Moments of a Single Entry of Circular Orthogonal Ensembles and Weingarten Calculus

Consider a symmetric unitary random matrix V = (v _ij )_{1 ≤ i, j ≤ N} from a circular orthogonal ensemble. In this paper, we study moments of a single entry v _ij . For a diagonal entry v _ii , we give the explicit values of the moments, and for an off-diagonal entry v _ij , we give leading and subleading terms in the asymptotic expansion with respect to a large matrix size N. Our technique is to apply the Weingarten calculus for a Haar-distributed unitary matrix.     

具有紧支撑正交非张量积小波的图像融合

提出了基于一种新的小波——具有紧支撑、正交性、伸缩矩阵为[^2 0 ^0 2]的非张量积小波的图像融合方法。首先根据非张量积小波理论,利用Daubechies构造的单变量滤波器构造出基于四通道的不可分的小波滤波器组,用此滤波器组对参加融合的图像进行分解,然后对低频部分采用取均值、高频部分采用系数绝对值取大的融合算法对分解子图进行融合,最后重构。并采用熵、交叉熵、互信息、均方根误差和峰值信噪比等指标对该方法进行了客观评价。对可见光图像与红外图像、远红外图像与近红外图像、遥感图像、多聚焦图像和其它多类图像的融合实验结果证明本方法有较好的融合效果,其融合性能与采用同样融合算法的张量积db2小波的融合方法的融合性能相当。     

New Terms for Compact Form of Electroweak Chiral Lagrangian

The compact form of the electroweak chiral Lagrangian is a reformulation of its original form and is expressed in terms of chiral rotated electroweak gauge fields, which is crucial for relating the information of underlying theories to the coefficients of the low-energy effective Lagrangian. However the compact form obtained in previous works is not complete. In this letter we add several new chiral invariant terms to it and discuss the contributions of these terms to the original electroweak chiral Lagrangian.     

Origin of the Nucleon Electromagnetic Form Factors Dipole Formula

Starting with the vector-meson-dominance parametrization of the electric and magnetic nucleon form factors, which are saturated just by the ground state vector-mesons , and , then aplying the strict Okubo-Zweig-Iizuka rule and the asymptotic behaviour of form factors as predicted by quark model of hadrons, the famous one-parameter dipole formula is derived. By its comparison with space-like data up to t=-5 GeV² the optimal value of the parameter under consideration is determined. Finaly, charge and magnetization distributions in proton and neutron are predicted.     

The Resultant on Compact Riemann Surfaces

We introduce a notion of the resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the Schottky double of the domain.     

用一个特殊的表示空间计算Sn群[n—1,1]表示的实正交形式

利用一个特殊的表示空间, 给出了S_n群表示[n—1, 1]的实正交形式的一般公式. 并举例说明了该技巧的一个应用.     

The Fisher-Hartwig Formula and Entanglement Entropy

Toeplitz matrices have applications to different problems of statistical mechanics. Recently it was used for calculation of entanglement entropy in spin chains. In the paper we review these recent developments. We use the Fisher-Hartwig formula, as well as the recent results concerning the asymptotics of the block Toeplitz determinants, to calculate entanglement entropy of large block of spins in the ground state of XY spin chain.     

在利用光碟测激光波长时观察到的一种现象及其解释

在利用光碟测激光波长的实验中,观察到同心激光圆环及环的内凸外陷,运用所学的光学知识对其成因进行分析、解释.     

The Green-Kubo Formula for the Spin-Fermion System

The spin-fermion model describes a two level quantum system (spin 1/2) coupled to finitely many free Fermi gas reservoirs which are in thermal equilibrium at inverse temperatures β _j . We consider non-equilibrium initial conditions where not all β _j are the same. It is known that, at small coupling, the combined system has a unique non-equilibrium steady state (NESS) characterized by strictly sitive entropy production. In this paper we study linear response in this NESS and prove the Green-Kubo formula and the Onsager reciprocity relations for heat fluxes generated by temperature differentials. Dedicated to Jean Michel Combes on the occasion of his sixtyfifth birthday     

The Legendre Structure of the Parisi Formula

We study easy quantum groups, a combinatorial class of orthogonal quantum groups introduced by Banica–Speicher in 2009. We show that there is a countable descending chain of easy quantum groups interpolating between Bichon’s free wreath product with the permutation group S_n and a semi-direct product of a permutation action of S_n on a free product. This reveals a series of new commutation relations interpolating between a free product construction and the tensor product. Furthermore, we prove a dichotomy result saying that every hyperoctahedral easy quantum group is either part of our new interpolating series of quantum groups or belongs to a class of semi-direct product quantum groups recently studied by the authors. This completes the classification of easy quantum groups. We also study combinatorial and operator algebraic aspects of the new interpolating series.     

The Munich Compact Light Source: initial performance measures

While large‐scale synchrotron sources provide a highly brilliant monochromatic X‐ray beam, these X‐ray sources are expensive in terms of installation and maintenance, and require large amounts of space due to the size of storage rings for GeV electrons. On the other hand, laboratory X‐ray tube sources can easily be implemented in laboratories or hospitals with comparatively little cost, but their performance features a lower brilliance and a polychromatic spectrum creates problems with beam hardening artifacts for imaging experiments. Over the last decade, compact synchrotron sources based on inverse Compton scattering have evolved as one of the most promising types of laboratory‐scale X‐ray sources: they provide a performance and brilliance that lie in between those of large‐scale synchrotron sources and X‐ray tube sources, with significantly reduced financial and spatial requirements. These sources produce X‐rays through the collision of relativistic electrons with infrared laser photons. In this study, an analysis of the performance, such as X‐ray flux, source size and spectra, of the first commercially sold compact light source, the Munich Compact Light Source, is presented.     

The Pion Electromagnetic Form Factor in a QCD-Inspired Model

We present detailed numerical results for the pion space-like electromagnetic form factor obtained within a recently proposed model of the pion electromagnetic current in a confining light-front QCD-inspired model. The model incorporates the vector meson dominance mechanism at the quark level, where the dressed photon with q⁺ > 0 decays in an interacting quark-antiquark pair, which absorbs the initial pion and produces the pion in the final state.     

The Weak Form Factor in Heavy to Light Mesons

The weak form factor in heavy to light mesons is discussed. We have analyzed two different approaches: Bauer-Stech-Wirbel approach and the perturbative QCD approach. It is pointed out that the nonperturbative contribution dominates the weak form factor in heavy to light mesons.     

Compact stars in Eddington inspired gravity

A new, Eddington inspired theory of gravity was recently proposed by Ba?ados and Ferreira. It is equivalent to general relativity in vacuum, but differs from it inside matter. This viable, one-parameter theory was shown to avoid cosmological singularities and turns out to lead to many other exciting new features that we report here. First, for a positive coupling parameter, the field equations have a dramatic impact on the collapse of dust, and do not lead to singularities. We further find that the theory supports stable, compact pressureless stars made of perfect fluid, which provide interesting models of self-gravitating dark matter. Finally, we show that the mere existence of relativistic stars imposes a strong, near optimal constraint on the coupling parameter, which can even be improved by observations of the moment of inertia of the double pulsar.     

对波动光学中条纹公式的思考

1 引言 在大学物理的部分教材中,关于波动光学的条纹公式表示为     

The Quest for a Microscopic Nuclear Mass Formula

After stressing how well the purely macroscopic 1935 mass formula of von Weizsäcker works, we discuss the general problem of deriving nuclear masses from basic nucleonic interactions. We then describe the very recent Skyrme-Hartree-Fock-BCS mass formula of Goriely et al., the first and only to be entirely microscopic. We conclude by stressing how much more work has to be done before reliable extrapolations can be made from the mass data out to the highly neutron-rich part of the nuclear chart where the r-process of nucleosynthesis takes place.