Metastability for a Stochastic Dynamics with a Parallel Heat Bath Updating Rule

We consider the problem of metastability for a stochastic dynamics with a parallel updating rule with single spin rates equal to those of the heat bath for the Ising nearest neighbors interaction. We study the exit from the metastable phase, we describe the typical exit path and evaluate the exit time. We prove that the phenomenology of metastability is different from the one observed in the case of the serial implementation of the heat bath dynamics. In particular we prove that an intermediate chessboard phase appears during the excursion from the minus metastable phase toward the plus stable phase.     

On Odd Laplace Operators

We consider odd Laplace operators acting on densities of various weights on an odd Poisson (= Schouten) manifold M. We prove that the case of densities of weight 1/2 (half-densities) is distinguished by the existence of a unique odd Laplace operator depending only on a point of an 'orbit space' of volume forms. This includes earlier results for the odd symplectic case, where there is a canonical odd Laplacian on half-densities. The space of volume forms on M is partitioned into orbits by the action of a natural groupoid whose arrows correspond to the solutions of the quantum Batalin–Vilkovisky equations. We compare this situation with that of Riemannian and even Poisson manifolds. In particular, we show that the square of an odd Laplace operator is a Poisson vector field defining an analog of Weinstein's 'modular class'.     

Wigner Functions and Tomograms of the Even and Odd Negative Binomial States

Using the coherent state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, the Wigner functions of the even and odd negative binomial states (NBSs) are obtained. We concentrate our analysis on the fact that the even and odd NBSs interpolate between the even and odd coherent states and the even and odd quasi-thermal states depending on the values of the parameters involved. Moreover, the tomograms of the even and odd NBSs are calculated by virtue of intermediate coordinate-momentum representation in quantum optics. Project 10574060 supported by the National Natural Science Foundation of China and project Q2007A01 supported by the Natural Science Foundation of Shandong Province.     

超小金属微粒超导电性的能级统计

用平均场理论的自洽方程计算了随机矩阵理论中三种系综(Gauss Orthogonal Ensemble;Gauss Unitary Ensemble;Gauss Symplectic Ensemble)所对应的电子能级的奇/偶电子数分布对临界电子能级间距的影响,得到了在不同的自旋-轨道耦合和磁场中奇/偶电子数分布的临界电子能级间距的定量关系以及奇电子数的Δ((0)随平均能间距o>的变化. 关键词：     

Kerr偶奇相干态及其非经典性

本文对Ker偶奇相干态及其非经典性质进行了研究。结果表明:Kerr偶相干态可呈现周期性的二阶压缩效应,Kerr奇相干态则不存在这种压缩效应;但两者均可呈现周期性的振幅平方压缩效应,这与通常偶奇相干态的情形有所不同。     

A New Short Proof of the Local Index Formula and Some of Its Applications

We give a new short proof of the index formula of Atiyah and Singer based on combining Getzlers rescaling with Greiners approach of the heat kernel asymptotics. As an application we can easily compute the CM cyclic cocycle of even and odd Dirac spectral triples, and then recover the Atiyah-Singer index formula (even case) and the Atiyah-Patodi-Singer spectral flow formula (odd case).An erratum to this article can be found at     

增光子奇偶相干态的相位特性

借助于Pegg-Barnett相位算符理论和数值计算方法,研究了增光子奇偶相干态的相位概率分布,在此基础之上,讨论了有关数算符和相位算符的压缩特性。结果表明,增光子奇偶相干态的相位概率分布与通常的奇偶相干态、非线性相干态不同,在这种新的奇偶相干态中,其Pegg-Barnett相位概率分布能明显地反映出不同的量子相位信息和干涉特性。同时发现,在参量α的某些不同的取值范围内,增光子奇偶相干态在数算符和相位算符分量上均存在压缩效应。     

Elementary excitations of topologically disordered systems

We have examined the elementary excitation spectra of continuous random networks having only even rings or both even and odd rings. We have shown that odd rings introduce localized states and suppress the density of states near a spectral bound associated with sign alteration in the spatial dependence of the state. While this is a general conclusion, we show it explicitly only for the nearest-neighbor tight-binding s-band and related magnon and phonon models. In the latter case, phonon softening or phonon hardening can result. In the former case, we show that frustration leads to localized magnons.     

偶奇相干态的q-类比

在偶奇相干态的基础上,构造出偶、奇q-相干态,并讨论了它们的光统计特性.计算分析表明:偶奇q-相干态的光统计特性,是完全不相同的.     

Odd symplectic geometry types on supermanifolds

Generalization of symplectic geometry on manifolds in a supersymmetric case is examined in the present work. In the even case, this leads either to even symplectic geometry, that is, the geometry on supermanifolds with the nondegenerate Poisson bracket, or to the geometry on the Fedosov even supermanifolds. In the odd case, two different scalar symplectic structures exist (namely, the odd closed differential 2-form and antibracket), which can be used to construct various symplectic geometry types on supermanifolds. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 52–57, February, 2008.     

正交偏振双色激光场作用下高次谐波的椭偏特性研究

通过数值求解二维含时薛定谔方程,理论研究了正交偏振双色激光场作用下H2+分子高次谐波发射和孤立阿秒脉冲的产生. 数值结果显示,改变激光场的强度比,可以调控高次谐波强度以及谐波椭偏率. 结果表明随着场强比的增加,y方向的谐波强度不断提高. 当场强比为1:2.5时,x方向和y方向分别仅有奇次谐波和偶次谐波产生,并且偶次谐波的强度比奇次谐波强度高2-3个数量级. 此时,奇次谐波的椭偏率最大可以达到0.3,偶次谐波的椭偏率接近于0. 此外,通过改变分子的准直角可以控制谐波的椭偏率,基于这一现象,利用椭圆偏振高次谐波的平台区合成了椭偏率为0.05的椭圆偏振阿秒脉冲链.     

奇偶q-变形相干态的高阶压缩效应

研究了奇偶q变形相干态中光场的高阶压缩效应.数值计算结果发现,奇偶q变形相干态中光场的高阶压缩效应与参数值q有关,当参数q取偏离1较大的值时,q变形奇偶相干态均可具有奇次方阶压缩效应却无偶次方阶压缩效应,这与通常奇偶相干态的压缩特性是不同的 关键词： 光场 q变形相干态 高阶压缩效应     

Analytical method for yrast line states in the interacting two—component Bose—Einstein condensate

The yrast spectrum for the harmonically trapped two-component Bose-Einstein condensate (BEC),omitting the difference between the two components,has been studied using an analytical method.The energy eigenstates and eigenvalues for L=0,1,2,3 are given,We illustrate that there are different eigenstate behaviours between the even L and odd L cases for the two-component BEC in two dimensions.Except for symmetric states,there are antisymmetric states for the permutation of the two components,which cannot reduce to those in a single condensate case when the value of L is odd.     

Phase Properties of New Even and Odd Nonlinear Coherent States

Using the Pegg–Barnett formalism of phase operator, we obtain phase probability distributions of new even and odd nonlinear coherent states. It is shown that the distributions for the states are rather different, and unlike the case of ordinary even and odd coherent states the Pegg–Barnett distribution clearly reflects the different character of quantum interference in the case of the new even and odd coherent states.     

Roy-型奇偶非线性相干态的位相概率分布

借助于数值计算方法，研究了Roy-型奇偶非线性相干态的位相概率分布特性.结果表明，它们的位相概率分布不同；与通常的奇偶相干态不同，在这种新的奇偶非线性相干态中，Pegg-Barnett位相概率分布能明显地反映出不同的量子干涉特性. 关键词： Roy-型奇偶非线性相干态 Pegg-Barnett位相算符公式 位相概率分布     

双参数形变谐振子奇偶相干态的高阶压缩特性

研究了双参数qs形变谐振子奇偶相干态中光场的高阶压缩特性,并用数值计算方法定量研究了形变参数q和s对这一特性的影响规律.结果表明,qs形变谐振子奇偶相干态均可能呈现奇次方阶压缩效应却无偶次方阶压缩效应,这与谐振子没有形变时的通常情况是不同的.当q和s取一定值时,在qs形变相干态中谐振子强度r²取值的一定范围内,这种反常特性的范围随着q偏离1越大s取值越小而变大.有关单参数q形变奇偶相干态的结论作为特例包含在本文的一般结论之中.     

Even and odd qs-coherent states and their photon-statistical properties

We construct explicitly even and odd qs-coherent states (qs-CSs), which are proved to form a representation of the quantum Heisenberg-Weyl algebra, and use the numerical method to study the influences of q and s deformations on photon-statistical properties of even and odd qs-CSs. It is shown that nonclassical properties of the even and odd qs-CSs are very different from those of the usual even and odd coherent states (CSs). It is found that the squeezing and antibunching effects appear for both even and odd qs-CSs in some range of the parameters q, s and r. The smaller the q (q < 1) and s, the larger the difference between the even and odd qs-CSs and the usual even and odd CSs.     

Theoretical study of the odd-even-order harmonic generation for asymmetric ions in non-Born-Oppenheimer approximation

We calculated the harmonic spectra generated from the asymmetric molecules of HD~+ and HeH~(2+). It is found that HD+produces only odd harmonics, while HeH~(2+)produces both odd and even harmonics. Further analysis reveals that for both HD~+ and HeH~(2+), the nuclear dipole acceleration can generate even harmonics, but it is three orders of magnitude lower than that of the electron. Hence, the electronic dipole acceleration dominates the harmonic generation. For HD~+,the electronic dipole acceleration only contributes to the generation of odd harmonics, but for HeH~(2+)it contributes to the generation of both odd and even harmonics. Besides, one concept of the broken degree of system-symmetry is proposed to explain the different odd-even property between the harmonic spectra of HD~+ and HeH~(2+).     

Investigation of the hyperfine structure of electronic levels in chromium atom

Measurements of the hyperfine structure (hfs) of electronic levels of the chromium atom were performed using two spectroscopic methods. For 7 energy levels (3 even parity and 4 odd parity) the magnetic dipole and electric quadrupole hyperfine interaction constants A and B were determined for the first time. In this case the method of laser induced fluorescence (LIF) on an atomic beam was used. The low lying metastable levels belonging to the term 3d⁴4s² a⁵D were remeasured by the method of laser-rf double resonance on an atomic beam (ABMR-LIRF). To improve the accuracy of hyperfine splittings measurements, the stability of the radio frequnecy (rf) generator was increased by the use of a frequency standard synchronized by a GPS signal. The values of the hfs intervals for these levels were determined with the accuracy of a few kHz. The improvement in accuracy enabled an estimation of the octupole-coupling constant C.