Intriguing accuracies of the exponential wave function expansions exploiting finite two-body correlation operators in calculations for many-electron systems

2006 ◽  
Vol 768 (1-3) ◽  
pp. 3-16 ◽  
Author(s):  
Peng-Dong Fan ◽  
Piotr Piecuch
Keyword(s):  
Wave Function ◽  
Electron Systems ◽  
Body Correlation

On the Role of the Pauli Antisymmetry Principle in Pericyclic Reactions

1997 ◽  
Vol 52 (10) ◽  
pp. 727-738
Author(s):  
Michael C. Böhm ◽  
Johannes Schütt
Keyword(s):  
Wave Function ◽  
Ground State ◽  
Statistical Difference ◽  
Pericyclic Reactions ◽  
Electron Systems ◽  
Electronic Wave Function ◽  
Quantum Statistical ◽  
Definition Of ◽  
Electronic Ground

Abstract In the present work we discuss the role of the Pauli antisymmetry principle (PAP) in synchronous pericyclic reactions. These reactions are allowed in the electronic ground state whenever the PAP does not act as a quantum constraint in the transition state. The possible suppression of the influence of the PAP is a peculiarity of π electron systems. The PAP is a hidden (= deactivated) variable in the π electron subspace of polyenes and (4n + 2) annulenes (n = 0, 1, 2,...). In 4n annulenes (n = 1, 2, 3,...) it leads to minority signs in the kinetic hopping matrix of the π electronic wave function and thus to an energetic destabilization. The quantum statistical difference between the above families of π systems renders possible a microscopical definition of the quantities “aromaticity” and “antiaromaticity”. The sign behaviour of the kinetic hopping elements is used in the discussion of pericyclic reactions. The present quantum statistical description of these reactions is related to the Dewar-Zimmermann and Woodward-Hoffmann rules.

scholarly journals Magnetic-field reentrant wave function hybridization in stacked one-dimensional electron systems

2010 ◽  
Author(s):  
S. S. Buchholz ◽  
P. S. Zapp ◽  
S. F. Fischer ◽  
U. Kunze ◽  
D. Schuh ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Electron Systems ◽  
Dimensional Electron ◽  
One Dimensional

scholarly journals Four-body correlation embedded in antisymmetrized geminal power wave function

2016 ◽  
Vol 145 (24) ◽  
pp. 244110 ◽  
Author(s):  
Airi Kawasaki ◽  
Osamu Sugino
Keyword(s):  
Wave Function ◽  
Power Wave ◽  
Body Correlation

Die Lösung der Schrödinger-Gleichung als eindimensionales Problem. IV. Erfassung von Korrelation am Beispiel der Zweielektronensysteme He und H2

1996 ◽  
Vol 51 (10-11) ◽  
pp. 1113-1122
Author(s):  
M. Pernpointner ◽  
H. Preuß
Keyword(s):  
Wave Function ◽  
Excited States ◽  
Integral Kernel ◽  
Electron Systems ◽  
Spin Part ◽  
Discretization Methods ◽  
Symmetry Properties ◽  
Spatial Part

Abstract After calculating ground and excited states of one-electron systems with improved discretization methods in Part III of this work it is shown that also correlation contributions can be yielded by this formalism. The more powerful discretization methods are applied to the two-electron systems He and H2. For multi-electron systems the symmetry properties of the wave function become important but in the case of two-electron systems an antisymmetric spin part can be separated and the integral kernel containing the spatial part of the wavefunction has therefore to be symmetric.

scholarly journals Crossover Induced Electron Pairing and Superconductivity by Kinetic Renormalization in Correlated Electron Systems

2018 ◽  
Vol 3 (3) ◽  
pp. 26 ◽  
Author(s):  
Takashi Yanagisawa ◽  
Mitake Miyazaki ◽  
Kunihiko Yamaji
Keyword(s):  
Wave Function ◽  
High Temperature ◽  
High Temperature Superconductivity ◽  
Electron System ◽  
Strongly Correlated ◽  
Electron Systems ◽  
Strongly Correlated Electron ◽  
Correlated Electron Systems ◽  
Correlated Electron ◽  
The Many

We investigate the ground state of strongly correlated electron systems based on an optimization variational Monte Carlo method to clarify the mechanism of high-temperature superconductivity. The wave function is optimized by introducing variational parameters in an exponential-type wave function beyond the Gutzwiller function. The many-body effect plays an important role as an origin of superconductivity in a correlated electron system. There is a crossover between weakly correlated region and strongly correlated region, where two regions are characterized by the strength of the on-site Coulomb interaction U. We insist that high-temperature superconductivity occurs in the strongly correlated region.

scholarly journals The collision of electrons with simple atomic systems and electron exchange

1931 ◽  
Vol 132 (820) ◽  
pp. 605-630 ◽  
Keyword(s):  
Wave Function ◽  
Essential Feature ◽  
Fundamental Importance ◽  
Electron Systems ◽  
Many Body ◽  
Atomic Systems ◽  
Symmetry Properties ◽  
Chemical Combination ◽  
New Statistics ◽  
Α Particles

One of the outstanding differences between classical theory and quantum mechanics is the importance which the latter attaches to the identity of particles. Although perfectly well realised before the introduction of modern quantum theory, the fact that two electrons are experimentally indistinguish­able did not introduce any novel features into the dynamics of many electron systems on Bohr’s theory. However, Heisenberg showed that these identity relations are of fundamental importance in many body problems, and was able to explain the formerly very puzzling characteristic of the spectrum of neutral helium, its division into two non-combining term systems. Owing to the identity of the particles, the wave function representing such a system must have certain symmetry properties; for the particles known in Nature this symmetry characteristic is that the function be either symmetric or anti-symmetric in the co-ordinates of the particles. For particles with a spin such as the electron and proton, only antisymmetry is allowed (Pauli’s principle), while for α-particles the wave function must be symmetrical. Since Heisenberg’s explanation of the helium spectrum the theory of anti-symmetric electron wave functions has been extended to describe the general features of the spectra of all atoms, while it appears from the work of Heitler and London that the theory is of fundamental importance in the explanation of chemical combination between atoms. Again, in furnishing a new statistics it is an essential feature of the theory of metals. As the effect of the identity relations depends on the fact that exchanging the electrons does not alter the system in any way, these effects are known as exchange phenomena.

scholarly journals Direct-exchange duality of the Coulomb interaction and collective excitations in graphene in a magnetic field

2017 ◽  
Vol 31 (26) ◽  
pp. 1750176 ◽  
Author(s):  
K. Shizuya
Keyword(s):  
Magnetic Field ◽  
Coulomb Interaction ◽  
Single Mode ◽  
Collective Excitations ◽  
Electron Systems ◽  
Many Body ◽  
Direct Exchange ◽  
Single Mode Approximation ◽  
New States ◽  
Body Correlation

In a magnetic field two-dimensional (2D) electron systems host, with quenched kinetic energy, a variety of many-body correlation phenomena, such as interaction-driven new states and associated collective excitations over them. In a magnetic field, the two-body operators pertinent to the 2D Coulomb interaction obey a crossing relation, with which the Coulomb interaction is also cast into the form of manifest exchange interaction. It is shown that active use of this direct/exchange duality of the interaction allows one to develop, within the framework of the single-mode approximation, a new efficient algorithm for handling a wide class of collective excitations. The utility of our algorithm is demonstrated by studying some examples of inter- and intra-Landau-level collective excitations in graphene and in conventional electron systems.

Analytic integration of contrast transfer functions

1988 ◽  
Vol 46 ◽  
pp. 822-823
Author(s):  
Peter Rez
Keyword(s):  
Wave Function ◽  
Transfer Function ◽  
Transfer Functions ◽  
Spherical Aberration ◽  
Continuous Distribution ◽  
Objective Lens ◽  
Direction Parallel ◽  
Scattering Angle ◽  
Analytic Integration ◽  
Image Position

In high resolution microscopy the image amplitude is given by the convolution of the specimen exit surface wave function and the microscope objective lens transfer function. This is usually done by multiplying the wave function and the transfer function in reciprocal space and integrating over the effective aperture. For very thin specimens the scattering can be represented by a weak phase object and the amplitude observed in the image plane is1where fe (Θ) is the electron scattering factor, r is a postition variable, Θ a scattering angle and x(Θ) the lens transfer function. x(Θ) is given by2where Cs is the objective lens spherical aberration coefficient, the wavelength, and f the defocus.We shall consider one dimensional scattering that might arise from a cross sectional specimen containing disordered planes of a heavy element stacked in a regular sequence among planes of lighter elements. In a direction parallel to the disordered planes there will be a continuous distribution of scattering angle.

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