含Hopf项和Maxwell-Chern-Simons项O(3)非线性σ模型的分数自旋和分数统计性质

研究了（2＋1）维时空中含Hopf项和Maxwell-Chern-Simons(MCS)项的非线性σ模型的分数自旋性质.根据约束Hamilton系统的Faddeev-Senjanovic(FS)路径积分量子化方案,对该系统进行量子化，由量子Noether定理给出了量子守恒角动量，说明了在量子水平上该系统仍具有分数自旋的性质. 关键词： 约束Hamilton系统 分数自旋 O(3)σ模型     

A Class of Potentials for Which Exact Semiclassical Quantization Can Be Achieved

We consider a class of potentials for which the exact semiclassical quantization is achieved by a certain modification of the quantization condition. A list of potentials for which the new quantization condition is exact coincides with the list of potentials for which the spectrum is determined by the factorization method. We construct a one-parameter family of quantization conditions including the supersymmetric WKB condition as a special case. The new condition allows considering the interrelations between different modifications of the leading approximation and their validity ranges and also allows developing new approximate methods for calculating spectra.     

High sensitivity cw-cavity ringdown and Fourier transform absorption spectroscopies of CO2

The absorption spectrum of ¹³CO₂ has been recorded by cw-cavity ringdown spectroscopy with a new set up based on fibered DFB lasers. By using a series of 31 DFB lasers, the spectrum of carbon dioxide could be recorded in the 6130-6750 cm⁻¹ region with a typical sensitivity of 5 × 10⁻¹⁰ cm⁻¹. The spectrum has also been recorded between 4400 and 8500 cm⁻¹ with a Fourier transform spectrometer associated with a multi-pass cell (maximum path length of 105 m). The new observations obtained both by FTS and CRDS represent a significant extension of the available data. For instance, more than 4000 line positions were measured and assigned in the CRDS spectrum while only 232 line positions are listed in the HITRAN database. Altogether, the band by band analysis has led to the determination of the rovibrational parameters of 65, 7, and 24 bands for the ¹³C¹⁶O₂, ¹⁶O¹³C¹⁷O, and ¹⁶O¹³C¹⁸O isotopomers, respectively. As some observed line positions show significant deviations from the predictions of the effective Hamiltonian model, the new observed line positions were gathered with the data available in the literature to refine the set of effective Hamiltonian parameters of the ¹³C¹⁶O₂ isotopic species. The refined set of 96 effective Hamiltonian parameters reproduces more than 14 650 line positions of ¹³C¹⁶O₂ with an RMS=0.002 cm⁻¹. A detailed comparison with the line positions retrieved from Venus spectra and the line list provided by HITRAN is also presented and discussed.     

From the Kovalevskaya to the Lagrange case in rigid body motion

We study the motion of a family of symmetric tops in which the center of mass is located between the symmety plane and the symmetry axis of the inertia matrix. We analyze the transition from the Kovalevskaya to the Lagrange integrable cases using Poincaré sections and symmetry lines. The fate of periodic orbits as a function of the location of the top's center of mass is analyzed. The critical points of the Kovalevskaya constant are calculated in terms of the energy, of the angular momentum about the vertical, and of the Kovalevskaya constant itself.     

关于赋权图中重圈的一个范型定理

设G=(V, E; w)为赋权图,定义G中点v的权度d_G^w(v)为G中与v相关联的所有边的权和.该文证明了下述定理: 假设G为满足下列条件的2 -连通赋权图: (i) 对G中任何导出路xyz都有w(xy)=w(yz); (ii)对G中每一个与K_1,3或K_1,3+e同构的导出子图T, T中所有边的权都相等并且min{max{d_G^w(x), d^w_G(y)}:d(x,y)=2,x,y∈ V(T)}≥ c/2. 那么, G中存在哈密尔顿圈或者存在权和至少为 c 的圈. 该结论分别推广了Fan^[5], Bedrossian等人^[2]和Zhang等人^[7]的相关定理     

Coprime ordering of cyclic planar difference sets

Motivated by a question about uniform dessins d’enfants, it is conjectured that every cyclic planar difference set of prime power order m≠4 can be cyclically ordered such that the difference of every pair of neighbouring elements is coprime to the module v?m²+m+1. We prove that this is the case whenever the number ω(v) of different prime divisors of v is less than or equal to 3. To achieve this we consider a graph related to the difference set and show that it is Hamiltonian.     

Picone type identities and definiteness of quadratic functionals on time scales

In this paper we derive a new sufficient condition for the nonnegativity of time scale quadratic functionals associated to time scale symplectic systems. To establish this result, a new global Picone formula is derived. Another proof of a special case of the result is shown to be obtained via a Sturmian comparison technique. Furthermore, we derive several new Picone type identities which, in particular, do not impose a certain delta-differentiability assumption, and we survey known ones from the literature. The results in this paper complete our earlier work on the definiteness of a time scale quadratic functional in terms of its corresponding time scale symplectic system.     

A variationally stable quasi-relativistic method: low-order approximation to the normalized elimination of the small component using an effective potential

A simple and variationally stable quasi-relativistic method based on a modified low-order (LO) approximation to the normalized elimination of the small component (NESC) method is presented. The modification of the original LO-NESC scheme implies the use of an energy-independent factor in the relativistic correction to the potential energy. This factor cuts off the potential energy at short distances from the nucleus and in this way restores the variational stability of LO-NESC. The new method, dubbed LO-NESC-effective potential (EP) was tested in calculations on one-, two- and many-electron atoms. The LO-NESC-EP can be easily implemented into the existing nonrelativistic quantum-chemical program codes because its Hamiltonian matrix can be expressed entirely in terms of the integrals appearing in a nonrelativistic calculation. Received: 1 April 2002 / Accepted: 23 June 2002 / Published online: 30 August 2002     

2维SU(NC)格点规范理论中夸克真空凝聚

用改进的Wilson夸克格点哈密顿量和变分法研究2维SU(N_C)规范场中夸克真空凝聚〈ψψ〉与夸克质量m_q和Wilson参数r的依赖关系. 结果表明: 对于给定的r, 当N_C=2,3,4,5,6,7,时, 〈ψψ〉_suba/(gN_C^3/2)的值随m_q的增大而减小. 对于较大的N_C(如N_C>3), 当m_q很小时, 〈ψψ〉_suba(gN_C^3/2)对r的依赖性很小, 但随着m_q的增大, 〈ψψ〉_suba/(gN_C^3/2)对r的依赖性增大, 且〈ψψ〉_suba/(gN_C^3/2)的值随r的增大而增大; 特别是, 当m_q→0时, 本文的格点结果与Zhitnitsky的连续理论分析结果(在弱耦合相中)很好地一致, 这意味着本文在m_q≠0时所得到的结果是可靠的.     

A Discrete Spectral Problem and Related Hierarchy of Discrete Hamiltonian Lattice Equations

Staring from a discrete matrix spectral problem, a hierarchy of lattice soliton equations is presented though discrete zero curvature representation. The resulting lattice soliton equations possess non-local Lax pairs. The Hamiltonian structures are established for the resulting hierarchy by the discrete trace identity. Liouville integrability of resulting hierarchy is demonstrated.