Generalized superposition of two squeezed states: generation and statistical properties

Superpositions of squeezed states were introduced by Sanders [Phys. Rev. A 39 (1998) 4284], Schleich et al. [Phys. Rev. A 38 (1988) 1177], Xin et al. [Phys. Rev. A 50 (1994) 2865], to investigate the occurrence of nonclassical properties of the quantized radiation field. In this report we present a generalized superposition state which interpolates between two arbitrary squeezed states. Nonclassical properties of this intermediate state as function of the interpolating parameters are studied, the previous results in the literature becoming a particularization of ours. An experimental proposal to generate this state is also presented.     

修正的振型叠加法的探讨

计算结果表明一般的振型叠加法计算无质量处的位移是不正确的.为了解决这个问题,本文给出修正的振型叠加法,用该方法计算结果完全符合问题的精确解.本文也给出了该方法的严格理论证明.     

Discrete matrix Riccati equations with superposition formulas

An ordinary differential equation is said to have a superposition formula if its general solution can be expressed as a function of a finite number of particular solution. Nonlinear ODE's with superposition formulas include matrix Riccati equations. Here we shall describe discretizations of Riccati equations that preserve the superposition formulas. The approach is general enough to include q-derivatives and standard discrete derivatives.     

关于叠加原理的讨论

本文以数学摆为例,说明不满足线性微分方程的物理规律不能应用叠加原理.通过晶格的微振动论述了对于同一线性系统用牛顿力学方法和分析力学方法处理,得到的结论是一致的.     

On existence of integrable solutions of a functional integral equation under Carathéodory conditions

We study the solvability of a functional integral equation in the space of Lebesgue integrable functions on an unbounded interval. Using the conjunction of the technique of measures of weak noncompactness with the classical Schauder fixed point principle we show that the equation in question is solvable in the mentioned function space. Our existence result is obtained under the assumption that functions involved in the investigated functional integral equation satisfy Carathéodory conditions. Moreover, that result generalizes several ones obtained earlier in many research papers and monographs.     

Stability of a superposition of shock waves with contact discontinuities for systems of viscous conservation laws

In this paper, we show the large time asymptotic nonlinear stability of a superposition of viscous shock waves with viscous contact waves for systems of viscous conservation laws with small initial perturbations, provided that the strengths of these viscous waves are small with the same order. The results are obtained by elementary weighted energy estimates based on the underlying wave structure and a new estimate on the heat equation.     

Emergence and collapse of quantum mechanical superposition: Orthogonality of reversible dynamics and irreversible diffusion

Based on the modelling of quantum systems with the aid of (classical) non-equilibrium thermodynamics, both the emergence and the collapse of the superposition principle are understood within one and the same framework. Both are shown to depend in crucial ways on whether or not an average orthogonality is maintained between reversible Schrödinger dynamics and irreversible processes of diffusion. Moreover, the said orthogonality is already in full operation when dealing with a single free Gaussian wave packet. In an application, the quantum mechanical “decay of the wave packet” is shown to simply result from sub-quantum diffusion with a specific diffusivity varying in time due to a particle’s changing thermal environment. The exact quantum mechanical trajectory distributions and the velocity field of the Gaussian wave packet, as well as Born’s rule, are thus all derived solely from classical physics.     

Superposition of two coherent states π out of phase with average photon number as relative phase

This paper discusses nonclassical features of the superposition of two coherent states π out of phase with each other and parameterized solely by amplitude α, that is, when the relative phase has a relationship with average photon number ∣α∣². In particular, it discusses oscillatory and sub-Poissonian photon statistics, degree of quadrature squeezing, and quasiprobability distribution functions. We examine that some nonclassical properties of these states are different from those of the even and odd coherent states.     

态|Ψn(2)>q的广义非线性等阶N次方H压缩效应

构造了一种新型的多模叠加态|Ψ_n⁽²⁾>_q=C_n^(R)|{-iZ_j^*}>_q+C_n⁽⁰⁾|{O_j}>_q;并首次详细地研究了此量子态的等阶N次方H压缩特性.大量的计算和分析表明:态|Ψ_n⁽²⁾>_q是一种多模典型的非经典光场;还发现了"相似压缩"等现象.     

用虚边界-最小二乘法求解弹性力学问题

本文提出了求解弹性力学问题的虚边界-最小二乘法。方法首先根据叠加原理建立了适用于各类边值问题的虚边界积分方程,采用最小二乘法逼近实际边界,从而求得虚拟力。文中给出了该方法的离散形式及计算实例。