GW方法: 基本原理, 最新进展及其在d-和f-电子体系中的应用

基于格林函数的多体微扰理论提供了描述材料基态和激发态性质的一个严格理论框架. 格林函数依赖于交换关联自能, 后者满足一组复杂的被称为Hedin方程的积分微分方程. GW方法是由对自能算符根据屏蔽库仑作用做多体微扰理论展开到第一项得到, 是目前描述扩展体系准粒子电子激发性质最为准确的第一原理方法. 本文概述了GW方法的基本原理, 并对最新的理论方法进展在一个统一的框架下进行了评述. 最后, 通过对若干典型实例的分析展示了针对d/f-电子体系的GW方法的现状.     

Invariances of the Operator Properties of Frame Multipliers Under Perturbations of Frames and Symbol

Let Φ and Ψ be frames for ? and let M_m,Φ,Ψ be a frame multiplier with the symbol m. In this paper, we restrict our investigation to show that the operator properties of M_m,Φ,Ψ are stable under the perturbations of Φ, Ψ, and m. Also, special attention is devoted to the study of invertible frame multipliers.     

Time change equations for Lévy-type processes

We consider time change equations for Lévy-type processes. In this context we generalize the results of Böttcher et al. (2013) significantly. Namely, we are able to incorporate measurable instead of continuous multipliers. This opens a gate to find whole classes of symbols for which corresponding processes do exist. In order to establish our results we carefully analyze the connection between time change equations and classical initial value problems. This relationship allows us to transfer well-known results from this classical subject of pure mathematics into the theory of stochastic processes. On the way to prove our main theorem we establish generalizations of results on paths of Lévy-type processes.     

The Faraday effect revisited: Thermodynamic limit

This paper is the second in a series revisiting the (effect of) Faraday rotation. We formulate and prove the thermodynamic limit for the transverse electric conductivity of Bloch electrons, as well as for the Verdet constant. The main mathematical tool is a regularized magnetic and geometric perturbation theory combined with elliptic regularity and Agmon-Combes-Thomas uniform exponential decay estimates.     

Persistence of traveling wave solutions in a bio-reactor model with nonlocal delays

By considering the random migration of individuals and the period of consuming the captured nutrient, we first introduce the nonlocal delays into a bio-reactor model. The persistence of nontrivial traveling wave solutions then is proved by combining the geometric singular perturbation theory with the center manifold theorem. From the viewpoint of biology, our results indicate that the nonlocality induced by small average delays is harmless to the growth of the species.     

A gap in the essential spectrum of a cylindrical waveguide with a periodic aperturbation of the surface

It is proved that small periodic singular perturbation of a cylindrical waveguide surface may open a gap in the essential spectrum of the Dirichlet problem for the Laplace operator. If the perturbation period is long and the caverns in the cylinder are small, the gap certainly opens. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Confined Quantum Hard Spheres

We present computer simulation and theoretical results for a system of N Quantum Hard Spheres (QHS) particles of diameter σ and mass m at temperature T, confined between parallel hard walls separated by a distance Hσ, within the range 1≤H≤∞. Semiclassical Monte Carlo computer simulations were performed adapted to a confined space, considering effects in terms of the density of particles ρ*=N/V, where V is the accessible volume, the inverse length H−1 and the de Broglie’s thermal wavelength λB=h/2πmkT, where k and h are the Boltzmann’s and Planck’s constants, respectively. For the case of extreme and maximum confinement, 0.5<H−1<1 and H−1=1, respectively, analytical results can be given based on an extension for quantum systems of the Helmholtz free energies for the corresponding classical systems.     

Generalization of the Hylleraas functional for calculating BSSE-free intermolecular interactions: further considerations

The generalized Hylleraas functional necessary for calculating BSSE-free intermolecular interactions is presented for the case when exclusion of BSSE results in non-Hermitian operators and the intra- and intermolecular interactions are treated in different orders of perturbations.     

Canards in a Surface Oxidation Reaction

Summary. Canards are periodic orbits for which the trajectory follows both the attracting and repelling parts of a slow manifold. They are associated with a dramatic change in the amplitude and period of a periodic orbit within a very narrow interval of a control parameter. It is shown numerically that canards occur in an appropriate parameter range in two- and three-dimensional models of the platinum-catalyzed oxidation of carbon monoxide. By smoothly connecting associated stable and unstable manifolds in an asymptotic limit, we predict parameter values at which such canards exist. The relationship between the canards and saddle-loop bifurcations for these models is also demonstrated. Excellent agreement is found between the numerical and analytical results.     

The Devil's Invention: Asymptotic, Superasymptotic and Hyperasymptotic Series

Singular perturbation methods, such as the method of multiple scales and the method of matched asymptotic expansions, give series in a small parameter which are asymptotic but (usually) divergent. In this survey, we use a plethora of examples to illustrate the cause of the divergence, and explain how this knowledge can be exploited to generate a 'hyperasymptotic' approximation. This adds a second asymptotic expansion, with different scaling assumptions about the size of various terms in the problem, to achieve a minimum error much smaller than the best possible with the original asymptotic series. (This rescale-and-add process can be repeated further.) Weakly nonlocal solitary waves are used as an illustration.