Monopole-Antimonopole Pair Dyons

Monopole-antimonopole pair (MAP) with both electric and magnetic charges are presented. The MAP possess opposite magnetic charges but they carry the same electric charges. These stationary MAP dyon solutions possess finite energy but they do not satisfy the first order Bogomol'nyi equations and are not BPS solutions. They are axially symmetric solutions and are characterized by a parameter, $-1\leq\eta\leq 1$ which determines the net electric charges of these MAP dyons. These dyon solutions are solved numerically when the magnetic charges of the dipoles are $n=\pm 1, \pm 2$ and when the strength of the Higgs field potential $\lambda=0, 1$. When $\lambda=0$, the time component of the gauge field potential is parallel to the Higgs field in isospin space and the MAP separation distance, total energy and net electric charge increase exponentially fast to infinity when $\eta$ approaches $\pm 1$. However when $\lambda=1$, all these three quantities approach a finite critical value as $\eta$ approaches $\pm 1$.Comment: 20 pages, 9 figures, 2 table

Monopole-Antimonopole Pair, Vortex Dyons Of The SU(2) Yang-Mills-Higgs Field Theory

Magnetic monopoles and dyons are topological soliton solutions in three space dimensions, which arise in Yang-Mills-Higgs gauge theory where the non-Abelian gauge group SU(2) is spontaneously broken by the Higgs �eld to a residual symmetry group U(1). While the magnetic charge is quantized due to topological arguments, the electric charge is not. In this thesis, the magnetic monopoles and dyons are studied in the context of the SU(2) Yang-Mills-Higgs �eld theory which is also known as the SU(2) Georgi- Glashow model

Generalized Jacobi Elliptic One-Monopole - Type A

We present new classical generalized one-monopole solution of the SU(2) Yang-Mills-Higgs theory with the Higgs field in the adjoint representation. We show that this generalized solution with $\theta$-winding number $m=1$ and $\phi$-winding number $n=1$ is an axially symmetric Jacobi elliptic generalization of the 't Hooft-Polyakov one-monopole. We construct this axially symmetric one-monopole solution by generalizing the large distance asymptotic solution of the 't Hooft-Polyakov one-monopole to the Jacobi elliptic functions and solving the second order equations of motion numerically when the Higgs potential is vanishing and non vanishing. These solutions are regular non-BPS finite energy solutions.Comment: 17 pages, 5 figure

Theory of phase transitions in ferroelectric superlattices / Lim Kok Geng

Ferroelectric superlattices comprising two or more different layers are currently a topic of active research because of their potential applications in memories and fundamental scientific interest. A thermodynamic model based on the Landau-Ginzburg theory is proposed to study the phase transitions in ferroelectric superlattices. An interface energy term is introduced in the free energy to describe the formation of intermixed layer with properties different from those of both layers. These intermixed layers are mutually coupled through the local polarization at interfaces. The effects of electrostatic coupling and interface intermixing on the internal electric field and polarization of superlattices which composed of alternate layers of ferroelectrics and paraelectrics are discussed. As an illustration, the model is applied to a superlattice consisting of a ferroelectric layer as PbTiO3 (PT) and a paraelectric layer as SrTiO3 (ST) on a ST substrate. Appropriate electrostatic boundary conditions are considered for the case of superlattice with polarization perpendicular to the surface or interface. The effect of interface intermixing and modulation period on the internal electric field and polarization are studied by changing the volume fraction or thickness ratio of the PT/ST superlattice. In addition, the spatially-varying internal electric field, dielectric susceptibility and polarization of these ferroelectric superlattices are calculated. Effects of modulation period and temperature on the internal electric field, dielectric susceptibility and polarization of these superlattices with inhomogeneous properties are examined. The polarization reversal in PT/ST superlattices with “switchable” polarization in intermixed layers is also studied. The dependence of polarization and internal electric field on an applied electric field is discussed. The polarization and internal electric field profiles at certain applied electric field are examined. Besides that, the effects of alternating interface charges, �s of the ferroelectric superlattices are studied by taking into account the intermixing at the iii interfaces between layers. The alternating interface charges enhance the polarization of ferroelectric superlattices, and lead to the formation of an effective internal electric field in the superlattices. Lastly, the thermodynamic model is extended to study the effect of composition and interface intermixing on ferroelectric properties of BaTiO3=BaxSr

Vortex ring dyons of the SU(2) Yang‐Mills‐Higgs model

We present an axially symmetric vortex ring dyons solutions of the SU(2) Yang‐Mills‐Higgs theory. These vortex rings carry electric charges that are determined by a parameter, −1⩽η⩽1.−1⩽η⩽1. They possess vanishing magnetic charge and are located at a ring centered around the z‐axis where the Higgs field vanishes. These stationary vortex ring dyon solutions possess finite energy but they do not satisfy the first order Bogomol’nyi equations. In the Bogomol’nyi‐Prasad‐Sommerfield (BPS) limit where the Higgs field potential is zero, the time component of the gauge field is parallel to the Higgs field in isospace. The total energy, net electric charge and diameter of the vortex ring increase exponentially to infinity when η approaches ±1.±1. On the contrary, when λ = 1,λ = 1, all these three values reach their critical value as η approaches ±1

Some comments on the string singularity of the Yang-Mills-Higgs theory

We are going to make use of the regulated polar angle which had been introduced by Boulware et al.. to show that in the SU(2) Yang‐Mills‐Higgs theory when the magnetic monopole is carried by the gauge field, the Higgs field does not carry the monopole and vice versa. In the Yang‐Mills‐Higgs theory, our solution shows that when the parameter ε ≠ 0,ε ≠ 0, the monopole is carried by the gauge field and there is a string singularity in the gauge field. When the parameter ε → 0,ε → 0, the monopole is transferred from the gauge field to the Higgs field and the string singularity disappeared. The solution is only singular at the origin, that is at r = 0r = 0 as it becomes the Wu‐Yang monopole

Tuning of polarization, internal electric field, and hysteresis loop behaviours in BaTiO₃/Ba_xSr_1-xTiO₃ superlattices

A thermodynamic model based on the Landau-Ginzburg theory is developed to study the polarization and hysteresis loop behaviors in ferroelectric superlattices with technologically important BaxSr1-xTiO3 (BST) solid solutions. Our study shows that the polarization, coercive field, and hysteresis loop behaviors can be tailored by changing the thickness ratio and the Ba/Sr content of BST. The study also found that the sign of the internal fields depends sensitively on both thickness ratio and Ba/Sr content of BST. Both results imply that the internal electric field of superlattice can be tuned to yield zero polarizing or depolarizing field via manipulation of thickness ratio and composition. These findings could pave the way to enhance the efficiency of ferroelectric photovoltaic devices by manipulating the internal electric field through thickness and composition

Interface-induced modifications of polarization in nanoscale ferroelectric superlattices

A thermodynamic model to study the effect of interface intermixing on polarization of ferroelectric superlattices composed of a ferroelectric and paraelectric layers is developed. Interface intermixing forms an intermixed layer with property different from its individual layers, leading to inhomogeneous ferroelectric properties in the superlattices. Polarization induces near the interface of paraelectric layers, which extends into the layer over a distance governed by its characteristic length. Dependence of polarization on periodic thickness indicates an interface-induced modification of ferroelectricity in superlattices. Enhancement in polarization of superlattices is shown to be possible, if certain interface property and periodic thickness met

Magnetic half-monopole solutions

We present exact SU(2) Yang‐Mills‐Higgs monopole solutions of one half topological charge. These non‐Abelian solutions possess gauge potentials which are singular along either the positive or the negative z‐axis and common magnetic fields that are singular only at the origin where the half‐monopole is located. These half‐monopoles are actually a half Wu‐Yang monopole and they can possess a finite point electric charge and become half‐dyons. They do not necessarily satisfy the first order Bogomol’nyi equations and they possess infinite energy density at r = 0