerical simulations, and experimental results. Furthermore, it is found that during the crossing, splitting and merging of vortices, the dynamical scaling law of relevant length is

ξ(t)\propto(t-t^*)

. However, if vortices are at rest during splitting or merging, the dynamical scaling law of relevant length is a constat.