Quantum magnetism of ultra-cold fermion systems with the symplectic symmetry

We numerically study quantum magnetism of ultra-cold alkali and alkaline-earth fermion systems with large hyperfine spin $F=3/2$, which are characterized by a generic $Sp(N)$ symmetry with N=4. The methods of exact diagonalization (ED) and density-matrix-renormalization-group are employed for the large size one-dimensional (1D) systems, and ED is applied to a two-dimensional (2D) square lattice on small sizes. We focus on the magnetic exchange models in the Mott-insulating state at quarter-filling. Both 1D and 2D systems exhibit rich phase diagrams depending on the ratio between the spin exchanges $J_0$ and $J_2$ in the bond spin singlet and quintet channels, respectively. In 1D, the ground states exhibit a long-range-ordered dimerization with a finite spin gap at $J_0/J_2>1$, and a gapless spin liquid state at $J_0/J_2 \le 1$, respectively. In the former and latter cases, the correlation functions exhibit the two-site and four-site periodicities, respectively. In 2D, various spin correlation functions are calculated up to the size of $4\times 4$. The Neel-type spin correlation dominates at large values of $J_0/J_2$, while a $2\times 2$ plaquette correlation is prominent at small values of this ratio. Between them, a columnar spin-Peierls dimerization correlation peaks. We infer the competitions among the plaquette ordering, the dimer ordering, and the Neel ordering in the 2D system.Comment: 16 page

Exact Solutions to Sourceless Charged Massive Scalar Field Equation on Kerr-Newman Background

The separated radial part of a sourceless massive complex scalar field equation on the Kerr-Newman black hole background is shown to be a generalized spin-weighted spheroidal wave equation of imaginary number order. While the separated angular part is an ordinary spheroidal wave equation. General exact solutions in integral forms and in power series expansion as well as several special solutions with physical interest are given for the radial equation in the non-extreme case. In the extreme case, power series solution to the radial equation is briefly studied. Recurrence relations between coefficients in power series expansion of general solutions and connection between the radial equation are discussed in both cases.Comment: 22 Pages, in LaTex, no figure, to appear in J. Math. Phy

Differential space-time block-coded OFDMA for frequency-selective fading channels

Combining differential Alamouti space-time block code (DASTBC) with orthogonal frequency-division multiple access (OFDMA), this paper introduces a multiuser/multirate transmission scheme, which allows full-rate and full-diversity noncoherent communications using two transmit antennas over frequency-selective fading channels. Compared with the existing differential space-time coded OFDM designs, our scheme imposes 10 restrictions on signal constellations, and thus can improve the spectral efficiency by exploiting efficient modulation techniques such as QAM, APSK etc. The main principles of our design are s follows: OFDMA eliminates multiuser interference, and converts multiuser environments to single-user ones; Space-time coding achieves performance improvement by exploiting space diversity available with multiple antennas, no matter whether channel state information is known to the receiver. System performance is evaluated both analytically and with simulations

Annihilation Type Radiative Decays of BB Meson in Perturbative QCD Approach

With the perturbative QCD approach based on $k_T$ factorization, we study the pure annihilation type radiative decays $B^0 \to \phi\gamma$ and $B^0\to J/\psi \gamma$. We find that the branching ratio of $B^0 \to \phi\gamma$ is $(2.7^{+0.3+1.2}_{-0.6-0.6})\times10^{-11}$, which is too small to be measured in the current $B$ factories of BaBar and Belle. The branching ratio of $B^0\to J/\psi \gamma$ is $({4.5^{+0.6+0.7}_{-0.5-0.6}})\times10^{-7}$, which is just at the corner of being observable in the $B$ factories. A larger branching ratio $BR(B_s^0 \to J/\psi \gamma) \simeq 5 \times 10^{-6}$ is also predicted. These decay modes will help us testing the standard model and searching for new physics signals.Comment: 4 pages, revtex, with 1 eps figur

Vibrational modes and lattice distortion of a nitrogen-vacancy center in diamond from first-principles calculations

We investigate vibrational properties and lattice distortion of negatively charged nitrogen-vacancy (NV) center in diamond. Using the first-principles electronic structure calculations, we show that the presence of NV center leads to appearance of a large number of quasilocalized vibrational modes (qLVMs) with different degree of localization. The vibration patterns and the symmetries of the qLVMs are presented and analyzed in detail for both ground and excited orbital states of the NV center. We find that in the high-symmetry ($C_{3v}$) excited orbital state a pair of degenerate qLVMs becomes unstable, and the stable excited state has lower ($C_{1h}$) symmetry. This is a direct indication of the Jahn-Teller effect, and our studies suggest that dynamical Jahn-Teller effect in the weak coupling regime takes place. We have also performed a detailed comparison of our results with the available experimental data on the vibrations involved in optical emission/absorption of the NV centers. We have directly demonstrated that, among other modes, the qLVMs crucially impact the optical properties of the NV centers in diamond, and identified the most important groups of qLVMs. Our results are important for deeper understanding of the optical properties and the orbital relaxation associated with lattice vibrations of the NV centers.Comment: 10 RevTeX pages, 10 EPS figure

An integrated approach to global synchronization and state estimation for nonlinear singularly perturbed complex networks

This paper aims to establish a unified framework to handle both the exponential synchronization and state estimation problems for a class of nonlinear singularly perturbed complex networks (SPCNs). Each node in the SPCN comprises both 'slow' and 'fast' dynamics that reflects the singular perturbation behavior. General sector-like nonlinear function is employed to describe the nonlinearities existing in the network. All nodes in the SPCN have the same structures and properties. By utilizing a novel Lyapunov functional and the Kronecker product, it is shown that the addressed SPCN is synchronized if certain matrix inequalities are feasible. The state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that dynamics (both slow and fast) of the estimation error is guaranteed to be globally asymptotically stable. Again, a matrix inequality approach is developed for the state estimation problem. Two numerical examples are presented to verify the effectiveness and merits of the proposed synchronization scheme and state estimation formulation. It is worth mentioning that our main results are still valid even if the slow subsystems within the network are unstable

Sudden stoppage of rotor in a thermally driven rotary motor made from double-walled carbon nanotubes

In a thermally driven rotary motor made from double-walled carbon nanotubes, the rotor (inner tube) can be actuated to rotate within the stator (outer tube) when the environmental temperature is high enough. A sudden stoppage of the rotor can occur when the inner tube has been actuated to rotate at a stable high speed. To find the mechanisms of such sudden stoppages, eight motor models with the same rotor but different stators are built and simulated in the canonical NVT ensembles. Numerical results demonstrate that the sudden stoppage of the rotor occurs when the difference between radii is near 0.34 nm at a high environmental temperature. A smaller difference between radii does not imply easier activation of the sudden rotor stoppage. During rotation, the positions and electron density distribution of atoms at the ends of the motor show that a sp(1) bonded atom on the rotor is attracted by the sp(1) atom with the biggest deviation of radial position on the stator, after which they become two sp(2) atoms. The strong bond interaction between the two atoms leads to the loss of rotational speed of the rotor within 1 ps. Hence, the sudden stoppage is attributed to two factors: the deviation of radial position of atoms at the stator's ends and the drastic thermal vibration of atoms on the rotor in rotation. For a stable motor, sudden stoppage could be avoided by reducing deviation of the radial position of atoms at the stator's ends. A nanobrake can be, thus, achieved by adjusting a sp(1) atom at the ends of stator to stop the rotation of rotor quickly.The authors are grateful for financial support from the National Natural-Science-Foundation of China (Grant Nos. 50908190, 11372100)