利用特殊函数和类比法有序化排列正负指数幂算符

研究算符函数的有序化排列是一项重要的数理任务.本文利用特殊函数和正规乘积排序与反正规乘积排序间的互换法则法导出了幂算符(αα^+)^±n和(α^+α)^±n的正规与反正规乘积排序.进一步,利用类比法得到了算符(XP)^±n和(PX)^±n的坐标-动量排序与动量-坐标排序式.最后,对新得到的这些算符结果的应用进行一些讨论.

Quantum fluctuations of mesoscopic damped mutual capacitance coupled double resonance RLC circuit in thermal excitation state

Mesoscopic damped mutual capacitance coupled double resonance circuit is quantized by the method of damped harmonic oscillator quantization. Hamiltonian is diagonalized by the method of unitary transformation. The energy spectra of this circuit are given. The quantum fluctuations of the charge and current of each loop are investigated by the method of thermo- field dynamics (TFD) in thermal excitation state,thermal squeezed vacuum state, thermal vacuum state and vacuum state. It is shown that the quantum fluctuations of the charge and current are related to not only circuit inherent parameter and coupled magnitude, but also quantum number of excitation, squeezed coefficients, squeezed angle and environmental temperature. And the quantum fluctuations increase with the increase of temperature and decay with time.

Relationship Between Wave Function and Corresponding Wigner Function Studied in Entangled State Representation

By using the explicit form of the entangled Wigner operator and the entangled state representation we derive the relationship between wave function and corresponding Wigner function for bipartite entangled systems. The technique of integration within an ordered product （IWOP） of operators is employed in our discussions.

New Route to Deducing Integration Formulas by Virtue of the IWOP Techniqu~

We point out a new route to deducing integration formulas, i.e., using the technique of integration within an ordered product （IWOP） of operators we derive some new integration formulas, which seems concise. As a by-product, some new operator identities also appear.

Wigner Function of Density Operator for Negative Binomial Distribution

By using the technique of integration within an ordered product （IWOP） of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator.

Four-mode coherent-entangled state and its application

A new kind of four-mode continuous variable coherent-entangled state is proposed in the Fock space by using the technique of integration within an ordered product, which exhibits both the properties of a coherent state and an entangled state, and spans a complete and orthonormal representation. The conjugate state of the four-mode continuous variable coherent-entangled state is derived by using the Fourier transformation. Moreover, a simple experimental protocol of generating a four-mode continuous variable coherent-entangled state is proposed by using beam splitters. As applications of this four-mode continuous variable coherent-entangled state, a four-mode entangled state and a four-mode squeezing-Fresnel operator are constructed.

A New Kind of Bipartite Entangled State Representation and its Application

We construct four linear composite operators for a two-particle system and give common eigenvectors of those operators. The technique of integration within an ordered product of operators is employed to prove that those common eigenvectors are complete and orthonormal. Therefore, a new intermediate coordinate-momentum representation for a two-particle system is proposed and applied to some two-body dynamic problems.

New Two-Mode Coherent-Intermediate-Entangled State and Its Squeezing Operator

The coherent-intermediate-entangled state ｜α, x）λ,v is proposed in the two-mode Fock Space, which exhibits both the properties of the coherent and entangled states. The ｜α, x）λ,v makes up a new quantum mechanical representation, and the completeness relation of ｜α, x）λ,v is proved by virtue of the technique of integral within an ordered product of operators. The corresponding squeezing operators are derived. Furthermore, Generalized P-representation is constructed in the coherent-intermediate-entangled state ｜α, x）λ,v and the Schmidt decomposition of ｜α, x）λ,v is investigated.

基于正弦控制因子的Lateral变异鲨鱼优化算法

针对传统鲨鱼优化算法在求解高维目标函数时,易早熟收敛,陷入局部最优的缺陷.提出一种基于正弦控制因子的Lateral变异鲨鱼优化算法.通过正弦曲线的特性和自适应惯性权重,改善了传统鲨鱼优化算法中由于随机选取控制因子数值大小可能导致算法在迭代后期全局搜索能力降低的问题,提高了算法在迭代后期的全局收敛能力,并对最佳鲨鱼位置引入Lateral变异策略,加强了算法跳出局部最优的可能性.改进后的算法对多个shifted单峰,多峰以及固定维测试函数进行求解,实验结果表明,对比多种不同优化算法而言,本文所提LSSO算法具有更高的收敛精度和搜索速度.