Surface waves in a crystal with switching Kerr nonlinearity

In this paper, we explore transverse electric surface waves propagating along the crystal with jump change of Kerr nonlinearity in dependence on field amplitude. The dielectric permittivity in the proposed model of nonlinearity is characterized by abruptly changing unperturbed dielectric constant and Kerr nonlinearity coefficient from one value to another when field amplitude exceeds the threshold value of the switching field. This allows to find exact solutions of model equations in different cases of nonlinearity signs, and to obtain the dependence of wave characteristics, including total power flux, on effective refractive index in explicit form. Such solutions describe two new types of nonlinear surface waves with specific structure depending on electric field amplitude. We derive the conditions of surface domain formation. It is found that the largest percentage of radiation is concentrated within the domain.     

Discrete solitons in nonlinear Schrödinger lattices with a power-law nonlinearity

We study the discrete nonlinear Schrödinger lattice model with the onsite nonlinearity of the general form, |u|^2σu. We systematically verify the conditions for the existence and stability of discrete solitons in the one-dimensional version of the model predicted by means of the variational approximation (VA), and demonstrate the following: monostability of fundamental solitons (FSs) in the case of the weak nonlinearity, 2σ+1<3.68; bistability, in a finite range of values of the soliton’s power, for 3.68<2σ+1<5; and the presence of a threshold (minimum norm of the FS), for 2σ+1≥5. We also perform systematic numerical simulations to study higher-order solitons in the same general model, i.e., bound states of the FSs. While all in-phase bound states are unstable, stability regions are identified for antisymmetric double solitons and their triple counterparts. These numerical findings are supplemented by an analytical treatment of the stability problem, which allows quantitively accurate predictions for the stability features of such multipulses. When these waveforms are found to be unstable, we show, by means of direct simulations, that they self-trap into a persistent lattice breather, or relax into a stable FS, or sometimes decay completely.     

Interface sharpness in the Ising model with long-range interaction

For the 3-dimensional Ising model with long-range interaction, Gibbs states are constructed that are small perturbations of non-translation-invariant ground states. These ground states are in one-to-one correspondence with the set of all rational planes.     

Surface wave propagation at the interface between lossy metamaterials medium and nonlinear media with arbitrary nonlinearity

The dispersion relation in a system that consists of a lossy metamaterials (MTMs) film surrounded by a linear substrate and a nonlinear cladding with an arbitrary nonlinearity is derived. The surface plasmonic (SP) wave at the interfaces between metamaterials (MTMs) and the nonlinear cover is recovered by taking certain limits. Lossy MTMs have simultaneously complex-negative permeability μ and complex-negative permittivity ε. Results are presented by plotting the SP frequency as a function of the nonlinearity at chosen damping factors. Both the real and imaginary parts are studied. Results also display the wave frequency as a function of plasma frequency. For comparison, the imaginary part is set to zero and curves are reproduced.     

电子与双声子相互作用对Holstein极化子的影响

在量子化的Holstein模型的基础上再考虑电子与双声子相互作用，运用相干态展开法，得到了一维分子晶体模型处于基态的极化子满足的非线性薛定谔方程及其定态孤子解、基态能量、晶格位移. 关键词： 相干态 极化子 孤立子 非线性薛定谔方程     

Localization of nonlocal symmetries and interaction solutions of the Sawada–Kotera equation

The nonlocal symmetry of the Sawada–Kotera(SK) equation is constructed with the known Lax pair. By introducing suitable and simple auxiliary variables, the nonlocal symmetry is localized and the finite transformation and some new solutions are obtained further. On the other hand, the group invariant solutions of the SK equation are constructed with the classic Lie group method.In particular, by a Galileo transformation some analytical soliton-cnoidal interaction solutions of a asymptotically integrable equation are discussed in graphical ways.     

Stationary wave packets in the Kerr nonlinear media with imaginary harmonic potential and linear gain

The existence of stationary wave packets in the nonlinear Kerr media with an imaginary harmonic potential and a linear gain is investigated. By employing a variational approach the existence of stable bright solitons is shown for the case of a defocusing nonlinearity. In focusing nonlinear media, the bright solitons have been shown to be unstable. The predictions of variational approach are confirmed by numerical simulations of the full modified NLS equation. The predicted stationary localized wave packets can be observed in a quasi-one-dimensional BEC with an imaginary optical potential and atoms feeding.     

Quantized vortex stability and interaction in the nonlinear wave equation

The stability and interaction of quantized vortices in the nonlinear wave equation (NLWE) are investigated both numerically and analytically. A review of the reduced dynamic law governing the motion of vortex centers in the NLWE is provided. The second order nonlinear ordinary differential equations for the reduced dynamic law are solved analytically for some special initial data. Using 2D polar coordinates, the transversely highly oscillating far field conditions can be efficiently resolved in the phase space, thus giving rise to an efficient and accurate numerical method for the NLWE with non-zero far field conditions. By applying this numerical method to the NLWE, we study the stability of quantized vortices and find numerically that the quantized vortices with winding number m=±1 are dynamically stable, and resp. |m|>1 are dynamically unstable, in the dynamics of NLWE. We then compare numerically quantized vortex interaction patterns of the NLWE with those from the reduced dynamic law qualitatively and quantitatively. Some conclusive findings are obtained, and discussions on numerical and theoretical results are made to provide further understanding of vortex stability and interactions in the NLWE. Finally, the vortex motion under an inhomogeneous potential in the NLWE is also studied.     

压缩真空场与原子非线性作用系统中原子的量子特性

研究了附加克尔介质的压缩真空场与二能级原子依赖强度耦合相互作用系统中原子的反转特性,并采用密度算符间的距离研究了该模型中原子量子态的演化规律.详细地讨论了克尔非线性作用的强度以及初始压缩真空场的压缩度对原子反转和原子量子态演化的影响.     

Nucleon-nucleon interaction with tensor forces in the quark compound bag model

A model forN-N interaction proposed earlier by two of us (VSB and VKG), has been extended to incorporate the tensor component of the nuclear force. Based on the quark compound bag model (QCB), the nucleon-nucleon potential has a short range repulsive core which is non-local and has a characteristic energy dependence and is expressed in terms of the parameters relating to the six-quark compound bag. To account for the low energy properties, this repulsive core interaction is supplemented by a phenomenological non-local potential containing both central (S-wave) and tensor components and operates only outside the QCB. Using this model, we analyse and compare the results with the experimental data for the electromagnetic form factors of the deuteron, theD-state observables, such as the quadrupole moment, theD-state probability, and theD/S ratio along with then-p scattering phase shifts up to about 400 MeV.     

Breather trapping and breather transmission in a DNA model with an interface

We study the dynamics of moving discrete breathers in an interfaced piecewise DNA molecule. This is a DNA chain in which all the base pairs are identical and there exists an interface such that the base pairs dipole moments at each side are oriented in opposite directions. The Hamiltonian of the Peyrard-Bishop model is augmented with a term that includes the dipole-dipole coupling between base pairs. Numerical simulations show the existence of two dynamical regimes. If the translational kinetic energy of a moving breather launched towards the interface is below a critical value, it is trapped in a region around the interface collecting vibrational energy. For an energy larger than the critical value, the breather is transmitted and continues travelling along the double strand with lower velocity. Reflection phenomena never occur. The same study has been carried out when a single dipole is oriented in opposite direction to the other ones. When moving breathers collide with the single inverted dipole, the same effects appear. These results emphasize the importance of this simple type of local inhomogeneity as it creates a mechanism for the trapping of energy. Finally, the simulations show that, under favorable conditions, several launched moving breathers can be trapped successively at the interface region producing an accumulation of vibrational energy. Moreover, an additional colliding moving breather can produce a saturation of energy and a moving breather with all the accumulated energy is transmitted to the chain.     

带有电子-双声子相互作用的一维铁磁性介观环的非经典本征态和非经典本征持续电流

在一维铁磁性织构介观环的基础上, 计及电子-双声子相互作用, 介入了三项非经典效应抑制电子-单声子相互作用引起的量子涨落效应: 1) 跳步电子-单声子相干态关联效应;2) 由压缩相干态引起的声子压缩态-单声子相干态间过程关联效应;3) 声子位移-声子压缩态的表象关联效应．从结果来看, 电子-双声子相互作用明显加强了压缩效应(增大压缩参量), 而跳步电子-单声子相干态关联效应引起本征能量大幅度下降, 持续电流大幅度增加．特别是介入了声子压缩态-单声子相干态间过程关联效应后, 声子压缩参量远大于理想压缩态相应的压缩参量, 有效地抑制了Debye-Waller(D-W)效应．当声子压缩态-单声子相干态间过程关联与声子位移重整化效应结合在一起时, 声子场的压缩将更大幅度地增加, D-W效应(参量w_ph)将更大幅度地减小, w_ph << w_ph⁽⁰⁾, 从而极大幅度地抑制了电子-单声子相互作用导致的量子涨落效应. 这样一来, 非经典态本征能量E_n极大幅度地下降, E_n << E_n⁽⁰⁾, 与此同时, 本征持续电流振幅I_n 则极大幅度地增大, I_n >> I_n⁽⁰⁾.     

Matter-wave solutions of Bose—Einstein condensates with three-body interaction in linear magnetic and time-dependent laser fields

We construct, through a further extension of the tanh-function method, the matter-wave solutions of Bose-Einstein condensates (BECs) with a three-body interaction. The BECs are trapped in a potential comprising the linear magnetic and the time-dependent laser fields. The exact solutions obtained include soliton solutions, such as kink and antikink as well as bright, dark, multisolitonic modulated waves. We realize that the motion and the shape of the solitary wave can be manipulated by controlling the strengths of the fields.     

Bright and dark solitons in the normal dispersion regime of inhomogeneous optical fibers: Soliton interaction and soliton control

Symbolically investigated in this paper is a nonlinear Schrödinger equation with the varying dispersion and nonlinearity for the propagation of optical pulses in the normal dispersion regime of inhomogeneous optical fibers. With the aid of the Hirota method, analytic one- and two-soliton solutions are obtained. Relevant properties of physical and optical interest are illustrated. Different from the previous results, both the bright and dark solitons are hereby derived in the normal dispersion regime of the inhomogeneous optical fibers. Moreover, different dispersion profiles of the dispersion-decreasing fibers can be used to realize the soliton control. Finally, soliton interaction is discussed with the soliton control confirmed to have no influence on the interaction. The results might be of certain value for the study of the signal generator and soliton control.     

Estimation of the solitary-wave energy content in solid dielectric media with optical strong nonlinearity in the far-infrared range

The energy content of temporal solitary far-infrared waves propagating in solid dielectric media according to the optical lossless cubic-quintic Schrödinger equation is estimated analytically. In fact the above energy content, which is one of the two fundamental invariant quantities associated with the equation in question, is found to be an affine function of a key nonlinearity parameter.     

Entanglement in the three-qubit Heisenberg model with next nearest neighbor interaction and a nonuniform magnetic field

Pairwise thermal entanglement in the three-qubit XXX Heisenberg model with next nearest neighbor interaction and a nonuniform magnetic field has been studied. It's found that the next nearest neighbor interaction has a great effect on the entanglement between the next nearest neighbor sites, but has slight effect on the nearest neighbor entanglement (NNE). Applying a magnetic field at the middle site enhances the next nearest neighbor entanglement (NNNE) sharply when there is a small field at the side sites and the next nearest neighbor coupling constant is positive. A staggered magnetic field helps to maintain nearest neighbor entanglement obviously.     

Study of the heavy molecular states in the quark model with meson exchange interaction

Some charmonium-like resonances such as X(3872) can be interpreted as possible D^(*)D^(*) molecular states. Within the quark model, we study the structure of such molecular states and the similar B^(*)D^(*) molecular states by taking into account the light meson exchange (π, η, ρ, ω and σ) between two light quarks from different mesons.     

Simulation of the Ising model,memory for Bell states and generation of four-atom entangled states in cavity QED

A scheme is proposed to simulate the Ising model and preserve the maximum entangled states (Bell states) in cavity quantum electrodynamics (QED) driven by a classical field with large detuning. In the strong driving and large-detuning regime, the effective Hamiltonian of the system is the same as the standard Ising model, and the scheme can also make the initial four Bell states of two atoms at the maximum entanglement all the time. So it is a simple memory for the maximal entangled states. The system is insensitive to the cavity decay and the thermal field and more immune to decoherence. These advantages can warrant the experimental feasibility of the current scheme. Furthermore, the genuine four-atom entanglement may be acquired via two Bell states through one-step implementation on four two-level atoms in the strong-driven model, and when two Greenberger-Horne-Zeilinger (GHZ) states are prepared in our scheme, the entangled cluster state may be acquired easily. The success probability for the scheme is 1. Supported by the National Natural Science Foundation of China (Grant No. 10774088) and the Key Program of the National Natural Science Foundation of China (Grant No. 10534030)     

Dynamics of fronts in optical media with linear gain and nonlinear losses

The dynamics of fronts, or kinks, in dispersive media with gain and losses is considered. It is shown that the front parameters, such as the velocity and width, depend on initial conditions. This result is not typical for dissipative systems. For exponentially decreasing initial conditions, the relations for the front parameters are found. A presence of the global bifurcation, when a soliton solution is replaced by the front solution, is demonstrated. It is also shown that in order to observe fronts, the front velocity should be larger than the characteristic velocity of the modulational instability.     

液相及固/液混合相区金属物态方程Grover模型存在的问题及修正

借助无序熵的概念, 直接推导出了液相金属的物态方程. 再利用固/液混合相区的熔化分数与其中固相、液相比体积之间的一般性关系, 替代了传统Grover模型中采用的熔化分数与温度成正比的近似条件, 得出更准确的固/液混合相区状态方程的表述形式. 修正后的物态方程解决了传统Grover模型中的固线、液线以及熔化线在P-T图上不一致的问题, 得到了更为符合物理事实的结果.