Sharp Regularity Results for Coulombic Many-Electron Wave Functions

We show that electronic wave functions of atoms and molecules have a representation =, where is an explicit universal factor, locally Lipschitz, and independent of the eigenvalue and the solution itself, and has second derivatives which are locally in L. This representation turns out to be optimal as can already be demonstrated with the help of hydrogenic wave functions. The proofs of these results are, in an essential way, based on a new elliptic regularity result which is of independent interest. Some identities that can be interpreted as cusp conditions for second order derivatives of are derived.© 2004 by the authors. This article may be reproduced in its entirety for non-commercial purposes.On leave from Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, 9220 Aalborg East, DenmarkAcknowledgement All four authors thank the organizers of the program Partial Differential Equations and Spectral Theory for invitations to the Mittag-Leffler Institute in 2002 where part of the work was done. Furthermore, parts of this work have been carried out at various institutions, whose hospitality is gratefully acknowledged: Aalborg University (SF, MHO, THO), The Erwin Schrödinger Institute (TØS), Université Paris-Sud (TØS), and the IHÉS (TØS). Financial support from the Danish Natural Science Research Council, European Science Foundation Programme Spectral Theory and Partial Differential Equations (SPECT), and EU IHP network Postdoctoral Training Program in Mathematical Analysis of Large Quantum Systems, contract no. HPRN-CT-2002-00277 is gratefully acknowledged. SF has been supported by a Marie Curie Fellowship of the European Community Programme Improving the Human Research Potential and the Socio-Economic Knowledge Base under contract number HPMF-CT-2002-01822, and by a grant from the Carlsberg Foundation. Finally, SF and TØS wish to thank I. Herbst for useful discussions at the Mittag-Leffler Institute.     

精确简洁解析的原子组态相互作用波函数的计算

使用广义Laguerre类型轨道,在组态相互作用框架内,发展并完善了一套精确、简洁、解析的原子(离子)波函数从头计算的Fortran程序,计算原子中电子的结构.通过对指定能态能量求其最小值实现对波函数节点位置和空间范围的优化,从而求出最优波函数.作为例子,计算了⁵G态下的Ti的能量最小值和优化波函数.     

Spectral Theorem of Many-Body Green＇s Functions When Complex Eigenvalues Appear

In this paper, an extended spectral theorem is given, which enables one to calculate the correlation functions when complex eigenvalues appear. To do so, a Fourier transformation with a complex argument is utilized. We treat all the Matsbara frequencies, including Fermionic and Bosonic frequencies, on an equal footing. It is pointed out that when complex eigenvalues appear, the dissipation of a system cannot simply be ascribed to the pure imaginary part of the Green function. Therefore, the use of the name fluctuation-dissipation theorem should be careful.     

Analytic Results for Gaussian Wave Packets in Four Model Systems: II. Autocorrelation Functions

The autocorrelation function, A(t), measures the overlap (in Hilbert space) of a time-dependent quantum mechanical wave function, (x, t), with its initial value, (x, 0). It finds extensive use in the theoretical analysis and experimental measurement of such phenomena as quantum wave packet revivals. We evaluate explicit expressions for the autocorrelation function for time-dependent Gaussian solutions of the Schrödinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a particle in a harmonic oscillator potential, and a system corresponding to an unstable equilibrium (the so-called inverted oscillator.) We emphasize the importance of momentum-space methods where such calculations are often more straightforwardly realized, as well as stressing their role in providing complementary information to results obtained using position-space wavefunctions.     

Slippery Wave Functions

Superfluids and superconductors show a very surprising behavior at low temperatures. As their temperature is reduced, materials of both kinds can abruptly fall into a state in which they will support a persistent, essentially immortal, flow of particles. Unlike anything in classical physics, these flows produce neither friction nor resistance. A major accomplishment of Twentieth Century physics was the development of an understanding of this very surprising behavior via the construction of partially microscopic and partially macroscopic quantum theories of superfluid helium and superconducting metals. Such theories come in two parts: a theory of the motion of particle-like excitations, called quasiparticles, and of the persistent flows itself via a huge coherent excitation, called a condensate. Two people, above all others, were responsible for the construction of the quasiparticle side of the theories of these very special low-temperature behaviors: Lev Landau and John Bardeen. Curiously enough they both partially ignored and partially downplayed the importance of the condensate. In both cases, this neglect of the actual superfluid or superconducting flow interfered with their ability to understand the implications of the theory they had created. They then had difficulty assessing the important advances that occurred immediately after their own great work. Some speculations are offered about the source of this unevenness in the judgments of these two leading scientists.     

Analytic Functions and Integrable Hierarchies–Characterization of Tau Functions

We prove the dispersionless Hirota equations for the dispersionless Toda, dispersionless coupled modified KP and dispersionless KP hierarchies using an idea from classical complex analysis. We also prove that the Hirota equations characterize the tau functions for each of these hierarchies. As a result, we establish the links between the hierarchies.     

One-Particle Distribution Functions and Thermodynamics of Crystals with Many-Body Forces. III. Perturbation Theory

The theory of crystalline state described in preceding papers is considered as a zeroth-order approximation. Statistical perturbation theory is used for the purpose of improving this approximation. The second-order corrections to the Helmholtz free energy and thermodynamic properties of strongly anharmonic crystals are derived. The properties of solid Ar, Kr, and Xe are calculated using various pair-potential functions in conjunction with the AXILROD -TELLER -MUTO three-body potential. The first quantum corrections are taken into account in the quasi-classical approximation. The result of computations are compared with the experimental data.     

One-Particle Distribution Functions and Thermodynamics of Crystals with Many-Body Forces. II. Quantum Corrections

Crystalline state is described by non-symmetrical distribution functions in a self-consistent field approximation. The first quantum corrections to the HELMHOLTZ free energy and thermodynamic properties of strongly anharmonic crystals with many-body interactions are calculated in the quasi-classical case. The properties of crystalline inert gases are computed using the pair potentials of LENNARD -JONES , of BARKER and POMPE , of BARKER and BOBETIC , and of BARKER , FISHER and WATTS , together with the AXILROD -TELLER -MUTO three-body forces. The results are compared with both the experimental data and Monte Carlo calculations.     

氢同位素双原子分子的解析势能函数

研究从重水中分离出T2 .首先 ,根据光谱常数导出氢同位素双原子分子ExtendedRydberg的分析函数 ,基于同位素效应计算OT(X2 Пi)的光谱常数 ,有助导出三原子分子 ,如DTO的解析势能函数 .将这些ExtendedRyd berg解析势能函数用于氘交换分离氚的热力学与分子反应动力学研究 .此外 ,由同位素位移极值得到当振动量子数vmax≈ 11.5 ,振动能级间隔△Ev(H2 )≈△Ev(T2 ) ,若v △Ev(T2 )和v>vmax时 ,△Ev(H2 ) <△Ev(T2 ) .因而 ,温度较低时 ,平衡移向T2 ;温度较高时 ,平衡移向H2 .与文献结果相似 ,而导出方法不同     

整数自旋协变波函数

对高自旋态的Bargmann-Wigner方程的解进行了改造,给出了一套系统地构造高自旋态(整数自旋)协变波函数的新方法.利用这种方法,分别构造了任意整数自旋粒子的协变波函数.     

Ground State Eigenfunction of Spheroidal Wave Functions

We study the spin-weighted spheroidal wave functions in the case of s = m = 0. Their eigenvalue problem is investigated by the perturbation method in supersymmetric quantum mechanics. In the first three terms of parameter a = a^2 w^2, the ground eigenvalue and eigenfunction are obtained. The obtained ground eigenfunction is elegantly in dosed forms. These results are new and very useful for the application of the spheroidal wave functions.     

Multi-Time Wave Functions Versus Multiple Timelike Dimensions

Multi-time wave functions are wave functions for multi-particle quantum systems that involve several time variables (one per particle). In this paper we contrast them with solutions of wave equations on a space–time with multiple timelike dimensions, i.e., on a pseudo-Riemannian manifold whose metric has signature such as \({+}{+}{-}{-}\) or \({+}{+}{-}{-}{-}{-}{-}{-}\), instead of \({+}{-}{-}{-}\). Despite the superficial similarity, the two behave very differently: whereas wave equations in multiple timelike dimensions are typically mathematically ill-posed and presumably unphysical, relevant Schrödinger equations for multi-time wave functions possess for every initial datum a unique solution on the spacelike configurations and form a natural covariant representation of quantum states.     

Multi-Band Gutzwiller Wave Functions for Itinerant Ferromagnetism

Multi-band Gutzwiller-correlated wave functions reconcile the contrasting concepts of itinerant band electrons versus electrons localized in partially filled atomic shells. The approximate evaluation of these variational ground states becomes exact in the limit of large coordination number. The result allows the identification of quasi-particle band structures for correlated electron systems. As a first application, we summarize a study of itinerant ferromagnetism in a two-band model, thereby elucidating the co-operation of the Coulomb repulsion and the Hund's-rule exchange. Then, we present results of calculations for ferromagnetic nickel, using a realistic 18 spin-orbital basis of 4s, 4p and 3d valence electrons. Good agreement with the experimental ground-state properties of nickel is obtained. In particular, the quasi-particle energy bands agree much better with the photo-emission and Fermi surface data than the band structure obtained from spin-density functional theory. Finally, we present results for the variational spinwave dispersion for our two-band model.     

自由基ClO和ClO_2的解析势能函数

运用密度泛函(B3LYP)方法,分别选用6-311+G(3df)和aug-cc-pV6Z基组,对ClO自由基和O_2分子进行了计算,并拟合了其M-S势能函数.采用密度泛函方法(B3LYP)在6-311G(3df)基组下对ClO_2自由基的结构进行了优化计算,得到:ClO_2自由基的稳态结构为C_(2v)构型,电子态为~2B_1、平衡核间距R_(clo)=0.14785 nm、键角/OClO=117.3107°、离解能D_e=2.7552 eV、基态振动频率ν_1(a_1)=451.3423 cm~(-1),v_2(a_1)=970.8289 cm~(-1),ν_3(b_2)=1123.5023 cm~(-1).采用多体项展式理论推导了ClO_2自由基的基态解析势能函数,其等值势能图准确再现了该分子的结构特征及其势阱深度与位置.分析讨论势能面的静态特征时得到:在ClO+O→ClO_2反应中存在两个对称的鞍点,分别位于(0.248 nm,0.152 nm)和(0.152 nm,0.248 nm)处,活化能为5.614 kcal/mol     

Covariance Constraints for Light Front Wave Functions

Light front wave functions (LFWFs) are often utilized to model parton distributions and form factors where their transverse and longitudinal momenta are tied to each other in some manner that is often guided by convenience. On the other hand, the cross talk of transverse and longitudinal momenta is governed by Poincaré symmetry and thus popular LFWF models are often not usable to model more intricate quantities such as generalized parton distributions. In this contribution a closer look to this issue is given and it is shown how to overcome the issue for two-body LFWFs.     

整数自旋粒子的方程和波函数

从高自旋态的Bargmann-Wigner方程出发,建立了整数自旋粒子的运动方程,通过求解方程得到了一套整数自旋粒子波函数,并建立了等效Largrange形式.     

六参数高精度双原子分子解析势能函数

提出一种构造解析势能函数的新方法,得到一种六参数解析势能函数,该势能函数适用于多种基本类型的双原子分子.用同核中性基态双原子分子Li₂-X¹Σ_g⁺、Na₂-X¹Σ_g⁺,异核带电基态双原子分子离子(BC)^--X³∏,异核中性激发态双原子分子PbS-A¹Σ⁺、BaO-A¹Σ,异核带电激发态双原子分子离子(CS)⁺-A²∏,同核中性激发态双原子分子K₂-B¹∏_u,同核带电激发态双原子分子离子N₂⁺-B²Σ_u⁺等共36个算例对该势能函数进行验证,计算结果与RKR(Rydberg-Klein-Rees)数据或振动能谱实验数据高精度符合.同时发现,在分子振动能谱计算精度方面,该势能函数总体上优于Murrell-Sorbie势能函数.