R-宇称破缺的相互作用研究

在LHC上，最小超对称标准模型中R-宇称破缺相互作用使LHC上tt对的产生有两种过程，一种是交换slepton粒子的t道的d_Rd_R→t_Lt_L过程，一种是交换squark粒子的u道的d_Rd_R→t_Rt     

四态叠加多模叠加态光场|Ψe(4),Ⅲ〉q的等阶N次方Y压缩

根据量子力学的线性叠加原理,构造了由多模偶相干态与多模虚偶相干态组成的第Ⅲ种四态叠加多模叠加态光场态|Ψ_e⁽⁴⁾,Ⅲ〉_q的等阶N次方Y压缩特性.结果发现:1) 当压缩阶数N=4m,(m=1,2,3,…)时,态|Ψ_e⁽⁴⁾,Ⅲ〉_q恒处于等阶数N-Y最小测不准态;2) 当压缩阶数N=4m′+2,(m′=0,1,2,…)时,在(θ₁-θ₂),q,R_j,r₁,r₂等取不同的组合定值下,态|Ψ_e⁽⁴⁾,Ⅲ〉_q可分别呈现出等阶N次方Y压缩效应与"半相干态"效应;3) 当压缩阶数N为奇数时,在(θ₁-θ₂),q,R_j,r₁,r₂等取不同的组合定值下,态|Ψ_e⁽⁴⁾,Ⅲ〉_q可呈现出等阶N次方Y压缩效应.     

第Ⅱ种强度不等的非对称两态叠加多模叠加态光场的任意奇数阶等阶N次方Y压缩

本文利用多模压缩态理论,研究了第Ⅱ种强度不等的非对称两态叠加多模叠加态光场|Ψ_Ⅱ^(ab)>_q的任意奇数阶等阶N次方Y压缩特性.结果发现:在压缩阶数N=2p+1的条件下,无论p=2m还是p=2m+1(m=0,1,2,3,…,…),只要构成态|Ψ_Ⅱ^(ab)>_q的两个不同的量子态|{-Z_j^(a)*}>_q与|{-iZ_j^(b)*}>_q的各对应模的强度(即平均光子数)和初始相位都不相等,亦即Rj(a)≠Rj(b)和φj(a)≠φj(b)(j=1,2,3,…,q),并且 R_j^(a)(2p+1)= R_j^(b)(2p+1),则当各对应模的初始相位φ_j^(a)与φ_j^(b)、各对应模的初始相位差(φ_j^(a)-φ_j^(b)),态间的初始相位差(θ_nq^(aR)-θ_nq^(bI))以及光子干涉项的幅度 =R_j^(a)R_j^(b)等分别满足一定的量子化条件时,态|Ψ_Ⅱ^(ab)>_q的第一及第二这两个正交分量总可分别呈现出周期性变化的、任意奇数阶等阶N次方Y压缩效应.这一结果,与现有报道的结果截然不同.     

受量子相位调制的两态叠加多模叠加态光场的广义非线性等阶N次方Y压缩

本文根据量子力学中的线性叠加原理,构造了由受量子相位调制的多模(即q模)虚相干态|{i^m₁Z_j}〉q及其相反态|{-i^m₂Z_j}〉q这两者的线性叠加所组成的一种新型的两态叠加多模叠加态光场|ψ_m1,m2⁽²⁾〉q.利用新近建立的多模压缩态理论,详细研究了态|ψ_m1,m2⁽²⁾〉q的广义非线性等阶N次方Y压缩特性.结果发现:1)无论态间的初始相位差(θ_m2-θm₁)、各模的初始相位φ_j、腔模总数q、压缩参量R_j以及两态叠加的几率幅r_m1和r_m2等取何值,无论压缩阶数N取奇还是取偶,只要相位调制因子m1和m2与压缩阶数N的关系满足一定的量子化条件,态|ψ_m1,m2⁽²⁾〉q就恒处于等阶N-Y最小测不准态.2)当态间的初始相位差(θ_m2-θm₁)在态间压缩区[2kθπ-π/2+ {R_j²[(m₂-m₁)π/2]},2kθπ+π/2+ {R_j²[(m₂-m₁)π/2]}]内取值时,无论压缩阶数N取奇还是取偶,只要相位调制因子m₁和m₂与N的关系式以及各模的初始相位φ_j等满足一定的量子化条件,态|ψ_m1,m2〉q就可呈现出周期性变化的,任意阶的等阶N次方Y压缩效应.3)利用相位调制因子m₁、m₂与压缩阶数N之间的解析关系式,可直接确定出|ψ_m1,m2〉q呈现等阶N次方Y压缩效应时的压缩阶数N.4)文献2、11、15关于等阶N次方Y压缩的研究结果,仅仅是本文所得普遍性结果在相位调制因子m₁和m₂取不同值时的特例.     

A remark on transition probability

Uhlmann's transition probability P(ψ, φ) of two normal states of a von Neumann algebra M, which is the supremum of |(Ψ, Φ)|² for all possible choices of representative vectors Ψ and Φ of ψ and φ, is shown to be the infimum of (∫d(μ_{ψ, e})^1/2)² for the induced measures μ_{ω, e}(B)=ω(e(B)) (B: Borel set in ℝ, ω=ψ, φ) for all possible projection-valued measures e belonging to M.     

核类似铜酸盐超导模型的sus(1,1)⊕sud(1,1)代数结构

由Iachello提出的核类似铜酸盐超导模型具有su(3)代数结构,其平均场近似下的Hamilton量可以写成su(3)生成元的线性组合.通过代数生成元的实现,该模型约化的Hamilton量具有su_s(1,1)⊕su_d(1,1)代数结构,利用相干算子U(θ,φ)的幺正变换,可得到系统约化Hamilton量的能隙方程及本征值,发现应用不同代数结构求解会得到不同侧重点的分析结果.     

第Ⅱ种强度不等的两态叠加多模叠加态光场的等阶N次方H压缩1腔模总数与压缩阶数两者之积取偶数的情形

利用多模压缩态理论研究了第种强度不等的非对称两态叠加多模叠加态光场|Ψ_Ⅱ^(ab)〉q的等阶N次方H压缩特性.结果发现:1)当腔模总数q与压缩阶数N的乘积取偶数,亦即qN=2p时,无论p=2m(m=1,2,3,…,…),还是p=2m+1(m=0,1,2,3,…,…),只要各模的初始相位差(φ_j^(a)-φ_j^(b))、态间的初始相位差(θ_nq^(aR)-θ_nq^(bR))及光子干涉项的幅度 1R_j^(a)R_j^(b)等分别满足一定的条件,则态|Ψ_||^(ab)〉q的第一和第二正交分量总可分别呈现出周期性变化的等阶N次方H压缩效应.2)当qN=2p且p=2m+1(m=0,1,2,3,…,…)时,若构成态|Ψ_Ⅱ^(ab)〉q的两个不同的量子光场态中各对应模的强度(即平均光子数)和初始相位相等,亦即R_j^(a)=R_j^(b)和φ_j^(a)=φ_j^(b)(j=1,2,3,…,q),则态|Ψ_Ⅱ^(ab)〉q可呈现出“等阶N次方H压缩简并”现象.     

第Ⅱ种强度不等的非对称两态叠加多模叠加态光场的偶数阶等阶N次方Y压缩

本文构造了由多模复共轭相干态的相反态|{-Z_j^(a)*}>_q与多模虚共轭相干态的相反态|{-iZ_j^(b)*}>_q这两者的线性叠加所组成的第Ⅱ种强度不等的非对称两态叠加多模叠加态光场|Ψ_Ⅱ^(ab)>_q,利用多模压缩态理论研究了态|Ψ_Ⅱ^(ab)>_q的任意偶数阶等阶N次方Y压缩特性.结果发现:1)在压缩阶数N取偶数,即N=2p的条件下,无论p=2m(m=1,2,3,…,…),还是p=2m+1(m=0,1,2,3,…,…),只要构成态|Ψ_Ⅱ^(ab)>_q的两个不同的量子光场态中各对应模的强度(即平均光子数)和初始相位都不相等,亦即R_j^(a)≠R_j^(b)和φ_j^(a)≠φ_j^(b)(j=1,2,3,…,q),并且 ,则当满足一定的量子化条件(或者在一些闭区间内连续取值)时,态|Ψ_Ⅱ^(ab)>_q总可呈现出周期性变化的、任意偶数阶的等阶N次方Y压缩效应.2)在N=2p且p=2m+1(m=0,1,2,3,…,…)的条件下,若R_j^(a)=R_j^(b)和φ_j^(a)=φ_j^(b)(j=1,2,3,…,q),态|Ψ_Ⅱ^(ab)>_q则可呈现出等阶N次方Y压缩简并现象.     

态|ψ3(3)〉q中广义磁场分量的N次方Y压缩效应

构造了由多模复共轭相干态|{Z_j^*}〉_q、多模复共轭虚相干态|{iZ_j^*}〉_q和多模真空态|{Q_j} 〉_q这三态的线性叠加所组成的第Ⅲ类三态叠加多模叠加态光场|ψ₃⁽³⁾〉_q.利用多模压缩态理论研究了态|ψ₃⁽³⁾〉_q中广义磁场分量的任意偶数次广义非线性等幂次N次方Y压缩特性.结果发现:在压缩次数N取偶数,只要各模的初始相位φ_j(j=1,2,3,…,…,q),态间的初始相位差(θ_i-θ₂)(i=1,3)和各单模相干态光场平均光子数R_j²之和 分别满足各自的取值条件,态|ψ₃⁽³⁾〉_q的广义磁场分量(即第一正交相位分量)就可呈现出周期性变化的、任意偶数次的广义非线性等幂次N次方Y压缩效应.     

用超短光脉冲简并四波混频测量介质弛豫率的研究

本文讨论用ps光脉冲简并四波混频测量非线性介质弛豫率和在适度或强的相位调制情况下测量激光脉冲宽度的方法,通过用计算机模拟及与实验结果比较,得出结论:对t_p>>τ_r和t_p<<τ_r两种极限情况,该方法是足够精确的.对τ_r/t_p的中间情况,该方法只能给出一个估计.     

空间变尺度因子球坐标系与四维时空度规

时空度规是广义相对论的一个基础性概念,是宇宙学和天体物理学建立模型的逻辑基础.将随时序参数变化的空间尺度 因子函数引入相对论四维时空间隔模型,研究空间球对称形式的四维平直时 空度规、Schwarzschild度规、Robertson-Walker (R-W)度规之间的变换条件.基于空间变尺度因子球坐标系的时空间隔, 通过严格的计算,推导出R-W度规中与k=±1对应的尺度因子函数解析解,还推导出星球外非真空条件下的四维时空度规. 提出了一种理解现代物理学非平直时空模型的新视角.     

Study on Charged Top-Pion Decay Processes

In the framework of top-color assisted technicolor (TC2) theory, we study the four decay processes of charged top-pion, i.e., Π⁺_t→ t\bar{b}, Π⁺_t→ c\bar{b}, Π⁺_t→ W⁺γ, Π⁺_t→ W⁺Z⁰. The decay branching ratio of these modes are calculated. The results show that the main decay channels of charged top-pion are the tree level modes: Π⁺_t → t\bar{b} and Π⁺_t → c\bar{b}. Light Π⁺_t is easier to be detected than heavy one at future coliders. So, the study provides us with some useful informations to search for charged top-pion.     

Projective and affine connections on S and integrable systems

It is known that the Korteweg–de Vries (KdV) equation is a geodesic flow of an L² metric on the Bott–Virasoro group. This can also be interpreted as a flow on the space of projective connections on S¹. The space of differential operators Δ⁽ⁿ⁾=∂ⁿ+u₂∂ⁿ⁻²++u_n form the space of extended or generalized projective connections. If a projective connection is factorizable Δ⁽ⁿ⁾=(∂−((n+1)/2−1)p₁)(∂+(n−1)/2p_n) with respect to quasi primary fields p_i’s, then these fields satisfy ∑_i=1ⁿ((n+1)/2−i)p_i=0. In this paper we discuss the factorization of projective connection in terms of affine connections. It is shown that the Burgers equation and derivative non-linear Schrödinger (DNLS) equation or the Kaup–Newell equation is the Euler–Arnold flow on the space of affine connections.     

One Electron Atom in Special Relativity with de Sitter Space-Time Symmetry

The de Sitter invariant Special Relativity (dS-SR) is SR with constant curvature, and a natural extension of usual Einstein SR (E-SR). In this paper, we solve the dS-SR Dirac equation of Hydrogen by means of the adiabatic approach and the quasi-stationary perturbation calculations of QM. Hydrogen atom is located in the light cone of the Universe. FRW metric and ΛCDM cosmological model are used to discuss this issue. To the atom, effects of de Sitter space-time geometry described by Beltrami metric are taken into account. The dS-SR Dirac equation turns out to be a time dependent quantum Hamiltonian system. We reveal that: (i) The fundamental physics constants m_e,h,e variate adiabatically along with cosmologic time in dS-SR QM framework. But the fine-structure constant α≡ e²/(hc) keeps to be invariant; (ii) (2s^1/2-2p^1/2)-splitting due to dS-SR QM effects: By means of perturbation theory, that splitting Δ E(z) are calculated analytically, which belongs to O(1/R²)-physics of dS-SR QM. Numerically, we find that when |R|～{10³Gly, 10⁴Gly, 10⁵Gly}, and z～{1,or 2}, the Δ E(z)>>1 (Lamb shift). This indicates that for these cases the hyperfine structure effects due to QED could be ignored, and the dS-SR fine structure effects are dominant. This effect could be used to determine the universal constant R in dS-SR, and be thought as a new physics beyond E-SR.     

Theoretical study of stereodynamics for the D'+DS(ν = 0,j = 0)→D'D+S abstraction reaction

Quasiclassical trajectory (QCT) calculations have been performed for the abstraction reaction, D' +DS(v = 0, j = 0)→D'D+S on a new LZHH potential energy surface (PES) of the adiabatic 3A' electronic state [Lü et al. 2012 J. Chem. Phys. 136 094308]. The collision energy effect on the integral cross section and product polarization are studied over a wide collision energy range from 0.1 to 2.0 eV. The cross sections calculated by the QCT procedure are in good accordance with previous quantum wave packet results. The three angular distribution functions, P(θ_r), P(φ_r), and P(θ_r,φ_r), together with the four commonly used polarization-dependent differential cross sections ((2π/σ)(ds₀₀/dω_t), (2π/σ)(ds₂₀/dω_t), (2π/σ)(ds₂₂₊/dω_t), (2π/σ)(ds_21-/dω_t)) are obtained to gain insight into the chemical stereodynamics of the title reaction. Influences of the collision energy on the product polarization are exhibited and discussed.     

Hamiltonian Formalism of de-Sitter Invariant Special Relativity

The Lagrangian of Einstein's special relativity with universal parameter c (SR_c) is invariant under Poincaré transformation, which preserves Lorentz metric η_μν. The SR_c has been extended to be one which is invariant under de Sitter transformation that preserves so-called Beltrami metric B_μν. There are two universal parameters, c and R, in this Special Relativity (denoted as SR_cR). The Lagrangian-Hamiltonian formulism of SR_cR is formulated in this paper. The canonic energy, canonic momenta, and 10 Noether charges corresponding to the space-time's de Sitter symmetry are derived. The canonical quantization of the mechanics for SR_cR-free particle is performed. The physics related to it is discussed.     

受限一维无自旋费米子系统的性质研究

本文借助于一维自旋1/2-XXZ模型的Bethe-ansatz精确解, 利用局域密度近似(LDA), 讨论了谐振势中一维无自旋费米子的密度分布, 得出了ρ-u相图(这里的ρ为无量纲的粒子数密度 变量u为相互作用强度)对相图的分析表明, 随着原子密度和近邻相互作用的变化, 系统出现五个不同的混合量子相通过对热力学硬度S_ρ的计算, 发现其可作为体系的序参量, 其奇异点可用以度量受限体系中量子相变的发生     

Stationary solutions in three-dimensional general relativity

All the stationary solutions of the three-dimensional vacuum Einstein equations are obtained. These include a class of multicenter solutions representing systems of massive and spinning point particles. The geodesic motion of a test particle in the one-particle metric is discussed. A class of geodesics contain finite intervals where the particle moves back in coordinate time, without violation of causality.     

Diagonal Metrics of Static, Spherically Symmetric Fields: The Geodesic Equations and the Mass-Energy Relation from the Coordinate Perspective

The geodesic equations for the general case of diagonal metrics of static, spherically symmetric fields are calculated. The elimination of the proper time variable gives the motion equations for test particles with respect to coordinate time and an account of “gravitational acceleration from the coordinate perspective”. The results are applied to the Schwarzschild metric and to the so-called exponential metric. In an attempt to add an account of “gravitational force from the coordinate perspective”, the special relativistic mass-energy relation is generalized to diagonal metrics involving location dependent and possibly anisotropic light speeds. This move requires a distinction between two aspects of the mass of a test particle (parallel and perpendicular to the field). The obtained force expressions do not reveal “gravitational repulsion” for the Schwarzschild metric and for the exponential metric.     

Preferential attachment network model with aging and initial attractiveness

In this paper, we generalize the growing network model with preferential attachment for new links to simultaneously include aging and initial attractiveness of nodes. The network evolves with the addition of a new node per unit time, and each new node has m new links that with probability Π_i are connected to nodes i already present in the network. In our model, the preferential attachment probability Π_i is proportional not only to k_i + A, the sum of the old node i's degree k_i and its initial attractiveness A, but also to the aging factor ${\tau }_{i}^{-\alpha }$, where τ_i is the age of the old node i. That is, ${{\rm{\Pi }}}_{i}\propto ({k}_{i}+A){\tau }_{i}^{-\alpha }$. Based on the continuum approximation, we present a mean-field analysis that predicts the degree dynamics of the network structure. We show that depending on the aging parameter α two different network topologies can emerge. For α < 1, the network exhibits scaling behavior with a power-law degree distribution P(k) ∝ k^−γ for large k where the scaling exponent γ increases with the aging parameter α and is linearly correlated with the ratio A/m. Moreover, the average degree k(t_i, t) at time t for any node i that is added into the network at time t_i scales as $k({t}_{i},t)\propto {t}_{i}^{-\beta }$ where 1/β is a linear function of A/m. For α > 1, such scaling behavior disappears and the degree distribution is exponential.