A Discrete Lax-Integrable Coupled System Related to Coupled KdV and Coupled mKdV Equations

A modified Korteweg-de Vries （mKdV） lattice is found to be also a discrete Korteweg-de Vries （KdV） equation. A discrete coupled system is derived from the single lattice equation and its Lax pair is proposed. The coupled system is shown to be related to the coupled KdV and coupled mKdV systems which are widely used in physics.     

Geometric Phase of a Coupled System

In this contribution, my main attention is paid to the study of the geometric phase of a two-level system.Asymptotic expansion of the eigenvalue and analytic information are obtained. The results are illustrated with an application to a specific atomic system.     

Strange—Nonchaotic—Attractor—Like Behaviors in Coupled Map SYstems

In a coupled map system,an attractor which seems to be strange nonchaotic attractor(SNA)is discovered for nonzero measure in parameter range,The attractor has nonpositive Lyapunov exponent(LE) and discrete structure.We call it strange-nonchaotic-attractor-like(SNA-like) behavior because the size of its size of its discrete structure decreases with the computing precision increasing and the true SNA does not change.The SNA-like behavior in the autonomous system is born when the truncation error of round-off is amplified to the size of the discrete part of the attractor during the long time interval of positive local LE.The SNA-like behavior is easily mistaken for a true SNA judging merely from the largest LE and the phase portrait in double precision computing.In non-autonomous system an SNA-like attractor is also found.     

Geometric Phase of a Coupled System

In this contribution, my main attention is paid to the study of the geometric phase ora two-level system.Asymptotic expansion of the eigenvalue and analytic information are obtained. The results are illustrated with an application to a specific atomic system.     

Rational Solutions in a Coupled Burgers System

Three types of the rational solutions for a new coupled Burgers system are studied in detail in terms of the reduction and decoupled procedures. The first two types of rational solutions are singular and valid for one type of model parameter c 〉 0, and another type of rational solutions is nonsingular at any type and valid for another type of model parameter c 〈 0.     

Exact Solutions of a Coupled Burgers System

The exact solutions of a new coupled Burgers system are studied in three different ways. The first type of solutions are found thanks to the coupled Burgers system possessing a simple single Burgers reduction. The second type of multiple soliton solutions are revealed via the decouple procedure. The third type of exact solutions are found by means of a prior ansatz and solutions of the heat conduction equation. Two different kinds of soliton fission phenomena of the model are discovered and a special type of completely elastic soliton collision without phase shift of the model is also displayed.     

Initial-Value Problem of a Coupled Dispersionless System: Dynamical System Approach

We investigate the dynamical behaviour of a coupled dispersionless system （CDS） by solving its initial-value problem following a dynamical system approach. As a result, we unearth a typical miscellaneous travelling waves including the localized and periodic ones. We also investigate the energy density of such waves and find that under some boundary conditions, the localized waves moving towards positive direction are more stable than the periodic waves which on contrary stand for the most conditions. stable travelling waves in another situation of boundary conditions.     

Similarity Reduction Analysis for a Coupled KdV System

Using the direct method for a coupled KdV system, six types of the similarity reductions are obtained. The group explanation of the results is also given. It is pointed out that, in order to find all the results by nonclassical Lie approach, two additional condition equations should be satisfied at the same time together with two original equations.     

Complexiton Solutions of a Special Coupled mKdV System

For a special coupled mKdV system, which can be derived from a two-layer fluid model, Hirota＇s bilinear direct method is used to construct and yield the complexiton solutions. The detailed physical properties of complexitons are filrther illustrated graphically.     

非共振耗散腔耦合系统的发射光谱

研究了非共振耗散二能级双原子与双单模腔耦合系统发射光谱的性质。探讨了原子和腔场之间的失谐、腔场衰减率及原子失相对该系统发射光谱的影响。结果表明,体系的腔场谱呈现出三重峰结构,原子发射谱呈现出二重峰结构。非共振情况时,腔场谱和原子发射谱的图像皆为非对称图像。在原子与腔场失谐时,与共振情况相比,峰位发生了明显的漂移,且中峰明显增大。增大腔场与原子的失谐,会引起边峰向低频段漂移,并改变其光谱强度;增大原子与腔场的失谐,可以使光谱整体向低频段漂移,并改变其所有峰的光谱强度。随着腔场衰减率的增大,共振情况下,会导致边峰的强度减小;失谐情况下,会导致所有峰的强度均减小。随着原子失相的增大,共振或失谐情况下,会使光谱所有峰的强度均减小。     

Resonant Photon-Assisted Tunneling Through a Coupled Double-Quantum-Dot System

An analytical formula of the tunneling current through a coupled double-quantumdot system in the presence of a time-dependent electric field is obtained by using the Keldysh nonequilibrium Green's function technique. The dependence of the time-averaged current on the frequency of the electric field, as well as the dependence of the multiphoton assisted tunneling on the strength of the electric field are studied. The features of I-V_dc characteristic are also investigated. Besides, we present a simplified formula which can be used to determine the heights of the resonant peaks conveniently.     

Similarity Reduction Analysis for a Coupled KdV System

Using the direct method for a coupled KdV system, six types of the similarity reductions are obtained. The group explanation of the results is also given. It is pointed out that, in order to find all the results by nonclassical Lie approach, two additional condition equations should be satisfied at the same time together with two original equations.     

Preference of Chaotic Synchronization in a Coupled Laser System

In a coupled laser system, the dynamics of the receiving laser is investigated when two separate transmitting lasers are injected into the receiving laser with different coupling strengths. It is shown that the phenomenon of preference of chaotic synchronization appears under appropriate coupling conditions. The receiving laser will entrain the pulses of either one or both transmitting lasers when the coupling is strong while it keeps its own dynamics when the coupling is weak.     

Miscellaneous Rotating Solitary Waves to a Coupled Dispersionless System

We investigate the soliton structure of a coupled dispersionless system describing a current-conducting string with infinite length within a magnetic field. Thus, following Hirota＇s method, we unwrap three typical localized waves with nonzero angular momentum depending strongly upon their angular velocities. Illustrating the soliton behavior of these waves, we focus our interests on breather-like waves and depict the elastic scattering amongst such waves.     

Transport for Stochastic System with Infinite Locally Coupled Oscillators

We consider the transport of particles for spatially periodic system with infinite locally coupled oscillatorsdriven by additive and multiplicative noises. A formula of the probability current derived by us shows that the couplingamong the infinite oscillators is an ingredient for transport. This coupling of the oscillators can induce transport ofparticles in the absence of the correlation of the additive and multiplicative noises, even without the multiplicative noise.     

Observation of Fano-Type Interference in a Coupled Cavity-Atom System

We present the experimental observation of the Fano-type interference in a coupled cavity-atom system by confining the laser-cooled ~(85)Rb atoms in an optical cavity.The asymmetric Fano profile is obtained through quantum interference in a three-level atomic system coherently coupled to a single mode cavity field.The observed Fano profile can be explained by the interference between the intra-cavity dark state and the polariton state of the coupled cavity-atom system.The possible applications of our observations include all-optical switching,optical sensing and narrow band optical filters.     

准周期聚焦–加速耦合系统的均温设计方法

强流质子直线加速器要求严格控制束流损失和束流发射度增长.理论已经证明,强的空间电荷作用在不同自由度之间的耦合,会因为其间的温度差异,通过束流的相干不稳定性,使束流发射度增长.因此,有必要按照均温的原则设计强流加速器.但是,由于质子直线加速器的各种加速结构均为准周期耦合系统,使得均温设计十分繁琐而难以达到完全均温.我们利用国际上通用的束流动力学软件TRACE3-D,给它补充了均温设计功能,通过与PARMILA程序的配合使用,可以方便地在加速器设计中实现均温条件.本文将介绍我们对TRACE3-D的修改补充,并以强流质子直线加速器设计实例,说明均温设计的必要性.     

Entanglement Properties in a Star Structure Coupled Cavities System

In this paper, the star structure coupled cavities system is composed of six single-mode cavities. One of them is at the center of the star structure, and other five cavities are at the five vertices of the star structure, respectively. The center cavity is connected with other five cavities by optical fibers. The situation is considered that six identical two-level atoms are separately trapped in six single-mode optical cavities, each atom resonantly interacts with cavity via a one-photon hopping, and the total excitation number of the system equals one. Negativity is adopted to quantify the degree of entanglement between two subsystems. The entanglement properties between atoms and that between cavities are investigated. The influences of atom-cavity coupling coefficient on the entanglement properties between two subsystems are studied. The results obtained using the numerical method show that the atom-atom entanglement is weakened, and the cavity-cavity entanglement is strengthened with the increase of atom-cavity coupling coefficient.