Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

自辐射场下UN2分子的光谱研究

对铀原子和氮原子分别使用相对论有效原子实势和6-311+G(d)基组, 采用优选的密度泛函B3P86方法, 研究了铀本身产生自辐射场(-0.005–0.005 a.u.)作用下UN₂基态分子的能隙E_g和谐振频率ν. 结果表明: UN₂分子在自辐射场中反对称伸缩振动频率ν₃(σ_g)和对称伸缩振动频率σ₁(σ_g)与实验值1051.1 cm^-1和1008.3 cm^-1 基本符合; E_g随自辐射场场强的增大而趋于减少, 占据轨道的电子容易被激发至空轨道而形成激发态; UN₂分子在自辐射场中趋于不稳定, N₂, O₂等更容易扩散到表面内层而腐蚀铀表面, 加剧了铀在自辐射场中的腐蚀.     

Rovibrational and energetic analysis of the hydroxyethynyl anion (CCOH−)

For the first time, high-level structural and rovibrational data are provided for the hyroxyethynyl anion, CCOH^?. CCOH^? is a promising molecule for interstellar detection even though no new anions have been observed in the interstellar medium for the past half-decade. The large dipole moment of the corresponding neutral radical may be key for its creation as has been hypothesised and supported for other anions known to exist in various astronomical environments. Highly accurate quartic force fields are employed where previous benchmarks have produced spectroscopic constants and anharmonic vibrational frequencies within 20 MHz and 1 cm^?1, respectively, of experiment. This same approach is applied here for CCOH^? and its deuterated isotopologue with the goal of assisting laboratory experiments and/or astronomical observers in the potential detection of this anion.     

Topological order in the phase diagram for high-temperature superconductors with point defects

Applying a Lindemann like criterion obtained previously by Kierfeld et al. [J. Kierfeld, T. Nattermann, T. Hwa, Phys. Rev. B 55 (1997) 626], we estimate the magnetic field and temperature for a high-T_c superconductor, at which a topologically ordered vortex glass phase becomes unstable with respect to a disorder-induced formation of dislocations. The employed criterion is shown to be equivalent to a conventional phenomenological Lindemann criterion including the values for the numerical factors, i.e., for the Lindemann number. The positional correlation length of the topologically ordered vortex glass is calculated.     

Near-field effect in optics of small objects composed of dipole atoms

A self-consistent problem of interaction of two dipole atoms separated by an unrestricted distance with the field of a quasi-resonance light wave was solved on the assumption that the investigated atoms are Lorentz linear oscillators and the polarizing fields inside the system consist of the Coulomb and the retarded parts. The solution obtained was investigated for the case where the atoms have the same polarizability and the distance between them is much smaller than the length of the external light wave. Formulas for the electric fields inside a small object and outside it have been obtained. It is shown that inside a small two-atom object there can take place longitudinal and transverse optical vibrations accompanied by corresponding dispersion effects depending on the interatomic distance and the angle between the axis of the system and the direction of propagation of the external light wave. The field outside the small object in the wave zone is linearly polarized when the external wave has linear polarization. However, the direction of polarization of the corresponding waves is largely determined by their frequency. It is also shown that the amplitude of the field outside the small object in the wave zone depends greatly on the frequency of the external field and the interatomic distance. The effects observed are considered as a near-field effect in optics of small objects. This phenomena makes it possible to investigate the structure of small objects with the use of optical radiation. Ul'yanovsk Branch of the Institute of Radio Engineering and Electronics, Russian Academy of Sciences, 48 Goncharov Str., Ul'yanovsk, 432700, Russia; e-mail: gadomsky@quant.univ.simbirsk.su. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 6, pp. 765–770, November–December, 1999.     

The Renormalization Group and Its Finite Lattice Approximations

We investigate finite lattice approximations to the Wilson renormalization group in models of unconstrained spins. We discuss first the properties of the renormalization group transformation (RGT) that control the accuracy of this type of approximation and explain different methods and techniques to practically identify them. We also discuss how to determine the anomalous dimension of the field. We apply our considerations to a linear sigma model in two dimensions in the domain of attraction of the Ising fixed point using a Bell–Wilson RGT. We are able to identify optimal RGTs which allow accurate computations of quantities such as critical exponents, fixed-point couplings and eigenvectors with modest statistics. We finally discuss the advantages and limitations of this type of approach.     

Field of a Point Source Within Perfectly Conducting Parallel-Plates in a Homogeneous Biisotropic Medium

The spherical wave scattering response by a perfectly conducting open–ended waveguide in a biisotropic medium is obtained. Interestingly, the vector diffraction problem is reduced to the scattering of a single scalar field, this scalar field being the normal component of either a left–handed or a right–handed Beltrami field. Here, we explicitly consider the scattering of the left–handed field component, that of the other scalar field being analogously tractable. The solution is constructed with the aid of the Wiener–Hopf technique.     

Some Remarks on the Cohomology of Krichever–Novikov Algebras

We calculate the continuous cohomology of the Lie algebra of meromorphic vector fields on a compact Riemann surface from the cohomology of the holomorphic vector fields on the open Riemann surface pointed in the poles. This cohomology has been given by Kawazumi. Our result shows the Feigin–Novikov conjecture.     

On the Snider equation

We study the physical content of the Snider quantum transport equation and the origin of a puzzling feature of this equation, which implies contradictory values for the one-particle density operator. We discuss in detail why the two values are in fact not very different provided that the studied particles have sufficiently large wave packets and only a small interaction probability, a condition which puts a limit on the validity of the Snider equation. In order to improve its range of application, we propose a reinterpretation of the equation as a mixed equation relating the real one-particle distribution function (on the left-hand side of the equation) to the free distribution (on the right-hand side), which we have introduced in a recent contribution. In its original form, the Snider equation is valid only when used to generate Boltzmann-type equations where collisions are treated as point processes in space and time (no range, no duration); in this approximation, virial corrections are not included, so that the real and free distributions coincide. If the equation is used beyond this approximation to generate nonlocal and density corrections, we conclude that the results are not necessarily correct.     

1.444 mm Nd:YAG激光器的实验研究

 在理论分析的基础上设计了直腔结构1.444 mm Nd:YAG激光器，并进行了实验研究。获得了1.444 mm激光输出，当泵浦能量为55 J时，其最高静态激光输出310 mJ。电-光转换效率为0.56%，斜效率为0.81%。并实现了1.444 mm调Q输出，脉冲输出能量18 mJ，脉宽150 ns。