32,421 research outputs found

### 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 $B$ 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)

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