Transition temperatures of the trapped ideal spinor Bose gas

The thermodynamic properties of the trapped ideal spinor Bose gas are studied in details with the constraints of fixed total number of atoms N, and magnetization M. The double transition temperatures, their corresponding corrections due to finite particle number, and the population of each component are investigated. The generalization to the ideal spinor Bose gas of hyperfine quantum number F is also discussed. We propose that the order and disorder parameters to describe the symmetry broken of condensation.     

Phase separation in the trapped spinor gases with anisotropic spin-spin interaction

We investigate the effect of the anisotropic spin-spin interaction on the ground state density distribution of the one dimensional spin-1 bosonic gases within a modified Gross-Pitaevskii theory both in the weakly interaction regime and in the Tonks-Girardeau (TG) regime. We find that for ferromagnetic spinor gas the phase separation occurs even for weak anisotropy of the spin-spin interaction, which becomes more and more obvious and the component of m_F=0 diminishes as the anisotropy increases. However, no phase separation is found for anti-ferromagnetic spinor gas in both regimes.     

Coreless vortex formation in a spinor Bose-Einstein condensate

Coreless vortices were phase imprinted in a spinor Bose-Einstein condensate. The three-component order parameter of F=1 sodium condensates held in a Ioffe-Pritchard magnetic trap was manipulated by adiabatically reducing the magnetic bias field along the trap axis to zero. This distributed the condensate population across its three spin states and created a spin texture. Each spin state acquired a different phase winding which caused the spin components to separate radially.     

Dynamics of spinor condensates and stochastic approach

The dynamics of the collective spin for Bose-Einstein condensates with nonlinear interactions, is studied within the framework of the two-component spinor. We discuss the spin resonance when the system is submitted to a periodically-modulated magnetic field at the zero temperature. In this case, the nonlinearity parameter controls the critical change between a localized and a homogeneous spin state. When the temperature is finite – or a random magnetic field is considered – the movement of the collective spin is governed by the Landau-Lifshitz-Gilbert equation, from which the complete Fokker-Planck equation is derived. This equation is the essential tool to describe the time-evolution of the probability distribution function for the collective spin. The functional integral approach is used to solve analytically examples of BEC spin behavior in a static magnetic field at finite temperature. We show how such a method can lead effectively to the complete solution of the Fokker-Planck equation for this kind of problems.     

Complex quantum gases: spinor Bose–Einstein condensates of trapped atomic vapors

We discuss the energy eigenstates, ground and spin mixing dynamics of a spin-1 spinor Bose–Einstein condensate for a dilute atomic vapor confined in an optical trap. Our results go beyond the mean field picture and are developed within a fully quantized framework.     

Nonlinear Spin and Pseudo-Spin Symmetric Dirac Equations

Nonlinear Dirac equations are obtained by variation of the spinor action whose Lagrangian components have the same conformal degree and the coupling parameter of the self-interaction term is dimensionless. In 1+1 space-time, we show that these requirements result in the “conventional” quartic form of the nonlinear interaction and present the general equation for various coupling modes. These include, but not limited to, the Thirring and Gross-Neveu models. We consider the spin and pseudo-spin symmetric models and obtain a numerical solution. We also propose a two-component “minimal” pseudo-scalar coupling model.     

The index of the scattering operator on the positive spectral subspace

We construct the scattering operator for a spinor field in a time dependent background by the Dyson expansion. Then we show that the restriction of the scattering operator to the positive spectral subspace (with respect to a reference Hamiltonian) is Fredholm. The computation of the index of this restriction is reduced to the index computation for an elliptic pseudodifferential operator of order zero. We obtain the index in terms of a cohomological formula by means of the Atiyah-Singer index theorem.     

Solutions of multi-component NLS models and Spinor Bose-Einstein condensates

Three- and five-component nonlinear Schrödinger-type models, which describe spinor Bose-Einstein condensates (BEC’s) with hyperfine structures F=1 and F=2, respectively, are studied. These models for particular values of the coupling constants are integrable by the inverse scattering method. They are related to symmetric spaces of BD.I-type for r=2 and r=3. Using conveniently modified Zakharov-Shabat dressing procedure we obtain different types of soliton solutions.     

玻色凝聚的原子自旋链中的非线性自旋波

研究了囚禁在光晶格中的旋量玻色-爱因斯坦凝聚体(BEC)形成的原子自旋链中的相干非线性自旋波的激发与调制不稳定性.通过解析分析，得到了调制不稳定性的一般判据以及其对原子自旋的长程耦合的依赖关系.在蓝失谐和红失谐光晶格的情况下，分别具体分析了长程非线性自旋耦合，包括光诱导的和静磁诱导的偶极-偶极相互作用对相干自旋波调制不稳定性的影响.     

Space-time evolution induced by spinor fields with canonical and non-canonical kinetic terms

We study spinor field theories as an origin to induce space-time evolution. Self-interacting spinor fields with canonical and non-canonical kinetic terms are considered in a Friedman–Robertson–Walker universe. The deceleration parameter is calculated by solving the equation of motion and the Friedman equation, simultaneously. It is shown that the spinor fields can accelerate and decelerate the universe expansion. To construct realistic models we discuss the contributions from the dynamical symmetry breaking.     

Dynamics and thermodynamics in spinor quantum gases

We discuss magnetism in spinor quantum gases theoretically and experimentally with emphasis on temporal dynamics of the spinor order parameter in the presence of an external magnetic field. In a simple coupled Gross–Pitaevskii picture we observe a dramatic suppression of spin dynamics due to quadratic Zeeman dephasing. In view of an inhomogeneous density profile of the trapped condensate we present evidence of spatial variations of spin dynamics. In addition we study spinor quantum gases as a model system for thermodynamics of Bose–Einstein condensation. As a particular example we present measurements on condensate magnetisation due to the interaction with a thermal bath. PACS 03.75.Mn; 03.75.Fi; 34.50.Pi     

T-duality and non-local supersymmetries

We study the non-localization of extended worldsheet supersymmetry under T-duality, when the associated complex structure depends on the coordinate with respect to which duality is performed. First, the canonical transformation which implements T-duality is generalized to the supersymmetric non-linear σ-models. Then, we obtain the non-local object which replaces the complex structure in the dual theory and write down the condition it should satisfy so that the dual action is invariant under the non-local supersymmetry. For the target space, this implies that the supersymmetry transformation parameter is a non-local spinor. The analogue of the Killing equation for this non-local spinor is obtained. It is argued that in the target space the supersymmetry is no longer realized in the standard way. The string theoretic origin of this phenomenon is briefly discussed.     

A Spinorization of a Constrained Vector System and a Spinor Reconstruction Theorem

An elementary method of conctructing a spinor from vectors satisfying constraint conditions is proposed. We consider orthonormal triad and tetrad as an orientable physical object and introduce parameter representations of them, in terms of the Euler angles and the pseudo-Euler angles. Having determined the transformation property of the parameters, we set up the spinor determining equation. This equation is solved. The solution (spinor) contains four arbitrary complex constants, in 3 + 1 dimensional space. Using the proposed method, we prove the spinor reconstruction theorem, i.e. the original Dirac spinor can be reconstructed from seven of the sixteen hermitian bilinear forms, except the overall phase factor (the gauge freedom of the 1st kind). The energy density of the spinor field is written in terms of currents and their space derivatives.     

Collective spin tunneling in spinor Bose-Einstein condensates

We investigate a novel aspect of rotational tunneling of the macroscopic spin for multicomponent spinor Bose-Einstein condensate (BEC). The Lagrangian is deduced from the multi-component BEC system formalism, and is written in terms of spin coherent states. From the effective Hamiltonian for the collective spin, the tunneling rate is obtained through a functional integral of the spin variable. It is pointed out that the cooperative effect between the Zeeman energy and the anisotropic nature of the spin-dependent inter-atomic interaction plays a key role for occurrence of collective spin tunneling.     

Spinors, Inflation, and Non-Singular Cyclic Cosmologies

We consider toy cosmological models in which a classical, homogeneous, spinor field provides a dominant or sub-dominant contribution to the energy-momentum tensor of a flat Friedmann-Robertson-Walker universe. We find that, if such a field were to exist, appropriate choices of the spinor self-interaction would generate a rich variety of behaviors, quite different from their widely studied scalar field counterparts. We first discuss solutions that incorporate a stage of cosmic inflation and estimate the primordial spectrum of density perturbations seeded during such a stage. Inflation driven by a spinor field turns out to be unappealing as it leads to a blue spectrum of perturbations and requires considerable fine-tuning of parameters. We next find that, for simple, quartic spinor self-interactions, non-singular cyclic cosmologies exist with reasonable parameter choices. These solutions might eventually be incorporated into a successful past- and future-eternal cosmological model free of singularities. In an Appendix, we discuss the classical treatment of spinors and argue that certain quantum systems might be approximated in terms of such fields.     

Indefinite charge for the classical spinor field

We define a conserved Lorentz vector for a two-component spinor field that obeys the Klein-Gordon equation and interpret it as a charge-current density. The corresponding total charge can take negative as well as positive values, which is not the case for the usual charge of the Dirac field. We consequently can define probability amplitudes for a relativistic quantum mechanics, and we solve the inhomogeneous equation by means of the causal Green function. This vector is not invariant under gauge transformations of the spinor field, and we cannot generalize the equation by the gauge invariant substitution to obtain the interaction with an electromagnetic field. In the limit of a massless field that obeys the Weyl equation, the charge vanishes.     

New cohomogeneity one metrics with Spin(7) holonomy

We construct new explicit non-singular metrics that are complete on non-compact Riemannian 8-manifolds with holonomy Spin(7). One such metric, which we denote by , is complete and non-singular on . The other complete metrics are defined on manifolds with the topology of the bundle of chiral spinors over S⁴, and are denoted by , and . The metrics on and occur in families with a non-trivial parameter. The metric on arises for a limiting value of this parameter, and locally this metric is the same as the one for . The new Spin(7) metrics are asymptotically locally conical (ALC): near infinity they approach a circle bundle with fibres of constant length over a cone whose base is the squashed Einstein metric on . We construct the covariantly constant spinor and calibrating 4-form. We also obtain an L²-normalisable harmonic 4-form for the manifold, and two such 4-forms (of opposite dualities) for the manifold.     

Any J-State Solution of the Duffin–Kemmer–Petiau Equation for a Vector Deformed Woods–Saxon Potential

By using the Pekeris approximation, the Duffin–Kemmer–Petiau (DKP) equation is investigated for a vector deformed Woods–Saxon (dWS) potential. The parametric Nikiforov–Uvarov (NU) method is used in calculations. The approximate energy eigenvalue equation and the corresponding wave function spinor components are calculated for any total angular momentum J in closed form. The exact energy equation and wave function spinor components are also given for the J?=?0 case. We use a set of parameter values to obtain the numerical values for the energy states with various values of quantum levels (n, J) and potential’s deformation constant q and width R.     

Killing spinors for the bosonic string and Kaluza–Klein theory with scalar potentials

The paper consists mainly of two parts. In the first part, we obtain well-defined Killing spinor equations for the low-energy effective action of the bosonic string with the conformal anomaly term. We show that the conformal anomaly term is the only scalar potential that one can add into the action that is consistent with the Killing spinor equations. In the second part, we demonstrate that Kaluza–Klein theory can be gauged so that the Killing spinors are charged under the Kaluza–Klein vector. This gauging process generates a scalar potential with a maximum that gives rise to an AdS spacetime. We also construct solutions of these theories.     

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).