[Colored solutions of Yang-Baxter equation from representations of U_{q}gl(2)]

We study the Hopf algebra structure and the highest weight representation of a multiparameter version of $U_{q}gl(2)$. The commutation relations as well as other Hopf algebra maps are explicitly given. We show that the multiparameter universal ${\cal R}$ matrix can be constructed directly as a quantum double intertwiner, without using Reshetikhin's transformation. An interesting feature automatically appears in the representation theory: it can be divided into two types, one for generic $q$, the other for $q$ being a root of unity. When applying the representation theory to the multiparameter universal ${\cal R}$ matrix, the so called standard and nonstandard colored solutions $R(\mu,\nu; {\mu}', {\nu}')$ of the Yang-Baxter equation is obtained.Comment: [14]pages, latex, no figure

Y(so(5)) symmtry of the nonlinear Schro¨\ddot{o}dinger model with four-cmponents

The quantum nonlinear Schr$\ddot{o}$dinger(NLS) model with four-component fermions exhibits a $Y(so(5))$ symmetry when considered on an infintite interval. The constructed generators of Yangian are proved to satisfy the Drinfel'd formula and furthermore, the $RTT$ relation with the general form of rational R-matrix given by Yang-Baxterization associated with $so(5)$ algebraic structure.Comment: 10 pages, no figure

Variational formulas of higher order mean curvatures

In this paper, we establish the first variational formula and its Euler-Lagrange equation for the total $2p$-th mean curvature functional $\mathcal {M}_{2p}$ of a submanifold $M^n$ in a general Riemannian manifold $N^{n+m}$ for $p=0,1,...,[\frac{n}{2}]$. As an example, we prove that closed complex submanifolds in complex projective spaces are critical points of the functional $\mathcal {M}_{2p}$, called relatively $2p$-minimal submanifolds, for all $p$. At last, we discuss the relations between relatively $2p$-minimal submanifolds and austere submanifolds in real space forms, as well as a special variational problem.Comment: 13 pages, to appear in SCIENCE CHINA Mathematics 201

Laser-induced charging of microfabricated ion traps

Electrical charging of metal surfaces due to photoelectric generation of carriers is of concern in trapped ion quantum computation systems, due to the high sensitivity of the ions' motional quantum states to deformation of the trapping potential. The charging induced by typical laser frequencies involved in doppler cooling and quantum control is studied here, with microfabricated surface electrode traps made of aluminum, copper, and gold, operated at 6 K with a single Sr$^+$ ion trapped 100 $\mu$m above the trap surface. The lasers used are at 370, 405, 460, and 674 nm, and the typical photon flux at the trap is 10$^{14}$ photons/cm$^2$/sec. Charging is detected by monitoring the ion's micromotion signal, which is related to the number of charges created on the trap. A wavelength and material dependence of the charging behavior is observed: lasers at lower wavelengths cause more charging, and aluminum exhibits more charging than copper or gold. We describe the charging dynamic based on a rate equation approach.Comment: 8 pages, 8 figure

Algebraic Bethe Ansatz for Integrable Extended Hubbard Models Arising from Supersymmetric Group Solutions

Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded Quantum Inverse Scattering Method. The Bethe ansatz equations for all these models are derived by using the algebraic Bethe ansatz method.Comment: 15 pages, RevTex, No figures, to be published in J. Phys.

Local stability of an endoreversible heat pump with linear phenomenological heat transfer law working in an ecological regime

AbstractBased on the optimal ecological performance parameters of a heat pump with linear phenomenological heat transfer law between working fluid and heat reservoirs, the local stability analysis of the endoreversible heat pump working in an ecological regime is studied. The steady state of the heat pump working at the maximum ecological function is steady. After a small perturbation, the system state exponentially decays to steady state with either of the two relaxation times. The effects of temperatures of heat reservoirs and heat transfer coefficients on the local stability of the system are discussed. Distribution information of phase portraits of the system is obtained. It is concluded that both the energetic properties and local stability of the system should be considered for designing the real heat pumps