求解Schrdinger方程的高阶紧致差分格式

基于Richardson外推法提出了一种求解Schrdinger方程的高阶紧致差分方法.该方法首先利用二阶微商的四阶精度紧致差分逼近公式对原方程进行求解,然后利用Richardson外推技术外推一次,得到了Schrdinger方程具有O(r~4+h~4)精度的数值解.通过Fourier分析方法证明了该格式是无条件稳定的.数值实验验证了该方法的高阶精度及有效性.     

Influence of temperature on thermodynamic properties of substituted aromatic compounds

This work presents experimental liquid densities and ultrasonic velocities for a collection of substituted aromatic compounds (isobutylbenzene, 1,3,5-trimethylbenzene, butylbenzene, isopropylbenzene, p-xylene, m-xylene and o-xylene) at the range of temperature 278.15–323.15 K and atmospheric pressure of a collection of halogenated and aromatic hydrocarbons. Fitting equations were applied to data in order to correlate for later computer-based design. The estimation of the studied properties was made by the application of different theoretical procedures. An equation of state based on the generalised Van der Waals theory which combines the Staverman–Guggenheim combinatorial term of lattice statistics with an attractive lattice gas expression and the free length theory (FLT) showed a good response at the studied conditions.     

Densities and viscosities of propylene carbonate with aromatic hydrocarbons (benzene, 1,4-dimethylbenzene and ethylbenzene) at 288.15, 298.15 and 308.15 K

Densities and viscosities of the binary mixtures of propylene carbonate with benzene, 1,4-dimethylbenzene and ethylbenzene were measured over the entire mole fraction range at 288.15, 298.15 and 308.15?K. Using the experimental values of densities and viscosities the excess molar volumes and viscosity deviations were calculated. The results were fitted by Redlich–Kister equation. The results were discussed in terms of intermolecular interactions.     

毛细管探针法测定液体表面张力系数的进一步研究

采用较大直径的毛细管对探针法测量液体表面张力系数做了进一步研究.文中引用了Prokhorov提出的改进的瑞利公式,介绍了表面张力系数α的各相关公式的适用范围.实验中利用毛细管探针法测量了几个不同温度下蒸馏水在一直径为5.744.nm的毛细管中的上升高度,用Prokhorov公式计算α.实验测得的蒸馏水的表面张力系数与公认值的百分误差约小于0.13%.最后对实验结果的误差原因进行了分析.     

具有非局部时滞的扩散Nicholson苍蝇方程的波前解

研究了具有非局部时滞的扩散Nicholson苍蝇方程,其中时滞由一个定义在所有过去时间和整个一维空间区域上的积分卷积表示.当时滞核是强生成核时,根据线性链式技巧和几何奇异扰动理论,获得了小时滞时波前解的存在性.     

Exact Solutions to Short Pulse Equation

In this paper, dependent and independent variable transformations are introduced to solve the short pulse equation. It is shown that different kinds of solutions can be obtained to the short pulse equation.     

Analytical Solitary Wave Solutions to a （3＋1）-Dimensional Gross-Pitaevskii Equation with Variable Coefficients

A （3＋1）-dimensional Gross-Pitaevskii （GP） equation with time variable coefficients is considered, and is transformed into a standard nonlinear Schrodinger （NLS） equation. Exact solutions of the （3＋1）D GP equation are constructed via those of the NLS equation. By applying specific time-modulated nonlinearities, dispersions, and potentials, the dynamics of the solutions can be controlled. Solitary and periodic wave solutions with snaking and breathing behavior are reported.     

Quasi-particle structure around a single vortex in high-Tc superconductors

For analyzing the checker-board like modulation of the local density of states (LDOS) around a vortex observed in the slightly overdoped Bi₂Sr₂CaCu₂O_x, we examined the effect of pseudogap state of high-T_c superconductors to the LDOS around the vortex. We first derived the Bogoliubov-de Gennes equation for d-wave superconductivity (d-SC) in the presence of d-spin density wave (d-SDW). Using the Fourier–Bessel expansion, we solved this equation for a single vortex state, numerically. We found that the peak of the bound states around E = 0 becomes small and modulation of the LDOS is observed for larger d-SDW order parameter.     

Classicalization times of parametrically amplified “Schrödinger cat” states coupled to phase-sensitive reservoirs

The exact Wigner function of a parametrically excited quantum oscillator in a phase-sensitive amplifying/attenuating reservoir is found for initial even/odd coherent states. Studying the evolution of negativity of the Wigner function we show the difference between the “initial positivization time” (IPT), which is inversely proportional to the square of the initial size of the superposition, and the “final positivization time” (FPT), which does not depend on this size. Both these times can be made arbitrarily long in maximally squeezed high-temperature reservoirs. Besides, we find the conditions when some (small) squeezing can exist even after the Wigner function becomes totally positive.