Critical Scaling Behaviors of Entanglement Spectra

We investigate the evolution of entanglement spectra under a global quantum quench from a short-range correlated state to the quantum critical point.Motivated by the conformal mapping,we find that the dynamical entanglement spectra demonstrate distinct finite-size scaling behaviors from the static case.As a prototypical example,we compute real-time dynamics of the eritanglement spectra of a one-dimensional transverse-field Ising chain.Numerical simulation confirms that the entanglement spectra scale with the subsystem size I as for the dynamical equilibrium state,much faster thanαIn^-1 l for the critical ground state.In particular,as a byproduct,the entanglement spectra at the long time limit faithfully gives universal tower structure of underlying Ising criticality,which shows the emergence of operator-state correspondence in the quantum dynamics.     

Combination Laws for Scaling Exponents and Relation to the Geometry of Renormalization Operators

Renormalization group has become a standard tool for describing universal properties of different routes to chaos—period-doubling in unimodal maps, quasiperiodic transitions in circle maps, dynamics on the boundaries of Siegel disks, destruction of invariant circles of area-preserving twist maps, and others. The universal scaling exponents for each route are related to the properties of the corresponding renormalization operators.     

Scaling Limits of Solutions of the Heat Equation for Singular Non-Gaussian Data

Limiting distributions of the parabolically rescaled solutions of the heat equation with singular non-Gaussian initial data with long-range dependence are described in terms of their multiple stochastic integral representations.     

Power Law Subordinacy and Singular Spectra.¶II. Line Operators

We study Hausdorff-dimensional spectral properties of certain “whole-line” quasiperiodic discrete Schr?dinger operators by using the extension of the Gilbert–Pearson subordinacy theory that we previously developed in [19]. Received: 21 October 1999 / Accepted: 21 December 1999     

Universality of a Double Scaling Limit near Singular Edge Points in Random Matrix Models

We consider unitary random matrix ensembles on the space of Hermitian n × n matrices M, where the confining potential V _s,t is such that the limiting mean density of eigenvalues (as n→∞ and s,t→ 0) vanishes like a power 5/2 at a (singular) endpoint of its support. The main purpose of this paper is to prove universality of the eigenvalue correlation kernel in a double scaling limit. The limiting kernel is built out of functions associated with a special solution of the P _I ² equation, which is a fourth order analogue of the Painlevé I equation. In order to prove our result, we use the well-known connection between the eigenvalue correlation kernel and the Riemann-Hilbert (RH) problem for orthogonal polynomials, together with the Deift/Zhou steepest descent method to analyze the RH problem asymptotically. The key step in the asymptotic analysis will be the construction of a parametrix near the singular endpoint, for which we use the model RH problem for the special solution of the P _I ² equation. In addition, the RH method allows us to determine the asymptotics (in a double scaling limit) of the recurrence coefficients of the orthogonal polynomials with respect to the varying weights on . The special solution of the P _I ² equation pops up in the n ^−2/7-term of the asymptotics.     

Bohr-Mottelson转动谱公式参数之间的新关系式

在利用Harris两参数公式研究Bohr-Mottelson转动谱公式参数之间的关系的基础上,改用Harris三参数公式,并由此提出了Bohr-Mottelson转动谱公式参数之间的新关系式,进而用I(I+1)四参数展开式计算了A～60,80,130,140,150,190区超形变偶偶核的基带和锕系和稀土区正常形变核基带,讨论了参数之间的关系,发现新关系式与实验较好地符合.     

On Field Theory Methods in Singular Perturbation Theory

Singular and supersingular finite rank perturbations of self-adjoint operators are studied using methods from renormalization theory for quantum fields. It is shown that the ideas from dimensional and Pauli–Villars regulatizations can be applied to determine uniquely certain finite rank supersingular perturbations. Approach is based on the regularization of homogeneous singular quadratic forms.     

应用遗传算法在FTIR图谱库中进行谱图检索

本文应用遗传算法在PC机上，WINDOWS操作系统上进行纯谱图的检索工作，使用了较简单的目标函数和选择函数，采用了自适应应变异技术，为了避免局优化的产生，在计算过程中的特定条件下引入新的染色体，并利用最佳个体的适应度用做收敛的判据，研究结果表明，即使是对较低浓度，峰形不尖锐的有机化合物来说，也可得到较好的检索结果。     

Fourier Transform Infrared and Raman Spectra of Metal Halide Complexes of 3,5-Lutedine in Relation to Their Structures

Abstract

Fourier transform infrared (4000-200 cm¹) and Raman (3500-50 cm^?1) spectra are reported for metal(II) halide 3,5-lutidine (3,5-dimethylpyridine) complexes of the following stoichiometries: M(3,5L)₄X₂ M=Co or Ni, X=C1 or Br; M=Mn or Cu, X=Br; M=Cd, X=I; M(3,5L)₃X₂ M=Fe, X=C1; M=Cu, X=Br; Hg(3,5L) X₂ X=C1 or Br.

Vibrational assignments are given for all the observed bands. Some structure- spectra correlations are found. For a given series of isomorphous complexes the sum of the difference between the liquid and ligand values of the vibrational modes of 3,5-lutidine is found to increase in the order of the second ionization potentials of the metals. The frequency shifts are also found to depend on the halogen.     

Solvatochromic Effect in the Optical Spectra of Calcofluor and its Relation to Fluorescent Staining of Yeast Cell Walls

Fluorescence spectral properties of calcofluor (a popular stain used to visualize cell walls of bacteria, yeast and fungi) has been studied. The analysis of calcofluor fluorescence emission spectra measured in a wide range of solvents (including media containing chitin), and in yeast cell suspensions has revealed that the solvatochromic properties of calcofluor ensue essentially from the by solvent-solute hydrogen bonding, or from the hydrogen bonding to cell wall polysaccharides with an eventual contribution of calcofluor aggregation at the cell surface. Preliminary data suggest that calcofluor emission spectra can be employed as a practical marker of variations in the quality of yeast cell wall.     

喀斯特典型地物混合光谱与复合覆盖度关系研究

喀斯特石漠化是我国西南喀斯特地区面临的主要生态环境问题之一。岩石裸露率以及植被覆盖度是石漠化主要的地面表现特征,也是评价石漠化的关键指标。由于喀斯特地区复杂的地貌情况,使得评价石漠化需要多种地物类型覆盖度信息。该文在实测光谱支持下,构建了系列光谱指数,初步分析了喀斯特地区典型地物混合光谱与复合覆盖度的关系。结果表明,光谱指数与覆盖度的相关性远远高于光谱反射率与覆盖度的相关性。植被指数和绿色植物(photosynthetic vegetation, PV)覆盖度有着很好的线性关系;该文构造的光谱指数和干枯植被覆盖度(non-photosynthetic vegetation, NPV)、土壤覆盖度有着较好的相关性,可决系数分别达0.70和0.73,显示了有估算NPV和土壤覆盖度的潜在能力。而光谱指数和裸岩率的相关系数稍低,最高达0.55,可以提供一定的裸岩率信息。所构建的4种指数形式中,表征光谱吸收特征深度的指数形式和NPV、土壤覆盖度以及裸岩率均拥有最高的相关性。这为高光谱遥感在喀斯特石漠化信息提取的应用进行了初步的探索。     

On Dilation Symmetries Arising from Scaling Limits

Quantum field theories, at short scales, can be approximated by a scaling limit theory. In this approximation, an additional symmetry is gained, namely dilation covariance. To understand the structure of this dilation symmetry, we investigate it in a nonperturbative, model independent context. To that end, it turns out to be necessary to consider non-pure vacuum states in the limit. These can be decomposed into an integral of pure states; we investigate how the symmetries and observables of the theory behave under this decomposition. In particular, we consider several natural conditions of increasing strength that yield restrictions on the decomposed dilation symmetry.     

On Modulational Instability of Turbulent Spectra

The character of the modulational instability of a Langmuir wave packet is usually assumed to be similar to that of the instability of a monochromatic pump Langmuir wave if the width of the packet is small when compared to the rate of the instability. This assumption has been confirmed only for the case corresponding to the “hydrodynamical” development of the modulational instability, i.e., for the case when the phase velocity of the modulational perturbations exceeds the ion thermal velocity. Here we consider the opposite case (when the phase velocity of the modulational perturbations is less than the ion thermal velocity) which corresponds to the “static” development of the instability. We demonstrate that the above assumption is valid for the situation considered.     

On the Ultra-Violet Spectra of GeCl

Bands of GeCl in the region 335-370 mm have been attributed to the ⁴σ X² transition on the basis of high resolution studies of the bands at 339.2 and 350.1 mm. The rotational analysis of the (0, 0) band of the ⁴σ^‐ _3/2-X²σ_3/2 subsystem has been carried out.     

On the Spectra of Carbon Nano-Structures

An explicit derivation of dispersion relations and spectra for periodic Schrödinger operators on carbon nano-structures (including graphene and all types of single-wall nano-tubes) is provided.     

Scaling with respect to disorder in time-to-failure

We revisit a simple dynamical model of rupture in random media with long-range elasticity to test whether rupture can be seen as a first-order or a critical transition. We find a clear scaling of the macroscopic modulus as a function of time-to-rupture and of the amplitude of the disorder, which allows us to collapse neatly the numerical simulations over more than five decades in time and more than one decade in disorder amplitude onto a single master curve. We thus conclude that, at least in this model, dynamical rupture in systems with long-range elasticity is a genuine critical phenomenon occurring as soon as the disorder is non-vanishing. Received: 11 July 1997 / Revised: 6 November 1997 / Accepted: 10 November 1997