Pseudo‐eigenvalue equation for natural orbitals of two‐electron systems and long range behavior

1979 ◽  
Vol 70 (12) ◽  
pp. 5919-5921 ◽  
Author(s):  
Harris J. Silverstone ◽  
Dennis P. Carroll ◽  
Robert Melville Metzger
Keyword(s):  
Long Range ◽  
Eigenvalue Equation ◽  
Electron Systems ◽  
Natural Orbitals

HEAVY FERMIONS — THEIR MAGNETISM AND SUPERCONDUCTIVITY

1993 ◽  
Vol 07 (01n03) ◽  
pp. 2-8 ◽  
Author(s):  
F. STEGLICH ◽  
C. GEIBEL ◽  
A. LOIDL ◽  
G. SPARN ◽  
C. D. BREDL ◽  
...  
Keyword(s):  
Long Range ◽  
Heavy Fermion ◽  
Local Moment ◽  
Antiferromagnetic Order ◽  
Electron Systems ◽  
Correlated Electron Systems ◽  
Cooperative Phenomena ◽  
Correlated Electron ◽  
Highly Correlated ◽  
Heavy Fermion Superconductivity

Heavy-fermion compounds are ideally suited to study cooperative phenomena in highly correlated electron systems. We discuss local-moment magnetism and heavy-fermion band magnetism in the exemplary systems CeCu 2 Ge 2 and Ni-rich Ce(Cu 1− x Ni x )2 Ge 2, respectively. In addition, the coexistence of long-range antiferromagnetic order and heavy-fermion superconductivity in UM 2 Al 3 (M: Ni, Pd) will be addressed.

scholarly journals Scattering and Its Applications to Various Atomic Processes: Elastic Scattering, Resonances, Photoabsorption, Rydberg States, and Opacity of the Atmosphere of the Sun and Stellar Objects

Atoms ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 78
Author(s):  
Anand K. Bhatia
Keyword(s):  
Elastic Scattering ◽  
Long Range ◽  
Short Range ◽  
Bound States ◽  
Rydberg States ◽  
Stellar Atmospheres ◽  
Electron Systems ◽  
Short Range Correlations ◽  
Hybrid Theory ◽  
Scattering Resonances

A scattering process can be a natural process or a process carried out in a laboratory. The scattering of particles from targets has resulted in important discoveries in physics. We discuss various scattering theories of electrons and positrons and their applications to elastic scattering, resonances, photoabsorption, excitation, and solar and stellar atmospheres. Among the most commonly employed approaches are the Kohn variational principle, close-coupling approximation, method of polarized orbitals, R-matrix formulation, and hybrid theory. In every formulation, an attempt is made to include exchange, long-range and short-range correlations, and to make the approach variationally correct. The present formulation, namely, hybrid theory, which is discussed in greater detail compared to other approximations, includes exchange, long-range correlations, and short-range correlations at the same time, and is variationally correct. It was applied to calculate the phase shifts for elastic scattering, the resonance parameters of two-electron systems, photoabsorption in two-electron systems, excitation of atomic hydrogen by an electron and positron impact, and to study the opacity of the Sun’s atmosphere. Calculations of polarizabilities, Rydberg states, and bound states of atoms are also discussed.

Strongly Correlated Electron Systems: Spin-Reflection Positivity and Some Rigorous Results

1998 ◽  
Vol 12 (07n08) ◽  
pp. 709-779 ◽  
Author(s):  
Shun-Qing Shen
Keyword(s):  
Hubbard Model ◽  
Long Range ◽  
Strongly Correlated Electron Systems ◽  
Strongly Correlated ◽  
Electron Systems ◽  
Strongly Correlated Electron ◽  
Rigorous Results ◽  
Correlated Electron Systems ◽  
Correlated Electron ◽  
Generalized Hubbard Model

Theory of spin-reflection positivity developed in recent years is reviewed. This theory makes use of symmetries in an electron system and theory of matrix to investigate the ground state properties. Existences of anti- and ferromagnetic long-range orders in itinerant electron systems, and of off-diagonal long-range order are two successful applications of the theory. In this article, the author attempt to summarize exact results proved by utilizing this theory and related topics. First a general theory and basic theorems are introduced. Second, based on the band structures of conduction electrons, existences of a singlet state with strongly antiferromagnetic correlation, a state with both anti- and ferromagnetic long-range orders, and a fully saturated ferromagnetic state are proved. The theory is applied to several of the main theoretical models for strongly correlated electron systems, such as the Heisenberg model, the Hubbard model, the Anderson model, the single- and multichannel Kondo model, and the generalized Hubbard model, and a series of rigorous results are found in these models. Third, it is proved that off-diagonal long-range order and charge-density wave exist in the ground states of the attractive Hubbard model and the generalized Hubbard model. A relation between pseudospin symmetry and the uniform density theorem is introduced. Fourth, the theory is applied successfully to explain experimental observations of oscillatory interlayer magnetic coupling in ultrathin magnetic films. Finally several unsolved problems are discussed. All results introduced in this article are mathematically exact.

Short and long range contributions to the inductive effect in π electron systems

1966 ◽  
Vol 291 (1425) ◽  
pp. 224-234 ◽  
Keyword(s):  
Long Range ◽  
Field Effect ◽  
Short Range ◽  
Inductive Effect ◽  
Electron Systems ◽  
Methyl Group ◽  
Range Type ◽  
Coulomb Type ◽  
Exchange Repulsion ◽  
Coulomb Attraction

It is shown that the inductive effect of a substituent can have contributions of both exchange and Coulomb type, but that the exchange terms can be treated empirically as though they arise from a short-range field effect. Calculations of the exchange terms for the halogens and the methyl group are in accord with the empirical values of inductive parameters deduced from spectroscopy. Evidence is given that for a methyl group the inductive perturbation is almost entirely of short range type and is probably dominated by the exchange terms but for a chloro substituent both the short range exchange repulsion and the long range Coulomb attraction are important.

Long‐Range Interaction in Two‐Electron Systems

1965 ◽  
Vol 42 (8) ◽  
pp. 2796-2801 ◽  
Author(s):  
W. J. Carr ◽  
M. Ashkin
Keyword(s):  
Long Range ◽  
Electron Systems ◽  
Range Interaction ◽  
Long Range Interaction

scholarly journals Homotopy Phases of FQHE with Long-Range Quantum Entanglement in Monolayer and Bilayer Hall Systems

Nanomaterials ◽  
2020 ◽  
Vol 10 (7) ◽  
pp. 1286
Author(s):  
Janusz Jacak
Keyword(s):  
Quantum Entanglement ◽  
Long Range ◽  
Electron Tunneling ◽  
Close Relation ◽  
Composite Nanomaterials ◽  
Topological Phases ◽  
Electron Systems ◽  
On Demand ◽  
Planar Electron ◽  
Topological Character

Correlated phases in Hall systems have topological character. Multilayer configurations of planar electron systems create the opportunity to change topological phases on demand using macroscopic factors, such as vertical voltage. We present an analysis of such phenomena in close relation to recent experiments with multilayer Hall setups including GaAs and graphene multi-layers. The consequences of the blocking or not of the inter-layer electron tunneling in stacked Hall configurations are analyzed and presented in detail. Multilayer Hall systems are thus tunable topological composite nanomaterials, in the case of graphene-stacked systems by both intra- and inter-layer voltage.

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