交流源作用下介观RLC电路系统量子态随时间的演化

根据量子不变量理论，同时考虑介观电容器极板间电子波函数的耦合作用和电路的耗散,研究介观RLC电路系统在交流电流源作用下动力学的演化过程，并且得到描述系统量子态随时间的演化算符.进一步的分析结果表明，介观RLC电路系统的波函数将由任意的初态演化到一般的压缩态. 关键词： 介观RLC电路 交变电源 不变量理论 时间演化算符     

New Operator Identities and Combinatorics Studied by Virtue of IWOP Technique

Using the coherent state representation we derive some new operator identities and study some mathematical relations in combinatorics. The technique of integral within an ordered product (IWOP) of operators plays an essential role in realizing our goal.     

多模海森堡代数的算符恒等式

利用算符代数中的分析方法,得到了多模海森堡(Heisenberg)代数中的BCH公式和压缩算符的展开式。     

“Eigen-Operator” Method of the Square of Schroedinger Operator in Interaction Picture and Its Application in Describing Parametric Amplifiers

We extend the method of searching “eigen-operator” of the square of the Schroedinger operator to the interaction picture, which not only helps to construct Hamiltonians of two kinds of parametric amplifiers but also leads to a new uncertainty relation regarding to the free Hamiltonian and the interacting Hamiltonian.     

Nonlinear Squeezed States and Multiplication Rule of Nonlinear Squeezing Operators Gained via Nonlinear Coherent State Representation and IWOP Technique

Using the nonlinear coherent state representation we derive nonlinear squeezed states and the multiplication rule of nonlinear squeezing operators. We find that the symplectic matrices multiplication rule in nonlinear coherent state projection operator representation maps into the multiplication rule of successive nonlinear squeezing operators.The technique of integral within an ordered product of operators plays an essential role in deriving the multiplication rule.     

一般阻尼随机微分方程的拟局部振荡算法

提出了一种模拟随机微分方程的拟局部振荡算法,即利用算符劈裂方法和势函数的泰勒展开,对噪声作用下耗散粒子的时间演化算符进行分解,得到了对应涨落行为的扩散算符和对应确定轨迹的漂移算符.其中局部简谐势场的涨落过程可获得解析解,而剩余的确定项则利用简单的Euler算法积分.应用到几个算例并与常用的两种算法相比较,结果表明:本算法随时间步长最稳定,可使用较大的时间步长.     

Correspondence between quantum-optical transform and classical-optical transform explored by developing Dirac’s symbolic method

By virtue of the new technique of performing integration over Dirac’s ket–bra operators, we explore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel–Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We cannot only find some new quantum mechanical unitary operators which correspond to the known optical transformations, deriving a new theorem for calculating quantum tomogram of density operators, but also can reveal some new classical optical transformations. For examples, we find the generalized Fresnel operator (GFO) to correspond to the generalized Fresnel transform (GFT) in classical optics. We derive GFO’s normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in the context of quantum optics. Especially, the introduction of quantum mechanical entangled state representations opens up a new area in finding new classical optical transformations. The complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Throughout our discussions, the coherent state, the entangled state representation of the two-mode squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used. All these have confirmed Dirac’s assertion: “...for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory”.     

连续纠缠态表象的几种Schmidt分解、物理意义与应用

在两粒子连续纠缠态表象|η〉的基础上分别导出了此纠缠态在坐标、动量表象和粒子数表象中的Schmidt分解,阐述了其物理意义.并且,用|η〉的Schmidt分解直接给出单模压缩算符对纠缠态的作用结果、双模平移算符的纠缠态表象以及平移算符在Fock空间的矩阵元.文章的讨论可以推广到多粒子连续纠缠态情形.     

New Bose Operator Realization of SU(2) Algebra and Its Application in Optical Propagation

We introduce a new Bose operator realization of SU(2) Lie algebra and applied it to optical propagation in GRIN media or some lens-setup.