Dynamics of spinor Bose–Einstein condensate subject to dissipation

We investigate the internal dynamics of the spinor Bose–Einstein condensates subject to dissipation by solving the Lindblad master equation. It is shown that for the condensates without dissipation its dynamics always evolve along a specific orbital in the phase space of(n_0, θ) and display three kinds of dynamical properties including Josephson-like oscillation, self-trapping-like oscillation, and ‘running phase'. In contrast, the condensates subject to dissipation will not evolve along the specific dynamical orbital. If component-1 and component-(-1) dissipate at different rates, the magnetization m will not conserve and the system transits between different dynamical regions. The dynamical properties can be exhibited in the phase space of(n_0, θ, m).     

Stationary two-black-hole configurations: A non-existence proof

Based on the solution of a boundary problem for disconnected (Killing) horizons and the resulting violation of characteristic black hole properties, we present a non-existence proof for equilibrium configurations consisting of two aligned rotating black holes. Our discussion is principally aimed at developing the ideas of the proof and summarizing the results of two preceding papers (Neugebauer and Hennig, 2009 [2], Hennig and Neugebauer, 2011 [3]). From a mathematical point of view, this paper is a further example (Meinel et al., (2008) [29]) for the application of the inverse (“scattering”) method to a non-linear elliptic differential equation.     

Some remarks on the geometry of superspace supergravity

In this note, we first give a quick presentation of the supergeometry underlying supergravity theories, using an intrinsic differential geometric language. For this, we adopt the point of view of Cartan geometries, and rely as well on the work of John Lott, who has found a unified geometrical interpretation of the torsion constraints for many supergravity theories, based on the use of H-structures. In this framework, the constraints amount to requiring first-order integrability of H-structures, for a specific supergroup H.The supergroup H used by Lott is not the usual diagonal representation of the Lorentz group on superspace, but an extension of the latter. This extension appears to be natural and it can be related to the super-Poincaré group. We also observe that the constraints arising from the requirement of first-order integrability have basically the same form, in any spacetime dimension.Looking at supergravity from an affine viewpoint (i.e. as a gauge theory for the super-Poincaré group), we show that requiring first-order integrability amounts to requiring the equivalence, up to gauge transformations, between infinitesimal gauge supertranslations acting on the supervielbein and infinitesimal superdiffeomorphisms acting on the supervielbein.The latter action is performed through a covariant Lie derivative, whose expression involves naturally the supertorsion tensor. We use this expression to show that the term added to the spin connection, in the supercovariant derivative of d=11 supergravity, has a natural superspace origin. In particular, the 4-form field strength is related to a specific component of the supertorsion tensor.We conclude by some general remarks concerning Killing spinors in geometry and supergravity, discussing their possible interpretations, as Killing vector fields on a specific supermanifold on one hand, and as parallel spinors for an appropriate connection on the other hand. We show that this last interpretation is very natural from the point of view of Klein and Cartan geometries.     

光格中旋量玻色-爱因斯坦凝聚的高阶非线性孤子激发

研究了一维光格中旋量玻色-爱因斯坦凝聚体的高阶非线性作用下的孤子激发,得出了用椭圆积分表示的明孤子解和特定参数条件下的暗孤子解析解,并求得了能量表达式.     

Generalized elastic curves in the Lorentz flat space <Emphasis Type="Italic">L</Emphasis><Superscript>4</Superscript>

In this paper, we study the extremals of the curvature energy actions on non-null curves in the four-dimensional Lorentz-Minkowski space. We derive the motion equations and find three Killing fields along the generalized elastic curves. We also construct a cylindrical coordinate system using these Killing fields and express the generalized elastic curves by means of quadratures.     

The extended trace identity and its application

The trace identity is extended to the general loop algebra. The Hamiltonian structures of the integrable systems concerning vector spectral problems and the multi-component integrable hierarchy can be worked out by using the extended trace identity. As its application, we have obtained the Hamiltonian structures of the Yang hierarchy, the Korteweg-de--Vries (KdV) hierarchy, the multi-component Ablowitz--Kaup--Newell--Segur (M-AKNS) hierarchy, the multi-component Ablowitz--Kaup--Newell--Segur Kaup--Newell (M-AKNS--KN) hierarchy and a new multi-component integrable hierarchy separately.     

Tunneling of Spinor Bose-Einstein Condensates in Optical Lattice

In this letter, we have studied the tunneling effects and fluctuations of spinor Bose-Einstein condensates in optical lattice. It is found that there exist tunneling effects and fluctuations between lattices l and l ＋ 1, l and l - 1, respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, tunneling effects disappear between lattices I and l＋ 1, and I and l - 1. In this case the fluctuations are a constant, and the magnetic soliton appears.     

SO（d,d;Z) Transformation Property for Gauge Fluxes and Ramond-Ramond Fields in Noncommutative Geometry

In this paper we study the spinor constructions of gauge fluxes and Ramond-Ramond fields on noncommutative tori T^d up to d=6. In which the spinor and conjugate spinor are distinguished and dual bases are also introduced.So that we can express the Chern-Simons Lagrangian in toroidal compactification as a product of spinors.     

旗流形的上同调环的自同态

本文应用李群理论,对紧单李群Ｇ,给出了旗流形 Ｇ／Ｔ的上同调环自同态的完全分类,并对典型群计算了相应自同态的Ｌｅｆｓｃｈｅｔｚ数．     

All-Optical Spin–Orbit Coupling of Light in Coherent Media Using Rotating Image

The possibility of all-optical spin–orbit coupling (SOC) of light is investigated based on a rotating spinor image traveling through an electromagnetically induced transparency (EIT) medium. It is shown that the paraxial evolution of the spinor image composed of two Laguerre–Gaussian (LG) modes with different frequencies can be analogous with the quantum dynamics of a spin-1/2 particle with strong and tunable SOC governed by the Pauli equation, where the spin-up and -down states have different effective masses. Using realistic EIT parameters with cold atoms, both the radial inhomogeneity of the strong control field and the atomic density distribution with comparable size are considered. The results confirm that the large group refractive index varying in the radial dimension mimicking the central potential can greatly enhance the spin–orbit interaction, leading to visible spatial quantization of the oppositely oriented spin states, equivalent to the two LG modes.