Quantum Doubles from a Class of Noncocommutative Weak Hopf Algebras

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products are constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid as well as a noncommutative and noncocommutative weak Hopf algebra are given, generalizing quantum doubles from a group and a noncommutative and noncocommutative Hopf algebra, respectively. Moreover, some characterisations of quantum doubles of finite dimensional biperfect weak Hopf algebras are obtained.Comment: LaTex 18 pages, to appear in J. Math. Phys. (To compile, need pb-diagram.sty, pb-lams.sty, pb-xy.sty and lamsarrow.sty

An Effective Model of Magnetoelectricity in Multiferroics RMn2O5RMn_2O_5

An effective model is developed to explain the phase diagram and the mechanism of magnetoelectric coupling in multiferroics, $RMn_2O_5$. We show that the nature of magnetoelectric coupling in $RMn_2O_5$ is a coupling between two Ising-type orders, namely, the ferroelectric order in the b axis, and the coupled magnetic order between two frustrated antiferromagnetic chains. The frustrated magnetic structure drives the system to a commensurate-incommensurate phase transition, which can be understood as a competition between a collinear or col-plane order stemming from the `order by disorder' mechanism and a chiral symmetry order. The low energy excitation is calculated and the effect of the external magnetic field is analyzed. Distinct features in the electromagnon spectrums in the incommensurate phase are predicted

Bifurcation Boundary Conditions for Switching DC-DC Converters Under Constant On-Time Control

Sampled-data analysis and harmonic balance analysis are applied to analyze switching DC-DC converters under constant on-time control. Design-oriented boundary conditions for the period-doubling bifurcation and the saddle-node bifurcation are derived. The required ramp slope to avoid the bifurcations and the assigned pole locations associated with the ramp are also derived. The derived boundary conditions are more general and accurate than those recently obtained. Those recently obtained boundary conditions become special cases under the general modeling approach presented in this paper. Different analyses give different perspectives on the system dynamics and complement each other. Under the sampled-data analysis, the boundary conditions are expressed in terms of signal slopes and the ramp slope. Under the harmonic balance analysis, the boundary conditions are expressed in terms of signal harmonics. The derived boundary conditions are useful for a designer to design a converter to avoid the occurrence of the period-doubling bifurcation and the saddle-node bifurcation.Comment: Submitted to International Journal of Circuit Theory and Applications on August 10, 2011; Manuscript ID: CTA-11-016

Lateral shift of the transmitted light beam through a left-handed slab

It is reported that when a light beam travels through a slab of left-handed medium in the air, the lateral shift of the transmitted beam can be negative as well as positive. The necessary condition for the lateral shift to be positive is given. The validity of the stationary-phase approach is demonstrated by numerical simulations for a Gaussian-shaped beam. A restriction to the slab's thickness is provided that is necessary for the beam to retain its profile in the traveling. It is shown that the lateral shift of the reflected beam is equal to that of the transmitted beam in the symmetric configuration.Comment: 14 pages, 4 figure

LDA+Gutzwiller Method for Correlated Electron Systems: Formalism and Its Applications

We introduce in detail our newly developed \textit{ab initio} LDA+Gutzwiller method, in which the Gutzwiller variational approach is naturally incorporated with the density functional theory (DFT) through the "Gutzwiller density functional theory (GDFT)" (which is a generalization of original Kohn-Sham formalism). This method can be used for ground state determination of electron systems ranging from weakly correlated metal to strongly correlated insulators with long-range ordering. We will show that its quality for ground state is as high as that by dynamic mean field theory (DMFT), and yet it is computationally much cheaper. In additions, the method is fully variational, the charge-density self-consistency can be naturally achieved, and the quantities, such as total energy, linear response, can be accurately obtained similar to LDA-type calculations. Applications on several typical systems are presented, and the characteristic aspects of this new method are clarified. The obtained results using LDA+Gutzwiller are in better agreement with existing experiments, suggesting significant improvements over LDA or LDA+U.Comment: 20 pages, 11 figure

A Magnetic Model of the Tetragonal-Orthorhombic Transition in the Cuprates

It is shown that a quasi two dimensional (layered) Heisenberg antiferromagnet with fully frustrated interplane couplings ({\it e.g.} on a body-centered tetragonal lattice) generically exhibits two thermal phase transitions with lowering temperature -- an upper transition at $T_{TO}$ (``order from disorder without order'') in which the lattice point-group symmetry is spontaneously broken, and a lower N\'{e}el transition at $T_{N}$ at which spin-rotation symmetry is broken. Although this is the same sequence of transitions observed in La$_2$CuO$_4$, in the Heisenberg model (without additional lattice degrees of freedom) $(T_{TO}-T_N) /T_N$ is much smaller than is observed. The model may apply to the bilayer cuprate La$_2$CaCuO$_6$, in which the transitions are nearly coincident.Comment: 10 pages, 4 figure

Herschel GASPS spectral observations of T Tauri stars in Taurus: unraveling far-infrared line emission from jets and discs

At early stages of stellar evolution young stars show powerful jets and/or outflows that interact with protoplanetary discs and their surroundings. Despite the scarce knowledge about the interaction of jets and/or outflows with discs, spectroscopic studies based on Herschel and ISO data suggests that gas shocked by jets and/or outflows can be traced by far-IR (FIR) emission in certain sources. We want to provide a consistent catalogue of selected atomic ([OI] and [CII]) and molecular (CO, OH, and H$_{2}$O) line fluxes observed in the FIR, separate and characterize the contribution from the jet and the disc to the observed line emission, and place the observations in an evolutionary picture. The atomic and molecular FIR (60-190 $\rm \mu m$) line emission of protoplanetary discs around 76 T Tauri stars located in Taurus are analysed. The observations were carried out within the Herschel key programme Gas in Protoplanetary Systems (GASPS). The spectra were obtained with the Photodetector Array Camera and Spectrometer (PACS). The sample is first divided in outflow and non-outflow sources according to literature tabulations. With the aid of archival stellar/disc and jet/outflow tracers and model predictions (PDRs and shocks), correlations are explored to constrain the physical mechanisms behind the observed line emission. The much higher detection rate of emission lines in outflow sources and the compatibility of line ratios with shock model predictions supports the idea of a dominant contribution from the jet/outflow to the line emission, in particular at earlier stages of the stellar evolution as the brightness of FIR lines depends in large part on the specific evolutionary stage. [Abridged Abstract]Comment: 37 pages, 27 figures, accepted for publication in A&