International Journal of Modern Physics B

Over the last 15 years, there has been rapid growth in applications of time-reversal symmetry of wave propagation to enhance communications and imaging through highly scattering media. These techniques exploit both temporal and spatial reciprocity to mitigate signal distortion created from the large number of independent propagation paths between a transmitter and receiver. The time-reversal process is often described by the time-reversal operator (TRO), or equivalently by the multistatic response matrix (MRM), defined by the transmit and receive system. A singular value decomposition of this operator (or MRM) is the starting point for many of the time-reversal imaging techniques. In addition to imaging, this decomposition can also be used to extract information about objects embedded within the propagation medium, i.e., target characterization. In this paper, we review the development of target characterization in time-reversal, with an emphasis on extracting information from small targets. We will analyze the MRM for both acoustic and electromagnetic scattering and show how the symmetry of the target is reflected in the properties of the singular value spectrum. Finally, we discuss several open problems and potential applications.

Based on our previous paper [H.-Y. Fan and H.-L. Lu, Int. J. Mod. Phys.19, 799 (2005)] and the two mutually-conjugate entangled state representations, we derive the convolution theorem of complex fractional Fourier transformation in the context of quantum mechanics. This approach seems convenient and neat.

We consider the Heisenberg model with two-, and three-spin exchange interactions on a zigzag ladder in a strong magnetic field. Using the recursion method for the partition function in Ising approximation we have found exact results for the magnetization. We have shown the existence of magnetization plateaus in the case of mutual two-, and three-spin exchanges at low temperatures and different exchange parameters. The system exhibits different magnetic behaviors, depending on the values of the exchange parameters.

The objective of this research work is to provide a systematic method to perform molecular dynamics simulation or evaluation for nano-scale interfacial friction between different materials in MEMS. A simplified model to simulate surface sliding between different kinds of material by molecular dynamics [MD] is proposed because the surface property is a dominant factor for the performance between two kinds of material in MEMS. The Newton's equations of motion are established by using the Morse potential function. An improved Verlet algorithm is employed to solve atom trajectories. Comparing the results of the computer simulation with experimental results in Ref. 1, the validity of the model is confirmed. The simulation results show that the preliminary stage and the last stage, when no interface is formed, the friction force fluctuates periodly and its peak value is smaller relatively, while at the intermediate stage, where the interface is formed, the friction force fluctuates periodly and its peak value is relatively bigger. The friction force is approximately proportional to the contact area. In the meantime, Cu sliding along Al with uniform speed and accelerated motion was also investigated, the mechanical properties between two surfaces were analyzed and a tentative computational simulation on the effect of the driving force was developed. The results lay a basis for future work.

The microcanonical ensemble given by Boltzmann is used in the computer Monte Carlo simulation of 2D classical XY-model with the modified nearest neighbour interaction potential suggested by Domany, Schick and Swendsen. A relatively simple method to identify first-order transition in computer simulations of a statistical system is described. The critical value of p² in this XY-model is determined using this method; which is found to increase with system size obeying a power law.

Results for the inhomogeneous structure of the hard-core repulsive Yukawa (HCRY) fluid and of the hard-core attractive Yukawa (HCAY) fluid in planar and in spherical micropores are presented. The density profiles are obtained by the recently proposed third order + second order perturbation density functional approximation (DFA) and compared with the results of open ensemble Monte Carlo simulation. As known from other recent studies, the reliability of the DFA theory considered in this work is very sensitive to the accuracy of the required bulk direct correlation function (DCF) obtained by the solution of the Ornstein–Zernike (OZ) equation combined by a suitable closure relation. Comparison between the DFA results and simulation data shows that for the HCRY fluid, the DFA theory utilizing the DCF obtained by the OZ equation supplemented by Malijevsky–Labik approximation satisfies the required accuracy for a broad range of conditions. The results for the nonuniform HCAY fluid obtained in our previous work via the mean spherical approximation (MSA)/OZ DCF showed larger disagreement in some cases. In addition, the MSA/OZ equation for the HCAY model failed to have a physical solution at subcritical temperatures when approaching the vapor–liquid coexistence curve. For this reason, an improved version of the theory incorporating nonlinear optimized random phase approximation (ORPA) in the OZ equation for the RDF calculation of the HCAY fluid is applied. This leads to much better agreement of the DFA predictions with the simulation data. In addition, the calculations can also be performed at the conditions at which the MSA/OZ equation has no physical solution.

In the present paper, we consider the interaction of a single mode radiation initially in a coherent state with an assembly of two two-level atoms in some different states using the Hamiltonian, H = ω(a⁺a + S_z)+g(a S₊ + a⁺ S_-) in the natural units, where a⁺ and a are the creation and annihilation operators for radiation, S_z, S_± are the collective Dicke operators, g is the coupling constant, ω is the energy of the photons and energy difference between the two atomic levels. We solve it exactly. We study ordinary squeezing and amplitude-squared squeezing of radiation for the general operators, and Y_θ=1/2(a²e^-iθ+a⁺²e^iθ), when atoms are fully excited, super-radiant or in the ground state. We get a large ordinary squeezing (nearly 88% squeezing) for the super-radiant atomic state, at a time, which is 0.451 of the first revival time, and this should be easily observable. We also get a large amplitude-squared squeezing (nearly 20%) at the time, which is about 0.033 of the first revival time. Variation of variances near their minima with coupling time gt, square root of mean photon number |α| and phase are also discussed.

This paper presents an active tracking control strategy of the four-dimensional hyperchaotic LC oscillator system based on the theory of stability of the linear system. This strategy can track all kinds of reference signals. It is also proved that the strategy can make the system converge to any desired smooth orbit exponentially in theory. Numerical simulations have shown that the proposed strategy can not only trace the given reference signals, but the response system can also be in different-structure synchronization with the drive system.