态|Ψ(3)>q中广义电场分量的偶数次N次方Y压缩

构造了由多模复共轭虚相干态、多模复共轭虚相干态的相反态和多模复共轭相干态的线性叠加所组成的一种新型的三态叠加多模叠加态光场|Ψ⁽³⁾>_q.利用多模压缩态理论,研究了态|Ψ⁽³⁾>_q中广义电场分量的偶数次等幂次N次方Y压缩特性.结果发现:态|Ψ⁽³⁾>_q是一种典型的三态叠加多模非经典光场;当压缩次数N等于2P且P为2m’+1(m’=0,1,2,…,…)时,如果各模的初始相位φ_j(j=1,2,3,…,…,q)、态间的初始相位差(θ₁-θ₂)、(θ₁-θ₃)和(θ₂-θ₃),以及各单模相干态光场的总的平均光子数等分别满足各自的取值条件,则在这种情况下态|Ψ⁽³⁾>_q的广义电场分量可呈现出偶数次的广义非线性等幂次2(2m’+1)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.     

第Ⅵ类两态叠加多模叠加态光场的等阶N次方Y压缩特性研究

本文构造了由多模相干态|{Z_j}〉q与多模虚相干态|{iZ_j}〉q这两者的线性叠加所组成的第Ⅵ类两态叠加多模叠加态光场|Ψ₆⁽²⁾〉q.利用多模压缩态理论,研究了态|Ψ₆⁽²⁾〉q的广义非线性等阶N次方Y压缩特性.结果发现:1)在压缩阶数N＝2p且p＝2l(l＝1,2,3,…,…)的条件下,无论各模的初始相位φ_j(j＝1,2,3,…,q)、态间的初始相位差(θ_pq^(R)-θ_pq^(I))以及各单相干态光场的平均光子数之和 R_j²等如何变化,态|ψ₆⁽²⁾〉q总是恒处于偶数阶等阶N-Y最小测不准态.2)在压缩阶数N＝2p且p＝2l+1(l＝0,1,2,3,…,…)的条件下,当各模的初始相位φj、态间的初始相位差(θ_pq^(R)-θ_pq^(I))以及各单模相干态光场的平均光子数之和 R_j²等分别满足一定的量子化条件(或者在特定的区间内连续取值)时,态|ψ₆⁽²⁾〉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偶数阶的等阶N次方Y压缩效应.     

态|Ψ(3)〉q中广义电场分量的不等幂次Nj次方Y压缩

利用多模压缩态理论,研究了由多模复共轭虚相干态|{iZ_j^*}〉q、多模复共轭虚相干态的相反态|{-iZ_j^*}〉q和多模复共轭相干态|{Z_j^*}〉q的线性叠加所组成的新型三态叠加多模叠加态光场|Ψ⁽³⁾〉_q中广义电场分量的偶数次不等幂次Nj次方Y压缩特性.结果发现:在各模的压缩次数N_j=2pj且pj=2m′j+1(m′j=0,1,2,3,…,…)和Nj′=2pj′且pj′=2m′j′+1(m′j′=0,1,2,3,…,…)的条件下,当各模的初始相位φ_j与φ_j′、态间的初始相位差(θ₁-θ₃)与(θ₂-θ₃),以及各单模相干态光场总的平均光子数之和qj=1R2j等分别满足一定的取值条件时,态|Ψ⁽³⁾〉_q的广义电场分量(即第二正交相位分量)总可呈现出周期性变化的、偶数次的广义非线性不等幂次N_j次方Y压缩效应.     

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.     

On the Fundamental Solution of a Linearized Homogeneous Coagulation Equation

We describe the fundamental solution of the equation that is obtained by linearization of the coagulation equation with kernel K(x, y) = (xy)^λ/2, around the steady state f(x) = x ^?(3+λ)/2 with ${\lambda \in (1, 2)}We describe the fundamental solution of the equation that is obtained by linearization of the coagulation equation with kernel K(x, y) = (xy)^λ/2, around the steady state f(x) = x ^−(3+λ)/2 with l ? (1, 2){\lambda \in (1, 2)} . Detailed estimates on its asymptotics are obtained. Some consequences are deduced for the flux properties of the particles distributions described by such models.     

一种新型的两态叠加多模Schrödinger猫态光场的等阶N次方Y压缩

本文根据量子力学的线性叠加原理,构造了由多模(即q模)相干态的相反态|{-Z_j}〉q及多模虚相干态|{Z_j}〉q这两者的线性叠加所组成的一种新型的多模Schrdinger猫态光场|Ψ⁽²⁾〉q,利用新近建立的多模压缩态理论,研究了态|Ψ⁽²⁾〉q的N次方Y压缩效应。结果发现:①当压缩阶数N=2p且p=2m(m=1,2,3,…,…)时,态|Ψ⁽²⁾〉q总是恒处于N-Y最小测不准态;②当压缩阶数N=2p且p=2m+1(m=0,1,2,3,…,…)时,如果各模的初始相位φ_j,态间的初始相位差θ_pq^(I)-θ_nq^(R)以及各单模相干态光场的平均光子数之总和 等满足一定的量子化条件,则态|Ψ⁽²⁾〉q可呈现出周期性变化的、任意阶的N次方Y压缩效应;③当压缩阶数N=2p′+1时,无论p′=2m(m=0,1,2,…,…)还是p′=2m+1(m=0,1,2,3,…,…),只要各模的初始相位φ_j满足一定的量子条件,则当两态叠加几率幅满足r_pq^(I)=r_nq^(R)时,态|Ψ⁽²⁾〉q就恒处于N-Y测不准态,始终不呈现N-Y最小测不准态和N次方Y压缩;而当r_pq^(I)≠r_nq^(R)时,态|Ψ⁽²⁾〉q始终不呈现N-Y测不准态、N-Y最小测不准态和N次方Y压缩效应。     

非奇异宇宙的理想气体自相似模型

通过引力作用下理想气体运动连续性方程的无量纲化,根据量纲理论Π定理,以尺度因子R(t)为物理量统一度量基准,发现了引力作用下理想气体宇宙模型的自相似性和一系列R(t)的解析解.基于R(t),可建立对应的、具有非欧氏几何特性的均匀膨胀时空坐标系S(t,ξ,θ,φ),并获得一个密度ρ为常数、速度u为零、压强p不为零的理想气体宇宙解.在这个解的形式中,光子红移量z所表现的是光子传播距离r,当红移量z较小时两者成正比(即哈勃定律).由均匀膨胀坐标系还可推导出Robertson-Walker度规(k= 关键词： 宇宙 自相似 哈勃定律     

A Construction of Blow up Solutions for Co-rotational Wave Maps

The existence of co-rotational finite time blow up solutions to the wave map problem from ${\mathbb{R}^{2+1} \to N}The existence of co-rotational finite time blow up solutions to the wave map problem from \mathbbR²⁺¹ ? N{\mathbb{R}^{2+1} \to N} , where N is a surface of revolution with metric d ρ ² + g(ρ)² dθ², g an entire function, is proven. These are of the form u(t,r)=Q(l(t)t)+R(t,r){u(t,r)=Q(\lambda(t)t)+\mathcal{R}(t,r)} , where Q is a time independent solution of the co-rotational wave map equation −u _tt  + u _rr  + r ⁻¹ u _r  = r ⁻² g(u)g′(u), λ(t) = t ^−1-ν, ν > 1/2 is arbitrary, and R{\mathcal{R}} is a term whose local energy goes to zero as t → 0.     

Atoms in Strong Magnetic Fields:¶The High Field Limit at Fixed Nuclear Charge

Let E(B,Z,N) denote the ground state energy of an atom with N electrons and nuclear charge Z in a homogeneous magnetic field B. We study the asymptotics of E(B,Z,N) as B→∞ with N and Z fixed but arbitrary. It is shown that the leading term has the form (ln B)² e(Z,N), where e(Z,N) is the ground state energy of a system of N bosons with delta interactions in one dimension. This extends and refines previously known results for N= 1 on the one hand, and N,Z→∞ with B/Z ³→∞ on the other hand. Received: 9 December 1999 / Accepted: 15 February 200     

Self-consistent diverted tokamak equilibria with nonzero edge current

The semi-analytical method, previously used to construct model double-null and single-null diverted tokamak equi- libria (Bingren Shi, Plasma Phys. Control Fusion 50 (2008) 085006, 51 (2009) 105008, Nucl. Fusion 51 (2011) 023004), is extended to describe diverted tokamak equilibria with nonzero edge current, including the Pfirsch–Schlüter(PS) cur- rent. The PS current density is expressed in a way suitable to describe a diverted tokamak configuration in the near separatrix region. The model equilibrium is expressed by only two terms of the exact separable solutions of the Grad– Shafranov equation, one of which is governed by a homogeneous ordinary differential equation, and the other by an inhomogeneous one. The particular merits of such a model configuration are that the internal region inside the separa- trix and a suitable scrape-off layer can be simultaneously described by this exact solution. To investigate the physics in the region near the X-point, the magnetic surfaces can be satisfactorily described by approximate hyperbolic curves.     

多模叠加态光场|ψ5(3)〉q中广义磁场4m次方Y压缩

构造了由多模复共轭相干态|{Z_j^*}〉_q、多模复共轭相干态的相反态|{-Z_j^*}〉_q以及多模虚相干态|{iZ_j^*}〉_q的线性叠加所组成的第Ⅴ类三态叠加多模叠加态光场|ψ₅⁽³⁾〉_q.利用多模压缩态理论研究了态|ψ₅⁽³⁾〉_q中广义磁场分量的等幂次N次方Y压缩特性.结果发现:当压缩次数N=2p且p=2m(m=1,2,3,…,…)时,只要各模的初始相位φ_j(j=1,2,…,…,q)、态间的初始相位差(θ₁-θ₂)、(θ₁-θ₃)和(θ₂-θ₃)以及受各模的初始相位φ_j调制的各单模相干态光场的平均光子数之和 等分别满足一定的取值条件,则态|ψ₅⁽³⁾〉_q的广义磁场分量就可呈现出周期性变化的广义非线性等幂次4m次方Y压缩效应.     

Dynamic-angle spinning of quadrupolar nuclei. 1990

In dynamic-angle spinning (DAS), a sample spins around an axis inclined at an angle θ(t) with respect to the magnetic field such that the averages of P_n(cosθ) are zero. The simplest case is where θ(t) assumes two discrete values θ₁ and θ₂ (complementary DAS angles) such that the averages of P₂(cosθ) and P₄(cosθ) are zero, thereby removing second-order quadrupolar (and dipolar) broadening. Examples of DAS complementary angles are θ₁=37.38° and θ₂=79.18°. Experimental details for DAS experiments are provided and applications to sodium-23 and oxygen-17 NMR illustrate the enhanced resolution achieved by removing the second-order broadening inherent in magic-angle spinning.     

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.     

Viscous fluids and Gauss–Bonnet modified gravity

We study effects of cosmic fluids on finite-time future singularities in modified f (R, G)-gravity, where R and G are the Ricci scalar and the Gauss–Bonnet invariant, respectively. We consider the fluid equation of state in the general form, ω = ω(ρ), and we suppose the existence of a bulk viscosity. We investigate quintessence region (ω > −1) and phantom region (ω < −1) and the possibility to change or avoid the singularities in f (R, G)-gravity. Finally, we study the inclusion of quantum effects in large curvature regime.     

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——2腔模总数与压缩阶数两者之积取奇数的情形

构造了由多模复共轭相干态的相反态|{-Z_j^(a)*}〉q和多模虚共轭相干态的相反态|{-Z_j^(b)*}〉q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(ab)Ⅱ〉q.利用多模压缩态理论,研究了态|Ψ(ab)Ⅱ〉q的等阶N次方H压缩特性.结果发现,在腔模总数与压缩阶数这两者之积取奇数,则当各对应模的初始相位、各对应模的初始相位差,态间的初始相位差、以及光子干涉项的幅度之和等分别满足一定的量子化条件时,态|Ψ(ab)Ⅱ〉q的第一及第二正交分量可分别呈现出周期性变化的等阶N次方H压缩效应.这与现有报道的结果截然不同.     

Mirnov coil data analysis for tokamak ADITYA

The spatial and temporal structures of magnetic signal in the tokamak ADITYA is analysed using recently developed singular value decomposition (SVD) technique. The analysis technique is first tested with simulated data and then applied to the ADITYA Mirnov coil data to determine the structure of current peturbation as the discharge progresses. It is observed that during the current rise phase, current perturbation undergoes transition from m=5 poloidal structure to m=4 and then to m=3. At the time of current termination, m=2 perturbation is observed. It is observed that the mode frequency remains nearly constant (≈10 kHz) when poloidal mode structure changes from m=4 to m=2. This may be either an indication of mode coupling or a consequences of changes in the plasma electron temperature and density scale length.     

第Ⅰ种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)Ⅰ>_q的偶数阶等阶N次方Y压缩特性.结果发现:在压缩阶数N取偶数情况下,只要构成态|Ψ_Ⅰ^(ab)Ⅰ>_q的两个量子光场态的强度(即平均光子数)不相等,则当各模的初始相位φ_j^(a)、φ_j^(b)(j＝1,2,3,…,q)、态间的初始相位差(θ_pq^(bI)-θ_nq^(aR))以及与上述的两个量子光场态相对应的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)Ⅰ>_q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.这一结果与现有文献报道的结果截然不同.     

Die Stromdichte eines quadratisch integrierbaren Klein-Gordon-Feldes mit Wechselwirkung

A four vector is constructed for the statistical interpretation of a relativistic scalar wave function which is not a solution of an interaction-free Klein-Gordon equation. The zero component of the four vector is positive definite, whereas the four components satisfy the equation of continuity. It is proved that these components, which are bilinear forms inΨ(x)=∫d ⁴pa(p)e^?ipxsatisfying the normalization condition(2π) ⁴(2m)^?1∫ d⁴pθ(p⁰)θ6(p²)¦a(p)¦²=1 reduce to the four-vector ofPetzold and co-workers if the transition fromΨ(x) to the free-particle wave functionΦ(x)=∫d ³¯pa(¯p)e^?ipxsatisfying(2π) ³ (2m)^?1∫(2p₀)^?1¦a (¯p)¦²d³¯p=1 is made in the proper way. The nonrelativistic limit in the case of relativistic interactions is also discussed.