One-dimensional harmonic lattice caricature of hydrodynamics: Second approximation

The long-time behavior of an infinite chain of coupled harmonic oscillators is studied. In addition to a limiting hydrodynamic (Euler-type) equation, the next approximation is investigated. The corresponding equation is derived.     

Ring Airy-Like Beams along Predesigned Parabolic Trajectories

By phase-modulating ring Airy Gaussian beams, ring Airy-like beams propagating along predesigned parabolic trajectories are presented which combine the properties of accelerating beams and abruptly autofocusing beams analytically and numerically for the first time. The enhancement of the quadratic term ratio α shortens the autofocus distance and increases the slope of the beams after autofocusing. Interestingly, the main lobe tends to break into pieces as α increases and the possible reasons have been discussed. Furthermore, the distribution factor β and the radius of the primary r₀ can prominently affect the autofocus distance and the intensity at the focal point but do not change the slope of the beams after the autofocusing. In addition, the self-healing properties are validated to be retainable while RAiG beams via predesigned parabolic trajectories with various α.     

两组份复合材料光学非线性性质的临界行为

对两组份非线性复合材料的光学非线性性质的临界行为进行了研究。考虑第一组份为非线性材料,其电流、电压间服从I=g1V x1V^β关系;而第二组份为线性材料,电流、电压间满足I—g2V,其中g1,x1是第一组份的线性电导和光学非线性极化率,g2是第二组份的线性电导,β是第一组份材料的光学非线性指数。分别采用了有效介质近似和相对电阻涨落的标度理论两种方法计算了系统有效响应的临界指数随光学非线性指数及维数的变化规律。用不同的方法得到系统的有效线性电导g和有效光学非线性极化率xe(β)的临界指数M(β)和N(β)的结论也不同。有效介质近似得到M(β)=1和N(β)=(β 1)/2,即M(β)与β和d都无关,而N(β)只与有β关而与d无关;而相对电阻涨落标度理论方法得到的M(β)和N(β)与β和d都有关。     

Thickness and local field effects on energy transfer rate in coupled quantum wells system: Linear regime

We investigate theoretically the dependence of energy transfer rate in Double-Quantum-Well system on the well thickness by using the balance equation formalism. Also, by including the local field correction in our calculations through the zero- and finite-temperature Hubbard approximations, we study the effect of the short-range interactions on the energy transfer phenomenon. Calculations consider both the static and dynamic screening approximations. Our numerical results predict that the energy transfer rate increases considerably by increasing the layers' thicknesses and by taking into account the short-range interactions, as well.     

Combined effect of the perpendicular magnetic field and dilute charged impurity on the electronic phase of bilayer AA-stacked hydrogenated graphene

We address the electronic phase engineering in the impurity-infected functionalized bilayer graphene with hydrogen atoms (H-BLG) subjected to a uniform Zeeman magnetic field, employing the tight-binding model, the Green's function technique, and the Born approximation. In particular, the key point of the present work is focused on the electronic density of states (DOS) in the vicinity of the Fermi energy. By exploiting the perturbative picture, we figure out that how the interaction and/or competition between host electrons, guest electrons, and the magnetic field potential can lead to the phase transition in H-BLG. Furthermore, different configurations of hydrogenation, namely reduced table-like and reduced chair-like, are also considered when impurities are the same and/or different. A comprehensive information on the various configurations provides the semimetallic and gapless semiconducting behaviors for unfunctionalized bilayer graphene and H-BLGs, respectively. Further numerical calculations propose a semimetal-to-metal and gapless semiconductor-to-semimetal phase transition, respectively, when only turning on the magnetic field. Interestingly, the results indicate that the impurity doping alone affects the systems as well, leading to semimetal-to-metal and no phase transition in the pristine system and hydrogenated ones, respectively. However, the combined effect of charged impurity and magnetic field shows that the pristine bilayer graphene is not influenced much as the functionalized ones and phase back transitions appear. Tuning of the electronic phase of H-BLG by using both types of electronic and magnetic perturbations play a decisive role in optical responses.     

加性信号调制下指数形式关联噪声驱动的单模激光的光强关联时间

采用线性化近似,计算了加性信号调制下的由具有指数关联的两白噪声驱动的单模激光增益模型的光强关联时间.发现两噪声间关联程度对光强关联时间随噪声强度的变化曲线有很大的影响,两噪声间关联程度取不同值时,光强关联时间随噪声强度的变化曲线中将出现极大值(即出现共振) 或极小值(即出现抑制) .     

一种研究非旋波近似演化问题的系统近似方法

以一个与玻色场耦合的二能级粒子为例，证实了在静态极化子问题的研究中取得成功的相干态近似方法，同样也能够有效地用于非旋波近似下量子系统的时间演化问题。结果同时表明，在一般情况下，哈密顿算符中的非旋波项不能被忽略；并提供了在频率空间进一步检测非旋波项效应的可能性。     

Quantum Dynamics in the Fermi–Pasta–Ulam Problem

We study a quantum chain of oscillators with nonlinear quartic interactions, under the “narrow packet” approximation. We analyse the dynamics of quantum corrections and the conditions at which the quantum solution for average complex amplitude converges to the corresponding classical unstable solution which describes the four-wave decay processes of phonons. We develop an asymptotic theory by using a small quasiclassical parameter, and determine the characteristic time scale for which the evolution of decay processes is essentially specified by quantum effects. AMS Subject classification: Primary: 35F10 Secondary: 35Q40, 35B40     

系综分布和它的小涨落近似

由“从正则分布出发，在小涨落近似下得出的能量涨落分布公式”求得的能量涨落的二次矩与直接由正则分布求得的二次矩完全相同，但分别由二求得的高次矩并不完全相同。