Shock Waves and Cosmological Matrix Models

We find the shock wave solutions in a class of cosmological backgrounds with a null singularity, each of these backgrounds admits a matrix description. A shock wave solution breaks all supersymmetry meanwhile indicates that the interaction between two static D0-branes cancel, thus provides basic evidence for the matrix description. The probe action of a D0-brane in the background of another suggests that the usual perturbative expansion of matrix model breaks down.Comment: 10 pages, harvmav, v2: some comments on instability added, v3: version to appear in JHE

Massive MIMO 1-Bit DAC Transmission: A Low-Complexity Symbol Scaling Approach

We study multi-user massive multiple-input single-output (MISO) systems and focus on downlink transmission, where the base station (BS) employs a large antenna array with low-cost 1-bit digital-to-analog converters (DACs). The direct combination of existing beamforming schemes with 1-bit DACs is shown to lead to an error floor at medium-to-high SNR regime, due to the coarse quantization of the DACs with limited precision. In this paper, based on the constructive interference we consider both a quantized linear beamforming scheme where we analytically obtain the optimal beamforming matrix, and a non-linear mapping scheme where we directly design the transmit signal vector. Due to the 1-bit quantization, the formulated optimization for the non-linear mapping scheme is shown to be non-convex. To solve this problem, the non-convex constraints of the 1-bit DACs are firstly relaxed, followed by an element-wise normalization to satisfy the 1-bit DAC transmission. We further propose a low-complexity symbol scaling scheme that consists of three stages, in which the quantized transmit signal on each antenna element is selected sequentially. Numerical results show that the proposed symbol scaling scheme achieves a comparable performance to the optimization-based non-linear mapping approach, while its corresponding complexity is negligible compared to that of the non-linear scheme.Comment: 15 page

Free field realization of current superalgebra gl(m∣n)kgl(m|n)_k

We construct the free field representation of the affine currents, energy-momentum tensor and screening currents of the first kind of the current superalgebra $gl(m|n)_k$ uniformly for $m=n$ and $m\neq n$. The energy-momentum tensor is given by a linear combination of two Sugawara tensors associated with the two independent quadratic Casimir elements of $gl(m|n)$.Comment: Latex file, 15 page

Periodic Modulation Effect on Self-Trapping of Two weakly coupled Bose-Einstein Condensates

With phase space analysis approach, we investigate thoroughly the self-trapping phenomenon for two weakly coupled Bose-Einstein condensates (BEC) in a symmetric double-well potential. We identify two kinds of self-trapping by their different relative phase behavior. With applying a periodic modulation on the energy bias of the system we find the occurrence of the self-trapping can be controlled, saying, the transition parameters can be adjusted effectively by the periodic modulation. Analytic expressions for the dependence of the transition parameters on the modulation parameters are derived for high and low frequency modulations. For an intermediate frequency modulation, we find the resonance between the periodic modulation and nonlinear Rabi oscillation dramatically affects the tunnelling dynamics and demonstrate many novel phenomena. Finally, we study the effects of many-body quantum fluctuation on self-trapping and discuss the possible experimental realization of the model.Comment: 7 pages, 11 figure

Electric and Magnetic Excitation of Coherent Magnetic Plasmon Waves in a One-dimensional Meta-chain

A one-dimensional diatomic meta-chain with equal-size holes and different-length slits is designed. Broadband coherent magnetic plasmon waves (MPW) are formed in such a system, excited by both the electric resonance in the slits and the magnetic resonance in the holes in a wide range of incidence angles (00-400) and broad frequency bands (200-230 THz). The dispersion properties of the MPW measured in our experiments agree with the theoretical calculation based on the Lagrange model. The coherent MPWs reported in this paper may have applications in subwavelength integrated nanocircuits

Dipolar-glass-like relaxor ferroelectric behaviour in the 0.5BaTiO3-0.5Bi(Mg1/2Ti1/2)O3 electroceramic

In this study, the dielectric and ferroelectric switching behaviour of 0.5BaTiO3-0.5Bi(Mg1/2Ti1/2)O3 (BT-BMT) ceramics are investigated. The BT-BMT ceramic exhibits a typical dipolar-glass-like, dielectric polarisation relaxation. This is attributed to the 15 distinct possible local A4B2 configurations around the O ions and the effect this unavoidable local compositional variability has on the dipole relaxation behaviour of inherent {1-D h111} dipole chains, arising from correlated off-centre displacements of Bi3+ and Ti4+ ions along local {111} directions. On the other hand, switchable polarisation under strong applied electric fields is observed on different length scales accompanied by the appearance of strong polarisation relaxation, as observed via time-delayed piezoresponse hysteresis loop measurements. These experimental results demonstrate that this BT-BMT ceramic is relaxor ferroelectric in nature, although it exhibits dipolar-glass-like dielectric relaxation behaviour.The authors J.W., Y.L., and R.L.W. acknowledge the support of the Australian Research Council (ARC) in the form of Discovery projects. Y.L. also appreciates support from the ARC Future Fellowships program

The classification of all single travelling wave solutions to Calogero-Degasperis-Focas equation

Under the travelling wave transformation, Calogero-Degasperis-Focas equation was reduced to an ordinary differential equation. Using a symmetry group of one-parameter, this ODE was reduced to a second order linear inhomogeneous ODE. Furthermore, we applied the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classification of all single travelling wave solutions to Calogero-Degasperis-Focas equation.Comment: 9 page