Improving the convergence of the many‐body perturbation expansion through a convenient summation of exclusion principle violating diagrams

1987 ◽  
Vol 87 (10) ◽  
pp. 5937-5948 ◽  
Author(s):  
Marie‐Bernadette Lepetit ◽  
Jean‐Paul Malrieu
Keyword(s):  
Perturbation Expansion ◽  
Exclusion Principle ◽  
Many Body ◽  
The Many

Wave-number dependence of the static screening function of an interacting electron gas. I. Lowest-order Hartree–Fock corrections

1970 ◽  
Vol 48 (2) ◽  
pp. 155-165 ◽  
Author(s):  
D. J. W. Geldart ◽  
Roger Taylor
Keyword(s):  
Coulomb Interaction ◽  
Ground State ◽  
Electron Gas ◽  
Perturbation Expansion ◽  
Wave Number ◽  
Many Body ◽  
Hartree Fock ◽  
The Many ◽  
Static Screening ◽  
Zero Frequency

The lowest-order Hartree–Fock contributions to the zero frequency screening function are examined for an interacting electron gas in its ground state. Computational methods are developed to treat singularities associated with the bare coulomb interaction and vanishing energy denominators of the many-body perturbation expansion. Numerical results are given. The wave-number dependence in the intermediate (k ~ kF) range differs considerably from that of previous estimates.

scholarly journals A GENERALIZATION OF QUANTUM STATISTICS

1996 ◽  
Vol 11 (10) ◽  
pp. 795-803 ◽  
Author(s):  
WEI CHEN ◽  
Y. JACK NG ◽  
HENDRIK VAN DAM
Keyword(s):  
Hilbert Space ◽  
Single Species ◽  
Exclusion Principle ◽  
Single Quantum ◽  
Many Body ◽  
Arbitrary Dimensions ◽  
Multiple Species ◽  
The Many ◽  
New Statistics ◽  
Algebra Of Operators

We examine a new fractional statistics for arbitrary dimensions, based on an extension of Pauli’s exclusion principle, to allow for finite multi-occupancies of a single quantum state. By explicitly constructing the many-body Hilbert space, we obtain a new algebra of operators and a new thermodynamics. The new statistics is different from fractional exclusion statistics. For a single species of particles it is equivalent to parafermi statistics; but their algebras are very different for the case of multiple species.

Accurate Kohn-Sham potential for the 1s2s 3S state of the helium atom: Tests of the locality and the ionization-potential theorems

2005 ◽  
Vol 83 (1) ◽  
pp. 85-90 ◽  
Author(s):  
Sten Salomonson ◽  
Fredrik Moller ◽  
Ingvar Lindgren
Keyword(s):  
Ionization Potential ◽  
Helium Atom ◽  
Ionization Energy ◽  
Pair Correlation ◽  
Energy Eigenvalue ◽  
Exclusion Principle ◽  
Many Body ◽  
Hartree Fock ◽  
Koopmans Theorem ◽  
The Many

The local Kohn–Sham potential is constructed for the 1s2s 3S state of the helium atom, using the procedure proposed by van Leeuwen and Baerends (Phys. Rev. A, 49, 2138 (1994)) and the many-body electron density, obtained from the pair-correlation program of Salomonson and Öster (Phys. Rev. A, 40, 5559 (1989)). The Kohn–Sham orbitals reproduce the many-body density very accurately, demonstrating the validity of the Kohn–Sham model and the locality theorem in this case. The ionization-potential theorem, stating that the Kohn–Sham energy eigenvalue of the outermost electron orbital agrees with the negative of the corresponding many-body ionization energy (including electronic relaxation), is verified in this case to nine digits. A Kohn–Sham potential is also constructed to reproduce the Hartree–Fock density of the same state, and the Kohn–Sham 2s eigenvalue is then found to agree with the same accuracy with the corresponding Hartree–Fock eigenvalue. This is consistent with the fact that in this model the energy eigenvalue equals the negative of the ionization energy without relaxation due to Koopmans' theorem. Related calculations have been performed previously, particularly for atomic and molecular ground states, but none of matching accuracy. In the computations presented here there is no conflict between the locality of the Kohn–Sham potential and the exclusion principle, as claimed by Nesbet (Phys. Rev. A, 58, R12 (1998)). PACS Nos.: 31.15.Ew, 31.15.Pf, 02.30.Sa

On the many-body theory of nuclear reactions

1968 ◽  
Vol 111 (1) ◽  
pp. 392-416 ◽  
Author(s):  
K DIETRICH ◽  
K HARA
Keyword(s):  
Nuclear Reactions ◽  
Many Body ◽  
Many Body Theory ◽  
The Many ◽  
Body Theory

Surfing the Quantum World

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Musical Instrument ◽  
Popular Science ◽  
Quantum Spin ◽  
Exclusion Principle ◽  
Maximum Height ◽  
Core Concepts ◽  
The Many ◽  
The One

Surfing the Quantum World bridges the gap between in-depth textbooks and typical popular science books on quantum ideas and phenomena. Among its significant features is the description of a host of mind-bending phenomena, such as a quantum object being in two places at once or a certain minus sign being the most consequential in the universe. Much of its first part is historical, starting with the ancient Greeks and their concepts of light, and ending with the creation of quantum mechanics. The second part begins by applying quantum mechanics and its probability nature to a pedagogical system, the one-dimensional box, an analog of which is a musical-instrument string. This is followed by a gentle introduction to the fundamental principles of quantum theory, whose core concepts and symbolic representations are the foundation for most of the subsequent chapters. For instance, it is shown how quantum theory explains the properties of the hydrogen atom and, via quantum spin and Pauli’s Exclusion Principle, how it accounts for the structure of the periodic table. White dwarf and neutron stars are seen to be gigantic quantum objects, while the maximum height of mountains is shown to have a quantum basis. Among the many other topics considered are a variety of interference phenomena, those that display the wave properties of particles like electrons and photons, and even of large molecules. The book concludes with a wide-ranging discussion of interpretational and philosophic issues, introduced in Chapters 14 by entanglement and 15 by Schrödinger’s cat.

Revealing the many-body interactions and valley-polarization behavior in Re-doped MoS2 monolayers

2021 ◽  
Vol 118 (11) ◽  
pp. 113101
Author(s):  
Xiaoli Zhu ◽  
Siting Ding ◽  
Lihui Li ◽  
Ying Jiang ◽  
Biyuan Zheng ◽  
...  
Keyword(s):  
Many Body ◽  
Polarization Behavior ◽  
Valley Polarization ◽  
Mos2 Monolayers ◽  
The Many ◽  
Many Body Interactions

scholarly journals Entangling Lattice-Trapped Bosons with a Free Impurity: Impact on Stationary and Dynamical Properties

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 290
Author(s):  
Maxim Pyzh ◽  
Kevin Keiler ◽  
Simeon I. Mistakidis ◽  
Peter Schmelcher
Keyword(s):  
Structural Changes ◽  
Many Body ◽  
Wide Range ◽  
Entropy Measures ◽  
Particle Level ◽  
The Many ◽  
The One ◽  
Tunneling Dynamics ◽  
The Individual ◽  
Trapped Bosons

We address the interplay of few lattice trapped bosons interacting with an impurity atom in a box potential. For the ground state, a classification is performed based on the fidelity allowing to quantify the susceptibility of the composite system to structural changes due to the intercomponent coupling. We analyze the overall response at the many-body level and contrast it to the single-particle level. By inspecting different entropy measures we capture the degree of entanglement and intraspecies correlations for a wide range of intra- and intercomponent interactions and lattice depths. We also spatially resolve the imprint of the entanglement on the one- and two-body density distributions showcasing that it accelerates the phase separation process or acts against spatial localization for repulsive and attractive intercomponent interactions, respectively. The many-body effects on the tunneling dynamics of the individual components, resulting from their counterflow, are also discussed. The tunneling period of the impurity is very sensitive to the value of the impurity-medium coupling due to its effective dressing by the few-body medium. Our work provides implications for engineering localized structures in correlated impurity settings using species selective optical potentials.

scholarly journals On the Many-Body Expansion of an Interaction Energy of Some Supramolecular Halogen-Containing Capsules

Molecules ◽  
2021 ◽  
Vol 26 (15) ◽  
pp. 4431
Author(s):  
Jiří Czernek ◽  
Jiří Brus
Keyword(s):  
Density Functional ◽  
Condensed Phases ◽  
Multicomponent Mixtures ◽  
Many Body ◽  
Symmetric Form ◽  
Functional Theory ◽  
Emergent Features ◽  
The Many ◽  
Surprising Fact ◽  
Dimethyl Benzene

A tetramer model was investigated of a remarkably stable iodine-containing supramolecular capsule that was most recently characterized by other authors, who described emergent features of the capsule’s formation. In an attempt to address the surprising fact that no strong pair-wise interactions between any of the respective components were experimentally detected in condensed phases, the DFT (density-functional theory) computational model was used to decompose the total stabilization energy as a sum of two-, three- and four-body contributions. This model considers complexes formed between either iodine or bromine and the crucial D4h-symmetric form of octaaryl macrocyclic compound cyclo[8](1,3-(4,6-dimethyl)benzene that is surrounded by arenes of a suitable size, namely, either corannulene or coronene. A significant enthalpic gain associated with the formation of investigated tetramers was revealed. Furthermore, it is shown that the total stabilization of these complexes is dominated by binary interactions. Based on these findings, comments are made regarding the experimentally observed behavior of related multicomponent mixtures.

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