Einstein--de Haas Effect in Dipolar Bose-Einstein Condensates

The general properties of the order parameter for a dipolar spinor Bose-Einstein condensate are discussed based on symmetries of interactions. An initially spin-polarized dipolar condensate is shown to dynamically generate a non-singular vortex via spin-orbit interactions -- a phenomenon reminiscent of the Einstein--de Haas effect in ferromagnets.Comment: 4 pages, 4 figures; Final versio

Spontaneous Circulation in Ground-State Spinor Dipolar Bose-Einstein Condensates

We report on a study of the spin-1 ferromagnetic Bose-Einstein condensate with magnetic dipole-dipole interactions. By solving the non-local Gross-Pitaevskii equations for this system, we find three ground-state phases. Moreover, we show that a substantial orbital angular momentum accompanied by chiral symmetry breaking emerges spontaneously in a certain parameter regime. We predict that all these phases can be observed in the spin-1 $^{87}$Rb condensate by changing the number of atoms or the trap frequency.Comment: final versio

Scalable Sparse Cox's Regression for Large-Scale Survival Data via Broken Adaptive Ridge

This paper develops a new scalable sparse Cox regression tool for sparse high-dimensional massive sample size (sHDMSS) survival data. The method is a local $L_0$-penalized Cox regression via repeatedly performing reweighted $L_2$-penalized Cox regression. We show that the resulting estimator enjoys the best of $L_0$- and $L_2$-penalized Cox regressions while overcoming their limitations. Specifically, the estimator is selection consistent, oracle for parameter estimation, and possesses a grouping property for highly correlated covariates. Simulation results suggest that when the sample size is large, the proposed method with pre-specified tuning parameters has a comparable or better performance than some popular penalized regression methods. More importantly, because the method naturally enables adaptation of efficient algorithms for massive $L_2$-penalized optimization and does not require costly data driven tuning parameter selection, it has a significant computational advantage for sHDMSS data, offering an average of 5-fold speedup over its closest competitor in empirical studies

Topological defect formation in quenched ferromagnetic Bose-Einstein condensates

We study the dynamics of the quantum phase transition of a ferromagnetic spin-1 Bose-Einstein condensate from the polar phase to the broken-axisymmetry phase by changing magnetic field, and find the spontaneous formation of spinor domain walls followed by the creation of polar-core spin vortices. We also find that the spin textures depend very sensitively on the initial noise distribution, and that an anisotropic and colored initial noise is needed to reproduce the Berkeley experiment [Sadler et al., Nature 443, 312 (2006)]. The dynamics of vortex nucleation and the number of created vortices depend also on the manner in which the magnetic field is changed. We point out an analogy between the formation of spin vortices from domain walls in a spinor BEC and that of vortex-antivortex pairs from dark solitons in a scalar BEC.Comment: 10 pages, 11 figure

The Wave Speed of Intergradation Zone in Two-Species Lattice Muellerian Mimicy Model

A spatially explicit model is studied to analyse the movement of coupled clines in two-species Muuellerian mimicry system as exemplified by the comimicking helicoiine butterflies in Central-South America "Heliconius erato" and "Heliconius melpomene". In this system, a pair of comimicking wing patterns of two species (mimicry ring) is found in a geographical region but another pair of wing patterns is found in a different geographical region. The distribution of mimicry rings thus forms a spatial mosaic in a large geographical scale, and the mechanism responsible for their stable maintenance has been a long-standing question in evolutionary biology. We here examine the speed of the movement of boundaries that divide the regions inhabited by different mimetic morphs in each comimicking species, by assuming coupled two-state stochastic cellular automatons where the flipping rate of the site occupied by a mimetic morph depends on the local density of the same morph and of the comimicking morph in the other species. The speed of cline movement shows a complex dependence on the coupling parameter between mimetic species -greater coupling of comimicking morphs between species slows down the cline movement only when the reduction in predation rate exhibits diminishing return to the increase of local mimetic morph density. The analytical predictions are confirmed by the results of Monte Carlo simulations. The speed of advance is quite different from that predicted from the conventional reaction-diffusion model, indicating that demographic stochasticity plays a critical role in determining the speed of cline movement. We also examine if the spatial heterogeneity in migration rate can stably maintain clines

On the classical equivalence of monodromy matrices in squashed sigma model

We proceed to study the hybrid integrable structure in two-dimensional non-linear sigma models with target space three-dimensional squashed spheres. A quantum affine algebra and a pair of Yangian algebras are realized in the sigma models and, according to them, there are two descriptions to describe the classical dynamics 1) the trigonometric description and 2) the rational description, respectively. For every description, a Lax pair is constructed and the associated monodromy matrix is also constructed. In this paper we show the gauge-equivalence of the monodromy matrices in the trigonometric and rational description under a certain relation between spectral parameters and the rescalings of sl(2) generators.Comment: 32pages, 3figures, references added, introduction and discussion sections revise

The classical origin of quantum affine algebra in squashed sigma models

We consider a quantum affine algebra realized in two-dimensional non-linear sigma models with target space three-dimensional squashed sphere. Its affine generators are explicitly constructed and the Poisson brackets are computed. The defining relations of quantum affine algebra in the sense of the Drinfeld first realization are satisfied at classical level. The relation to the Drinfeld second realization is also discussed including higher conserved charges. Finally we comment on a semiclassical limit of quantum affine algebra at quantum level.Comment: 25 pages, 2 figure

Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence

We consider \gamma-deformations of the AdS_5xS^5 superstring as Yang-Baxter sigma models with classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). An essential point is that the classical r-matrices are composed of Cartan generators only and then generate abelian twists. We present examples of the r-matrices that lead to real \gamma-deformations of the AdS_5xS^5 superstring. Finally we discuss a possible classification of integrable deformations and the corresponding gravity solution in terms of solutions of CYBE. This classification may be called the gravity/CYBE correspondence.Comment: 18 pages, no figure, LaTeX, v2:references and further clarifications adde