Solution to the Bargmann－Wigner equation for a half-integral spin

A rigorous method to solve the Bargmann－Wigner equation for an arbitrary half-integral spin is presented and explicit relativistic wavefunctions for an arbitrary half-integral spin are deduced.     

自旋为2的Bargmann-Wigner方程的严格解

在坐标表象中严格求解自旋为2的Bargmann-Wigner方程,导出了自旋为2的场（m≠0）的相对论性场方程和动量表象波函数。     

自旋为整数的Bargmann-Wigner方程的严格解

从自旋为任意整数的Bargmann-Wigner方程出发,导出了自旋为整数的场的易于求解的相对论性波动方程,在坐标表象中求解此方程,严格导出了自旋为整数的场的场函数.     

Schwinger Bose实现下自旋相干态Wigner函数的特性分析

在Schwinger Bose实现下,引入纠缠态表象及Wigner算符在该表象下的表示,得到自旋相干态的Wigner函数,数值计算画出相空间中Wigner函数的分布图,并加以分析,发现在SchwingerBose实现下自旋相干态确实体现出纠缠特性。     

周期场作用下自旋的主方程及其稳定态

用Robertson理论推导一个在纵磁场和横周期场作用下的自旋的运动方程。得到了阻尼和自旋稳定态对外场强度、频率及与热库的耦合系数的依赖关系。讨论了自旋稳定态的结构及其形成原因。关键词：     

自旋为5/2的Bargmann-Wigner方程的严格解

在坐标表象中严格求解自旋为5/2的Bargmann-Wigner方程,导出了自旋为5/2的场(m≠0)的相对论性方程和动量表象波函数关键词：自旋为5/2的场(m≠0)Bargmann-Wigner方程坐标表象严格解     

高自旋场对Vaidya-Bonner黑洞熵的贡献

利用改进的brick-wall模型推导出自旋为2的引力场对动态Vaidya-Bonner 黑洞熵的贡献, 在自然单位制中其值为A/2;这表明,当选择与标量场相同的截断因子时,其熵为标量场的2 倍,为Dirac 场的4/7.关键词：Vaidya-Bonner黑洞黑洞熵高自旋场薄膜brick-wall模型     

整数自旋粒子的方程和波函数

从高自旋态的Bargmann-Wigner方程出发,建立了整数自旋粒子的运动方程,通过求解方程得到了一套整数自旋粒子波函数,并建立了等效Largrange形式.     

高自旋场对静态球对称黑洞熵的贡献

利用改进后的brick wall模型,研究具有高自旋的引力场对静态球对称黑洞熵的贡献.结果表明：在静态球对称黑洞中,自旋为2的引力场的量子熵仍与视界面积成正比.当选择与标量场相同的截断因子时,其量子熵为标量场的两倍,为Dirac场的4/7.关键词：黑洞熵brick wall模型自旋场Teukolsky型主方程     

原子核的赝自旋对称性近似

基于相对论平均场理论,讨论了Dirac方程中严格的赝自旋对称性,以及实际原子核中的近似赝自旋对称性.在严格的赝自旋对称性下,除赝自旋单态外,所有的态都有简并的赝自旋伙伴态,而且赝自旋双重态的径向量子数相同.以正常核²⁰⁸Pb和奇特核²⁶⁴Pb为例,分析了赝离心势和赝自旋–轨道耦合势的贡献,发现对于赝自旋单态,赝离心势恒为零;对赝自旋双重态,赝自旋–轨道耦合势的贡献很小,赝自旋对称性近似满足;但对于闯入态,相对于赝离心势,赝自旋–轨道耦合势的贡献很大,赝自旋对称性被完全破坏,也即闯入态不具有赝自旋伙伴态的可能原因.     

Some New Properties of Wigner Function Studied in Entangled State Representation

Based on the Wigner operator in the entangled state representation we study some new important properties of Wigner function for bipartite entangled systems, such as size of an entangled state, upper bound of Wigner functions, etc. These discussions demonstrate the beauty and elegance of the entangled state representation.     

Analytical method of spectra calculations in the Bargmann representation

We formulate a universal method for solving an arbitrary quantum system which, in the Bargmann representation, is described by a system of linear equations with one independent variable, such as one- and multi-photon Rabi models, or N level systems interacting with a single mode of the electromagnetic field and their various generalizations. We explain three types of conditions that determine the spectrum and show their usage for two deformations of the Rabi model. We prove that the spectra of both models are just zeros of transcendental functions, which in one case are given explicitly in terms of confluent Heun functions.     

Master Equation in Phase Space for a Uniaxial Spin System

A master equation, for the time evolution of the quasi-probability density function of spin orientations in the phase space representation of the polar and azimuthal angles is derived for a uniaxial spin system subject to a magnetic field parallel to the axis of symmetry. This equation is obtained from the reduced density matrix evolution equation (assuming that the spin-bath coupling is weak and that the correlation time of the bath is so short that the stochastic process resulting from it is Markovian) by expressing it in terms of the inverse Wigner-Stratonovich transformation and evaluating the various commutators via the properties of polarization operators and spherical harmonics. The properties of this phase space master equation, resembling the Fokker-Planck equation, are investigated, leading to a finite series (in terms of the spherical harmonics) for its stationary solution, which is the equilibrium quasi-probability density function of spin “orientations” corresponding to the canonical density matrix and which may be expressed in closed form for a given spin number. Moreover, in the large spin limit, the master equation transforms to the classical Fokker-Planck equation describing the magnetization dynamics of a uniaxial paramagnet.     

Full spectrum of the Rabi model

It is shown that in the Rabi model, for an integer value of the spectral parameter x, in addition to the finite number of the classical Judd states there exist infinitely many possible eigenstates. These eigenstates exist if the parameters of the problem are zeros of a certain transcendental function; in other words, there are infinitely many possible choices of parameters for which integer x belongs to the spectrum. Moreover, it is shown that the classical Judd eigenstates appear as degenerate cases of the confluent Heun function.     

Two-Mode Wigner Operator in 〈ξ| Representation and 〈τ| Representation

We derive the two-mode Wigner operator in the 〈ξ| representation and 〈τ| representation, where |ξ〉 is common eigenvector of the mass-weighted relative coordinate and the mass-combinatorial momentum.and |τ〉 common eigenvector of the mass-weighted relative coordinate and the mass-combinatorial momentum. As an application,we calculate the Wigner function of some two-mode state.     

Quantum dynamics of a nano-rod under compression

A nano-rod under compression, which is capacitively coupled to a Cooper-pair box, can be modelled in terms of a quartic oscillator linearly interacting with a tunnelling pseudo-spin. We have integrated numerically the quantum dynamics of this system in the partial Wigner representation and calculated the pseudo-spin population difference. Depending on the coupling, we have verified that the quantum tunnelling of the oscillator can lead to a more effective reduction of the Rabi oscillation amplitude of the pseudo-spin. Such findings suggest an experimental set-up that might be able to discriminate between the quantum and the classical motion of a nano-rod.