Spatial weak-light solitons in an electro-magnetically induced nonlinear waveguide

We show that a weak probe light beam can form spatial solitons in an electro-magnetically induced transparency (EIT) medium composed of four-level atoms and a coupling light field. We find that the coupling light beam can induce a highly controllable nonlinear waveguide and exert very strong effects on the dynamical behavior of the solitons. Hence, in the EIT medium, it is not only possible to produce spatial solitons at very low light intensities but also simultaneously control these solitons by using the coupling-light-induced nonlinear waveguide.Comment: 5 pages, 5 figures. Phys. Rev. Lett. 90, 183901 (2003

A Simple Method of Calculating Commutators in Hamilton System with Mathematica Software

As a powerful tool in scientific computation, Mathematica offers us algebraic computation, but it does not provide functions to directly calculate commutators in quantum mechanics. Different from present software packets to deal with noncommutative algebra, such as NCAlgebra and NCComAlgebra, one simple method of calculating the commutator in quantum mechanics is put forward and is demonstrated by an example calculating SO(4) dynamical symmetry in 3 dimensions Coulomb potential. This method does not need to develop software packets but rather to directly write program in Mathematica. It is based on the connection between commutator in quantum mechanics and Poisson bracket in classical mechanics to perform calculations. Both the length and the running time of this example are very short, which demonstrates that this method is simple and effective in scientific research. Moreover, this method is used to calculate any commutator in Hamilton system in principle. In the end some deficiencies and applications are discussed.Comment: 8 pages, Latex, no figure

A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations

In this work, we present a second-order nonuniform time-stepping scheme for the time-fractional Allen-Cahn equation. We show that the proposed scheme preserves the discrete maximum principle, and by using the convolution structure of consistency error, we present sharp maximum-norm error estimates which reflect the temporal regularity. As our analysis is built on nonuniform time steps, we may resolve the intrinsic initial singularity by using the graded meshes. Moreover, we propose an adaptive time-stepping strategy for large time simulations. Numerical experiments are presented to show the effectiveness of the proposed scheme. This seems to be the first second-order maximum principle preserving scheme for the time-fractional Allen-Cahn equation.Comment: 22pages, 22 figures, 2 table

Competition between phase coherence and correlation in a mixture of Bose-Einstein condensates

Two-species hard-core bosons trapped in a three-dimensional isotropic harmonic potential are studied with the path-integral quantum Monte Carlo simulation. The double condensates show two distinct structures depending on how the external potentials are set. Contrary to the mean-field results, we find that the heavier particles form an outer shell under an identical external potential whereas the lighter particles form an outer shell under the equal energy spacing condition. Phase separations in both the spatial and energy spaces are observed. We provide physical interpretations of these phase separations and suggest future experiment to confirm these findings.Comment: 4 pages, 4 figures, submitted to Physical Review Letter

A Global Algorithm for Training Multilayer Neural Networks

We present a global algorithm for training multilayer neural networks in this Letter. The algorithm is focused on controlling the local fields of neurons induced by the input of samples by random adaptations of the synaptic weights. Unlike the backpropagation algorithm, the networks may have discrete-state weights, and may apply either differentiable or nondifferentiable neural transfer functions. A two-layer network is trained as an example to separate a linearly inseparable set of samples into two categories, and its powerful generalization capacity is emphasized. The extension to more general cases is straightforward

Condensate-profile asymmetry of a boson mixture in a disk-shaped harmonic trap

A mixture of two types of hard-sphere bosons in a disk-shaped harmonic trap is studied through path-integral quantum Monte Carlo simulation at low temperature. We find that the system can undergo a phase transition to break the spatial symmetry of the model Hamiltonian when some of the model parameters are varied. The nature of such a phase transition is analyzed through the particle distributions and angular correlation functions. Comparisons are made between our calculations and the available mean-field results on similar models. Possible future experiments are suggested to verify our findings.Comment: 4 pages, 4 figure

Traffic flow and efficient routing on scale-free networks: A survey

Recently, motivated by the pioneer works in revealing the small-world effect and scale-free property of various real-life networks, many scientists devote themselves to studying complex networks. In this paper, we give a brief review on the studies of traffic flow and efficient routing on scale-free networks, including the traffic dynamics based on global routing protocol, Traffic dynamics based on local routing protocol, and the critical phenomena and scaling behaviors of real and artificial traffic. Finally, perspectives and some interesting problems are proposed.Comment: A brief review on recent progress of network traffi

Integrated Facility Location and Production Scheduling in Multi-Generation Energy Systems

In this paper, we investigate the energy system design problems with the multi-generation technologies, i.e., simultaneous generation of multiple types of energy. We propose a long-term planning model which integrates macro-level strategic decisions such as facility location and multi-generation technology investment, and micro-level operational decisions such as production planning and energy transportation. Our results illustrate the economic value of multi-generation technologies in lieu of the spatio-temporal demand uncertainty for energy. In particular, we show that the multi-generation technologies can reduce demand uncertainty by risk pooling both within and across different facilities

Variational study of the one dimensional t-J model

We find the Gutzwiller projected Fermi sea wave function(GWF) has the correct phase structure to describe the kink nature of the doped holes in the ground state of the one dimensional $t-J$ model. We find the failure of the GWF for general value of $J/t$ and electron density $n$ can be attributed to the residual charge correlation in the ground state. We find such residual charge correlation is well described by a XXZ-type effective Hamiltonian. Based on these observations, a Pfaffian-type variational wave function is proposed and is found to reproduce correctly the global phase diagram and corresponding correlation functions of the one dimensional $t-J$ model, including the Luther-Emery phase in the low electron density and large $J/t$ region.Comment: 8 pages, 8 figure

Spin Charge Recombination in Projected Wave Functions

We find spin charge recombination is a generic feature of projected wave functions. We find this effect is responsible for a series of differences between mean field theory prediction and the result from projected wave functions. We also find spin charge recombination plays an important role in determining the dissipation of supercurrent, the quasiparticle properties and the hole - hole correlation.Comment: 13 pages,7 figure