scholarly journals Analyticity of the One-Particle Density Matrix

2021 ◽  
Author(s):  
Peter Hearnshaw ◽  
Alexander V. Sobolev
Keyword(s):  
Density Matrix ◽  
Particle Density ◽  
Real Analytic ◽  
The One ◽  
Coulombic Systems

AbstractIt is proved that the one-particle density matrix $$\gamma (x, y)$$ γ ( x , y ) for multi-particle Coulombic systems is real analytic away from the nuclei and from the diagonal $$x = y$$ x = y .

Density cumulant functional theory: The DC-12 method, an improved description of the one-particle density matrix

2013 ◽  
Vol 138 (2) ◽  
pp. 024107 ◽  
Author(s):  
Alexander Yu. Sokolov ◽  
Andrew C. Simmonett ◽  
Henry F. Schaefer
Keyword(s):  
Density Matrix ◽  
Particle Density ◽  
Functional Theory ◽  
The One

scholarly journals The Energy-Density Functional of an Electron Gas in Locally Linear Approximation of the One-Body Potential

1972 ◽  
Vol 27 (8-9) ◽  
pp. 1176-1186 ◽  
Author(s):  
R. Baltin
Keyword(s):  
Energy Density ◽  
Density Matrix ◽  
Density Functional ◽  
Particle Density ◽  
Parametric Representation ◽  
Kinetic Energy Density ◽  
Linear Potential ◽  
Energy Density Functional ◽  
The One ◽  
Body Potential

Abstract For a system of independent electrons moving in a common one-body potential V (r) an integral representation of Dirac's density matrix is evaluated in the approximation that V(r) at the point r is replaced by a linear potential with a gradient equal to the gradient of V at r. The particle density ᵨ, ∇ᵨ and the kinetic-energy density εk are derived from the density matrix. After eliminating the potential and its gradient a parametric representation for εk in terms of ᵨ and y = |∇ᵨ |½ ᵨ-⅔ is obtained. Explicit analytical expressions are given in the limits y → 0 and y → ∞ and compared with the inhomogeneity corrections of Kirzhnits and v. Weizsäcker.

Static properties of the 2D Hubbard model on a 4×4 cluster

1989 ◽  
Vol 03 (12) ◽  
pp. 1865-1873 ◽  
Author(s):  
Alberto Parola ◽  
Sandro Sorella ◽  
Stefano Baroni ◽  
Michele Parrinello ◽  
Erio Tosatti
Keyword(s):  
Density Matrix ◽  
Hubbard Model ◽  
Particle Density ◽  
Numerical Study ◽  
Exact Diagonalization ◽  
Exact Results ◽  
Power Method ◽  
Static Properties ◽  
Simple Power ◽  
The One

A numerical study of the 2D Hubbard model at various fillings has been performed. The static properties of 10, 14 and 16 electrons on a 4×4 cluster have been studied by exact diagonalization at intermediate couplings. A simple “power method” has been used in order to minimize memory requirements. Spin-spin, charge-charge and hole-hole correlations have been computed together with the one particle density matrix. This computation provides the first exact results on such a system, which can be used as a test for existing simulation algorithms.

Relationships between Jaynes entropy of the one-particle density matrix and Shannon entropy of the electron densities

2002 ◽  
Vol 116 (21) ◽  
pp. 9213-9221 ◽  
Author(s):  
Robin P. Sagar ◽  
Juan Carlos Ramı́rez ◽  
Rodolfo O. Esquivel ◽  
Minhhuy Hô ◽  
Vedene H. Smith
Keyword(s):  
Density Matrix ◽  
Shannon Entropy ◽  
Particle Density ◽  
Electron Densities ◽  
The One
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