Separability Criteria Based on the Weyl Operators

Entanglement as a vital resource for information processing can be described by special properties of the quantum state. Using the well-known Weyl basis we propose a new Bloch decomposition of the quantum state and study its separability problem. This decomposition enables us to find an alternative characterization of the separability based on the correlation matrix. We show that the criterion is effective in detecting entanglement for the isotropic states, Bell-diagonal states and some PPT entangled states. We also use the Weyl operators to construct an detecting operator for quantum teleportation.     

Three-step iterations for nonlinear accretive operator equations

In this paper, we suggest and analyze a three-step iterative scheme for solving nonlinear strongly accretive operator equation Tx=f without continuous condition in a uniformly smooth Banach space. Our results include the Ishikawa, Mann and Noor iterations as special cases. The results presented in this paper improve and extend almost all the current results in the more general setting.     

Quadrupolar matter-wave soliton in two-dimensional free space

We study two-dimensional (2D) matter-wave solitons in the mean-field models formed by electric quadrupole particles with long-range quadrupole–quadrupole interaction (QQI) in 2D free space. The existence of 2D matter-wave solitons in the free space was predicted using the 2D Gross–Pitaevskii Equation (GPE). We find that the QQI solitons have a higher mass (smaller size and higher intensity) and stronger anisotropy than the dipole–dipole interaction (DDI) solitons under the same environmental parameters. Anisotropic soliton–soliton interaction between two identical QQI solitons in 2D free space is studied. Moreover, stable anisotropic dipole solitons are observed, to our knowledge, for the first time in 2D free space under anisotropic nonlocal cubic nonlinearity.     

方解石棱镜分束角高度对称性的设计

研究ｏ、ｅ双输出棱镜分束角的对称性。指出经特殊设计的双渥拉斯顿棱镜产生的ｏ、ｅ光的分束角具有高度的对称性。     

The Gravitational Deflection of Light in f(R)-Gravity

Gravitation deflects light, which has been confirmed by a large number of observation data. f(R)-gravity is modification of Einstein’s gravity. According to the field equations obtained by the action of the f(R) form, a similar Schwarzschild metric is obtained. According to the condition that four-dimension momenta of the photon return to zero and conservation of covariant momenta, we obtain an equation of photon motion in a specific form of f(R)-gravity. We solve the equation to get gravitational deflection angle of light that grazes surface of sun and the calculation result is consistent with the experimental observation data.     

Experimental evidence of the vibrational coupling of nearest neighbours in 1D spin crossover polymers of rigid bridging ligands

The nuclear inelastic scattering signatures of the low spin centres of the methanosulphonate, tosylate and perchlorate salts of the spin crossover polymer ([Fe(II)(4-amino-1,2,4-triazole)₃]⁺²) _n have been compared for the pure low-spin phase, for the mixed high-spin and low-spin phases, as well as for Zn(II) diluted samples. Within this series a change in the spectral pattern in the 320–500 cm^?1 region is observed involving the decrease of the intensities of a band at ～320 cm^?1 and those over 400 cm^?1 as the molar fraction of the low-spin centres decreases. On the basis of the DFT calculations (B3LYP/CEP-31G) this effect is interpreted in terms of vibrational coupling of the iron centres of the same spin.     

Low-dimension self-interstitial diffusion in α-Zr

The mobility of self-interstitials in α-zirconium (α-Zr) is studied with molecular dynamic (MD) and molecular static (MS) simulations, using Ackland’s many-body inter-atomic potential. The basal crowdion configuration is found to be the ground state. Four types of diffusion jumps can be identified via MS, in-plane in-line, in-plane off-line, out-of-plane in-line and out-of-plane off-line. The in-plane migration is dominated by one-dimensional crowdion motion along the [110] directions, interrupted from time to time by off-line or out-of-plane jumps. Based on the MS results, the activation energies and pre-exponentials for the diffusion processes are determined by fits to the Arrhenius plots of D_c and D_a. The diffusional anisotropy factor D_c/D_a is also obtained, and compares well with experimental results. The mean frequency of each type of jumps is then found using Monte Carlo simulation, and is reported as a function of temperature. The mean lifetime and mean free path of the one-dimensional mobility are then obtained. The 1-D mean free path is found to be unimportant for sink separations involved under the usual irradiation damage conditions. Received: 4 March 2002 / Accepted: 4 April 2002 / Published online: 10 September 2002 RID="*" ID="*"Corresponding author. E-mail: Chung.Woo@polyu.edu.hk