New Bosonic Operator Ordering Identities Gained by the Entangled State Representation and Two-Variable Hermite Polynomials

Based on the technique of integration within an ordered product of operators, we derive new bosonicoperators‘ ordering identities by using entangled state representation and the properties of two-variable Hermite poly-nomials H and vice versa. In doing so, some concise normally (antinormally) ordering operator identities, such asa man =:Hm,n(a ,a):, ana m = (-i)m n:Hm,n(ia ,ia): are obtained.     

New Bosonic Operator Ordering Identities Gained by the Entangled State Representation and Two－Variable Hermite Polynomials

Based on the technique of integration within an ordered product of operators,we derive new bosonic operators‘ ordering identities by using entangled state representation and the properties of two-variable Hermite poly-nomials Hm,n,and vice versa,In doing so,some concise normally (antinormally)ordering operator identities,such as a^ma^n=:Hm,n(a,a):,a^na^m=(-i)^m n:Hm,n(ia,ia):are obtained.     

Weyl Ordering Expansion of Power Product of Coordinate and Momentum Operators

By virtue of the technique of integration within Weyl ordered of operators we derive the formula of Weyl ordering expansion of power product of coordinate and momentum operators （√2Q）^m（√2iP） ^τ=：： Hm,r （√2Q, √2iP）：：, the introduction of two-variable Hermite polynomial Hm,r brings much convenience to the study of Weyl correspondence.     

New useful special function in quantum optics theory

By virtue of the operator Hermite polynomial method [Fan H Y and Zhan D H 2014 Chin. Phys. B 23 060301] we find a new special function which is useful in quantum optics theory, whose expansion involves both power-series and Hermite polynomials, i.e.,min(m,n)∑l-0n!m!(-1)l l!(n-l)!(m-l)!/Hn-l(x)ym-l≡■n,m(x,y).By virtue of the operator Hermite polynomial method and the technique of integration within ordered product of operators(IWOP) we derive its generating function. The circumstance in which this new special function appears and is applicable is considered.     

New approach to Q-P （P-Q） ordering of quantum mechanical operators and its applications

In this paper, we introduce a new way to obtain the Q-P （P-Q） ordering of quantum mechanical operators, i.e., from the classical correspondence of Q-P （P-Q） ordered operators by replacing q and p with coordinate and momentum operators, respectively. Some operator identities are derived concisely. As for its applications, the single （two-） mode squeezed operators and Fresnel operator are examined. It is shown that the classical correspondence of Fresnel operator’s Q-P （P-Q） ordering is just the integration kernel of Fresnel transformation. In addition, a new photo-counting formula is constructed by the Q-P ordering of operators.     

The s-ordered expansions of the operator function about the combined quadrature μX + νP

A general framework applicable to deriving the s-ordered operator expansions is presented in this paper.We firstly deduce the s-ordered operator expansion formula of density operator ρ a?,a and introduce the technique of integration within the sordered product of operators (IWSOP).Based on the deduction and the technique,we derive the s-ordered expansions of operators (μX + νP)n and Hn (μX + νP) (linear combinations of the coordinate operator X and the momentum operator P,Hn (x) is Hermite polynomial),respectively,and discuss some special cases of s=1,0,-1.Some new useful operator identities are obtained as well.     

Two-Variable Hermite Function as Quantum Entanglement of Harmonic Oscillator＇s Wave Functions

We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator＇s wave functions. The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S（γ）Hm,n （μa1^＋, μa2^＋│00〉, which is the minimum uncertainty state for sum squeezing, in （ η│representation is calculated.     

The N-mode squeezed state with enhanced squeezing

It is known that exp [iλ (Q1P1i/2)] is a unitary single-mode squeezing operator,where Q1,P1 are the coordinate and momentum operators,respectively.In this paper we employ Dirac’s coordinate representation to prove that the exponential operator S n ≡ exp [iλ sum((QiPi+1+Qi+1Pi))) from i=1 to n ],(Qn+1=Q1,Pn+1=P1),is an n-mode squeezing operator which enhances the standard squeezing.By virtue of the technique of integration within an ordered product of operators we derive S n ’s normally ordered expansion and obtain new n-mode squeezed vacuum states,its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.     

Nonclassicality of a two-variable Hermite polynomial state

The nonclassicality of the two-variable Hermite polynomial state is investigated. It is found that the two-variable Hermite polynomial state can be considered as a two-mode photon subtracted squeezed vacuum state. A compact expression for the Wigner function is also derived analytically by using the Weyl-ordered operator invariance under similar transformations. Especially, the nonclassicality is discussed in terms of the negativity of the Wigner function. Then violations of Bell’s inequality for the two-variable Hermite polynomial state are studied.     

New Operator Ordering Formulas Related to Hermite Polynomials Derived by Virtue of IWOP Technique

By virtue of the technique of integration within an ordered product of operators and the fundamentaloperator identity Hn(X) = 2n : Xn :, where X is the coordinate operator and Hn is the n-order Hermite polynomials,:: is the normal ordering symbol, we not only simplify the derivation of the main properties of Hermite polynomials,but also directly derive some new operator identities regarding to Hn(X). Operation for transforming f(X) → :f(X) :is also discussed.     

高速摄影技术在泥沙研究中的应用

本文应用高速摄影方法来观察明渠粗糙定床近床区域的泥沙颗粒运动,获得了近床区域内单颗泥沙在粗糙定床上的跳跃高度的变化规律为: 随机变量 服从Γ—分布: 同时,还获得了颗粒单步跃长的随机分市密度函数亦为Γ—分布:      

卟啉和金属卟啉的荧光寿命

在单光子计数仪器上测量了一系列卟啉自由碱和金属卟啉的荧光寿命.在光动力治癌疗法中用作光敏剂的HPD缓冲溶液呈现双指数荧光褒减.τ=3ns的短寿命组分是聚集态HPD的表征,而τ=14ns的长寿命组分是单体HPD的表征,HP缓冲溶液却呈现单指数衰减.有七个卟啉或其金属络合物的寿命是初次报导.某些卟啉化合物的实测寿命与计算值符合良好.     

Applying invariant eigen-operator method to deriving normal coordinates of general classical Hamiltonian

For classical Hamiltonian with general form H = 1/2 ∑ ij Mijpipj + 1/2 ∑ ij Lijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator (IEO) method (Fan et al. 2004 Phys. Lett. A 321 75) to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.     

Rotational analysis and line intensities of the HCO band at 296 K

This paper computes the rotational energy levels of the HCO transition, especially, the higher values of the rotational quantum numbers N_{Ka Kc} and K_a, with the rotational constants which are obtained via B3LYP method with 6-311G basis set, and the results show that the calculated frequencies using the computed vibration--rotation energy levels are in reasonable agreement with the data from the experiment. Meanwhile, the line intensities of HCO are first reported, the results are of significance for the studying HCO.     

第Ⅰ种非对称两态叠加多模叠加态光场等阶N次方H压缩——1.腔模总数与压缩阶数两者之积取偶的情形

本文利用多模压缩态理论研究了第Ⅰ种非对称两态叠加多模叠加态光场|Ψ_Ⅰ^(ab)>_q的广义非线性等阶N次方H压缩特性.结果发现:在腔模总数q与压缩阶数N这两者之积qN为偶数亦即qN=2p的条件下,无论p=2m(m=1,2,3,…,…)还是p=2m+1(m=0,1,2,…,…),当两非对称态中各模的初始相位和 =φ_j^(a)、 =φ_j^(b)、态间的初始相位差(θ_pq^bI-θ_nq^aR),以及各单模相干态光场的光子干涉项之和 =[R_j^(a)R_j^(b)]cos(φ_j^(a)-φ_j^(b))]等满足一定条件时,态|Ψ_Ⅰ^(ab)>_q可分别呈现出周期性变化的奇数模-偶数阶、偶数模-奇数阶和偶数模-偶数阶的等阶N次方H压缩效应.     

Interband absorption and luminescence in small quantum dots under strong magnetic fields

Interband absorption and luminescence of quasi-two-dimensional, circularly symmetric, N_e-electron quantum dots are studied at high magnetic fields, 8B60 T, and low temperatures, T2 K. In the N_e=0 and 1 dots, the initial and final states of such processes are fixed, and thus the dependence on B of peak intensities is monotonic. For larger systems, ground state rearrangements with varying magnetic field lead to substantial modifications of the absorption and luminescence spectra. Collective effects are seen in the N_e=2 and 3 dots at “filling fractions” and .     

Tree-level contributions to the rare decays , , and in the Standard Model

The tree-level contributions to the rare decays , , and are analyzed and compared to those occurring in , , and . It is shown that these purely long-distance contributions, arising from the exchange of a charged lepton, can be significant in B⁺ decays for an intermediate τ, potentially blurring the distinction between the modes used to extract B⁺→τ⁺ν_τ and those used to probe the genuine short-distance and FCNC transitions. Numerically, the tree-level contributions are found to account for 98%, 12% and 14% of the total , , and rates, respectively.     

准一维聚合物中的声学极化子

本文讨论准一维聚合物中的一维电子通过形变势与三维声学声子相互作用,对弱耦合和中间耦合情形,导出了极化子基态能量和有效质量。结果表明,在这种混合维数模型中,可形成稳定的极化子。