Magnetic properties of a spin-3 Chromium condensate

We study the ground state properties of a spin-3 Cr condensate subject to an external magnetic field by numerically solving the Gross-Piteavskii equations. We show that the widely adopted single-mode approximation is invalid under a finite magnetic field. In particular, a phase separation like behavior may be induced by the magnetic field. We also point out the possible origin of the phase separation phenomenon.Comment: 6 pages, 5 figure

Tau function and Hirota bilinear equations for the Extended bigraded Toda Hierarchy

In this paper we generalize the Sato theory to the extended bigraded Toda hierarchy (EBTH). We revise the definition of the Lax equations,give the Sato equations, wave operators, Hirota bilinear identities (HBI) and show the existence of $tau$ function $\tau(t)$. Meanwhile we prove the validity of its Fay-like identities and Hirota bilinear equations (HBEs) in terms of vertex operators whose coefficients take values in the algebra of differential operators. In contrast with HBEs of the usual integrable system, the current HBEs are equations of product of operators involving $e^{\partial_x}$ and $\tau(t)$.Comment: 29 pages, to appear Journal of Mathematical Physics(2010

Low Mass Dark Matter and Invisible Higgs Width In Darkon Models

The Standard Model (SM) plus a real gauge-singlet scalar field dubbed darkon (SM+D) is the simplest model possessing a weakly interacting massive particle (WIMP) dark-matter candidate. In this model, the parameters are constrained from dark matter relic density and direct searches. The fact that interaction between darkon and SM particles is only mediated by Higgs boson exchange may lead to significant modifications to the Higgs boson properties. If the dark matter mass is smaller than a half of the Higgs boson mass, the Higgs boson can decay into a pair of darkons resulting in a large invisible branching ratio. The Higgs boson will be searched for at the LHC and may well be discovered in the near future. If a Higgs boson with a small invisible decay width will be found, the SM+D model with small dark matter mass will be in trouble. We find that by extending the SM+D to a two-Higgs-doublet model plus a darkon (THDM+D) it is possible to have a Higgs boson with a small invisible branching ratio and at the same time the dark matter can have a low mass. We also comment on other implications of this model.Comment: RevTeX, 15 pages, 11 figures. A few typos corrected and some references adde

``Fermi Liquid'' Shell Model Approach to Composite Fermion Excitation Spectra in Fractional Quantum Hall States

Numerical results for the energy spectra of $N$ electrons on a spherical surface are used as input data to determine the quasiparticle energies and the pairwise ``Fermi liquid'' interactions of composite Fermion (CF) excitations in fractional quantum Hall systems. The quasiparticle energies and their interactions are then used to determine the energy spectra, $E$ vs total angular momentum $L$, of states containing more than two quasiparticles. The qualitative agreement with the numerical results gives a remarkable new confirmation of the CF picture.Comment: LaTex, 4 pages, including 4 .eps-figures, to be appear in pr

Control of photon propagation via electromagnetically induced transparency in lossless media

We study the influence of a lossless material medium on the coherent storage and quantum state transfer of a quantized probe light in an ensemble of $\Lambda$-type atoms. The medium is modeled as uniformly distributed two-level atoms with same energy level spacing, coupling to a probe light. This coupled system can be simplified to a collection of two-mode polaritons which couple to one transition of the $\Lambda$-type atoms. We show that, when the other transition of $\Lambda$-type atoms is controlled by a classical light, the electromagnetically induced transparency can also occur for the polaritons. In this case the coherent storage and quantum transfer for photon states are achievable through the novel dark states with respect to the polaritons. By calculating the corresponding dispersion relation, we find the ensemble of the three-level atoms with $\Lambda$-type transitions may serve as quantum memory for it slows or even stops the light propagation through the mechanism of electromagnetically induced transparency. the corresponding dispersion relation, we find the ensemble of the three-level atoms with $\Lambda$-type transitions may serve as quantum memory for it slows or even stops the light propagation through the mechanism of electromagnetically induced transparency.Comment: 10 pages, 5 figure

Some Issues in a Gauge Model of Unparticles

We address in a recent gauge model of unparticles the issues that are important for consistency of a gauge theory, i.e., unitarity and Ward identity of physical amplitudes. We find that non-integrable singularities arise in physical quantities like cross section and decay rate from gauge interactions of unparticles. We also show that Ward identity is violated due to the lack of a dispersion relation for charged unparticles although the Ward-Takahashi identity for general Green functions is incorporated in the model. A previous observation that the unparticle's (with scaling dimension d) contribution to the gauge boson self-energy is a factor (2-d) of the particle's has been extended to the Green function of triple gauge bosons. This (2-d) rule may be generally true for any point Green functions of gauge bosons. This implies that the model would be trivial even as one that mimics certain dynamical effects on gauge bosons in which unparticles serve as an interpolating field.Comment: v1:16 pages, 3 figures. v2: some clarifications made and presentation improved, calculation and conclusion not modified; refs added and updated. Version to appear in EPJ

e±e^\pm Excesses in the Cosmic Ray Spectrum and Possible Interpretations

The data collected by ATIC, PPB-BETS, FERMI-LAT and HESS all indicate that there is an electron/positron excess in the cosmic ray energy spectrum above $\sim$ 100 GeV, although different instrumental teams do not agree on the detailed spectral shape. PAMELA also reported a clear excess feature of the positron fraction above several GeV, but no excess in anti-protons. Here we review the observational status and theoretical models of this interesting observational feature. We pay special attention to various physical interpretations proposed in the literature, including modified supernova remnant models for the $e^\pm$ background, new astrophysical sources, and new physics (the dark matter models). We suggest that although most models can make a case to interpret the data, with the current observational constraints the dark matter interpretations, especially those invoking annihilation, require much more exotic assumptions than some astrophysical interpretations. Future observations may present some ``smoking-gun'' observational tests to differentiate among different models and to identify the correct interpretation to the phenomenon.Comment: 48 pages, including 10 figures and 1 tabel. Invited review to be published in IJMP