Effect of Spin Current on Uniform Ferromagnetism: Domain Nucleation

Large spin current applied to a uniform ferromagnet leads to a spin-wave instability as pointed out recently. In this paper, it is shown that such spin-wave instability is absent in a state containing a domain wall, which indicates that nucleation of magnetic domains occurs above a certain critical spin current. This scenario is supported also by an explicit energy comparison of the two states under spin current.Comment: 4 pages, 1 figure, REVTeX, rivised version, to appear in Physical Review Letter

Addressing Item-Cold Start Problem in Recommendation Systems using Model Based Approach and Deep Learning

Traditional recommendation systems rely on past usage data in order to generate new recommendations. Those approaches fail to generate sensible recommendations for new users and items into the system due to missing information about their past interactions. In this paper, we propose a solution for successfully addressing item-cold start problem which uses model-based approach and recent advances in deep learning. In particular, we use latent factor model for recommendation, and predict the latent factors from item's descriptions using convolutional neural network when they cannot be obtained from usage data. Latent factors obtained by applying matrix factorization to the available usage data are used as ground truth to train the convolutional neural network. To create latent factor representations for the new items, the convolutional neural network uses their textual description. The results from the experiments reveal that the proposed approach significantly outperforms several baseline estimators

Zero-brane approach to quantization of biscalar field theory about topological kink-bell solution

We study the properties of the topologically nontrivial doublet solution arisen in the biscalar theory with a fourth-power potential introducing an example of the spontaneous breaking of symmetry. We rule out the zero-brane (non-minimal point particle) action for this doublet as a particle with curvature. When quantizing it as the theory with higher derivatives, we calculate the quantum corrections to the mass of the doublet which could not be obtained by means of the perturbation theory.Comment: some references were adde

Domain Walls in SU(5)

We consider the Grand Unified SU(5) model with a small or vanishing cubic term in the adjoint scalar field in the potential. This gives the model an approximate or exact Z$_2$ symmetry whose breaking leads to domain walls. The simplest domain wall has the structure of a kink across which the Higgs field changes sign ($\Phi \to -\Phi$) and inside which the full SU(5) is restored. The kink is shown to be perturbatively unstable for all parameters. We then construct a domain wall solution that is lighter than the kink and show it to be perturbatively stable for a range of parameters. The symmetry in the core of this domain wall is smaller than that outside. The interactions of the domain wall with magnetic monopole is discussed and it is shown that magnetic monopoles with certain internal space orientations relative to the wall pass through the domain wall. Magnetic monopoles in other relative internal space orientations are likely to be swept away on collision with the domain walls, suggesting a scenario where the domain walls might act like optical polarization filters, allowing certain monopole ``polarizations'' to pass through but not others. As SU(5) domain walls will also be formed at small values of the cubic coupling, this leads to a very complicated picture of the evolution of defects after the Grand Unified phase transition.Comment: 6 pages, 1 figure. Animations can be viewed at http://theory4.phys.cwru.edu/~levon/figures.htm

Spin textures in rotating two-component Bose-Einstein condensates

We investigate two kinds of coreless vortices with axisymmetric and nonaxisymmetric configurations in rotating two-component Bose-Einstein condensates. Starting from the Gross-Pitaevskii energy functional in a rotating frame, we derive a nonlinear sigma model generalized to the two-component condensates. In terms of a pseudospin representation, an axisymmetric vortex and a nonaxisymmetric one correspond to spin textures referred to as a "skyrmion" and a "meron-pair", respectively. A variational method is used to investigate the dependence of the sizes of the stable spin textures on system parameters, and the optimized variational function is found to reproduce well the numerical solution. In the SU(2) symmetric case, the optimal skyrmion and meron-pair are degenerate and transform to each other by a rotation of the pseudospin. An external rf-field that couples coherently the hyperfine states of two components breaks the degeneracy in favor of the meron-pair texture due to an effective transverse pseudomagnetic field. The difference between the intracomponent and intercomponent interactions yields a longitudinal pseudomagnetic field and a ferromagnetic or an antiferromagnetic pseudospin interaction, leading to a meron-pair texture with an anisotropic distribution of vorticity.Comment: 14 pages, 15 figure

A Solution of the Maxwell-Dirac Equations in 3+1 Dimensions

We investigate a class of localized, stationary, particular numerical solutions to the Maxwell-Dirac system of classical nonlinear field equations. The solutions are discrete energy eigenstates bound predominantly by the self-produced electric field.Comment: 12 pages, revtex, 2 figure

Localization of Gauge Fields and Monopole Tunnelling

We study the dynamical localization of a massless gauge field on a lower-dimensional surface (2-brane). In flat space, the necessary and sufficient condition for this phenomenon is the existence of confinement in the bulk. The resulting configuration is equivalent to a dual Josephson junction. This duality leads to an interesting puzzle, as it implies that a localized massless theory, even in the Abelian case, must become confining at exponentially large distances. Through the use of topological arguments we clarify the physics behind this large-distance confinement and identify the instantons of the brane world-volume theory that are responsible for its appearance. We show that they correspond to the (condensed) bulk magnetic charges (monopoles), that occasionally tunnel through the brane and induce weak confinement of the brane theory. We consider the possible generalization of this effect to higher dimensions and discuss phenomenological bounds on the confinement of electric charges at exponentially large distances within our Universe.Comment: 11 pages, 3 figures, improvements in the presentation, version to appear in Physical Review

Microscopic Theory of Skyrmions in Quantum Hall Ferromagnets

We present a microscopic theory of skyrmions in the monolayer quantum Hall ferromagnet. It is a peculiar feature of the system that the number density and the spin density are entangled intrinsically as dictated by the W$$ algebra. The skyrmion and antiskyrmion states are constructed as W$_{\infty }$-rotated states of the hole-excited and electron-excited states, respectively. They are spin textures accompanied with density modulation that decreases the Coulomb energy. We calculate their excitation energy as a function of the Zeeman gap and compared the result with experimental data.Comment: 15 pages (to be published in PRB

Existence of Multiple Vortices in Supersymmetric Gauge Field Theory

Two sharp existence and uniqueness theorems are presented for solutions of multiple vortices arising in a six-dimensional brane-world supersymmetric gauge field theory under the general gauge symmetry group $G=U(1)\times SU(N)$ and with $N$ Higgs scalar fields in the fundamental representation of $G$. Specifically, when the space of extra dimension is compact so that vortices are hosted in a 2-torus of volume |\Om|, the existence of a unique multiple vortex solution representing $n_1,...,n_N$ respectively prescribed vortices arising in the $N$ species of the Higgs fields is established under the explicitly stated necessary and sufficient condition \[ n_i<\frac{g^2v^2}{8\pi N}|\Om|+\frac{1}{N}(1-\frac{1}{N}[\frac{g}{e}]^2)n,\quad i=1,...,N,] where $e$ and $g$ are the U(1) electromagnetic and SU(N) chromatic coupling constants, $v$ measures the energy scale of broken symmetry, and $n=\sum_{i=1}^N n_i$ is the total vortex number; when the space of extra dimension is the full plane, the existence and uniqueness of an arbitrarily prescribed $n$-vortex solution of finite energy is always ensured. These vortices are governed by a system of nonlinear elliptic equations, which may be reformulated to allow a variational structure. Proofs of existence are then developed using the methods of calculus of variations.Comment: 23 page

Families of stable and metastable solitons in coupled system of scalar fields

In this paper, we obtain stable and metastable soliton solutions of a coupled system of two real scalar fields with five five discrete points of vacua. These solutions have definite topological charges and rest energies and show classical dynamical stability. From a quantum point of view, however, the V-type solutions are expected to be unstable and decay to D-type solutions. The induced decay of a V-type soliton into two D-type ones is calculated numerically, and shown to be chiral, in the sense that the decay products do not respect left-right symmetry.Comment: 9 pages and 5 figure