scholarly journals On the Spin Projection Operator and the Probabilistic Meaning of the Bipartite Correlation Function

2019 ◽  
Vol 50 (1) ◽  
pp. 27-39 ◽  
Author(s):  
Ana María Cetto ◽  
Andrea Valdés-Hernández ◽  
Luis de la Peña
Keyword(s):  
Correlation Function ◽  
Projection Operator ◽  
Spin Projection

An improved hierarchy for turbulent magnetized plasma Part 1. Theory

1972 ◽  
Vol 7 (2) ◽  
pp. 337-362
Author(s):  
Eldon J. Linnebur ◽  
Terry Kammash
Keyword(s):  
Magnetic Field ◽  
Correlation Function ◽  
Time Dependence ◽  
Projection Operator ◽  
Kinetic Equations ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Turbulent Plasma ◽  
Magnetized Plasma ◽  
Consistent Manner

The kinetic equations for infinite homogeneous turbulent plasma in a magnetic field are analyzed using a projection operator which allows the time dependence to be maintained in a more exact and consistent manner than has been possible heretofore. By introducing approximations on the multi-time correlation function rather than the fluctuations, as is conventionally done, a hierarchy of equations is obtained which predicts different behaviour for the system especially in connexion with wave-wave interations. These effects are further highlighted by showing how the present results reduce to those obtained by various authors.

Assessing the Calculation of Exchange Coupling Constants and Spin Crossover Gaps Using the Approximate Projection Model to Improve Density Function Calculations

2019 ◽  
Author(s):  
Xianghai Sheng ◽  
Lee Thompson ◽  
Hrant Hratchian
Keyword(s):  
Density Functional Theory ◽  
Exchange Coupling ◽  
Density Functional ◽  
Spin Crossover ◽  
Coupling Constants ◽  
Spin Projection ◽  
Coupling Constant ◽  
Projection Model ◽  
Functional Theory

This work evaluates the quality of exchange coupling constant and spin crossover gap calculations using density functional theory corrected by the Approximate Projection model. Results show that improvements using the Approximate Projection model range from modest to significant. This study demonstrates that, at least for the class of systems examined here, spin-projection generally improves the quality of density functional theory calculations of J-coupling constants and spin crossover gaps. Furthermore, it is shown that spin-projection can be important for both geometry optimization and energy evaluations. The Approximate Project model provides an affordable and practical approach for effectively correcting spin-contamination errors in molecular exchange coupling constant and spin crossover gap calculations.

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