Method of m-particle density matrices of the canonical ensemble in the description of states of quantum systems

1976 ◽  
Vol 27 (3) ◽  
pp. 539-548 ◽  
Author(s):  
K. S. Matviichuk
Keyword(s):  
Canonical Ensemble ◽  
Particle Density ◽  
Quantum Systems ◽  
Density Matrices

Is it Reasonable to Obtain Information on the Polarizability and Hyperpolarizability Only from the Electron Density?

2018 ◽  
Vol 71 (4) ◽  
pp. 295 ◽  
Author(s):  
Dylan Jayatilaka ◽  
Kunal K. Jha ◽  
Parthapratim Munshi
Keyword(s):  
Density Matrix ◽  
Electron Density ◽  
Ground State ◽  
Density Functional ◽  
Particle Density ◽  
Density Matrices ◽  
Hartree Fock ◽  
Electron Density Matrix ◽  
Ground State Electron ◽  
Side Result

Formulae for the static electronic polarizability and hyperpolarizability are derived in terms of moments of the ground-state electron density matrix by applying the Unsöld approximation and a generalization of the Fermi-Amaldi approximation. The latter formula for the hyperpolarizability appears to be new. The formulae manifestly transform correctly under rotations, and they are observed to be essentially cumulant expressions. Consequently, they are additive over different regions. The properties of the formula are discussed in relation to others that have been proposed in order to clarify inconsistencies. The formulae are then tested against coupled-perturbed Hartree-Fock results for a set of 40 donor-π-acceptor systems. For the polarizability, the correlation is reasonable; therefore, electron density matrix moments from theory or experiment may be used to predict polarizabilities. By constrast, the results for the hyperpolarizabilities are poor, not even within one or two orders of magnitude. The formula for the two- and three-particle density matrices obtained as a side result in this work may be interesting for density functional theories.

Statistical mean-field theory of finite quantum systems: canonical ensemble formulation

2006 ◽  
Vol 39 (30) ◽  
pp. L499-L505 ◽  
Author(s):  
S A Ponomarenko ◽  
M E Sherrill ◽  
D P Kilcrease ◽  
G Csanak
Keyword(s):  
Field Theory ◽  
Canonical Ensemble ◽  
Mean Field Theory ◽  
Mean Field ◽  
Quantum Systems ◽  
Finite Quantum Systems

Visualizing Covalency and Multiple Bonds in Terms of the Electronic Single-Particle Density Matrix

2001 ◽  
Vol 215 (10) ◽  
Author(s):  
T. Asthalter ◽  
M. Walter
Keyword(s):  
Single Particle ◽  
Organic Molecules ◽  
Graphical Representation ◽  
Particle Density ◽  
Electron System ◽  
Covalent Bonding ◽  
Density Matrices ◽  
Multiple Bonds ◽  
Single Particle Density ◽  
Isoelectronic Series

Two-dimensional cuts through spin-integrated single-particle density matrices (SPDMs) have proven to be a valuable tool to discuss the nature of chemical bonding independent of the degree of rotation of the underlying orbitals in Hilbert space. Starting from a straightforward concept for the interpretation of σ bonds, we briefly present how the transition from purely ionic to mainly covalent bonding is mirrored in the off-diagonal features of the SPDM in the isoelectronic series LiF, BeO and BN. Furthermore, we outline one of several possible ways to extend the graphical representation and interpretation of SPDMs to the case of π bonds in organic molecules and apply it to the conjugated π-electron system 1,6-hexadiynediol.

CANONICAL FORM AND SEPARABILITY OF PPT STATES IN ${\mathcal C}^2\otimes {\mathcal C}^M\otimes {\mathcal C}^N$ COMPOSITE QUANTUM SYSTEMS

2003 ◽  
Vol 01 (03) ◽  
pp. 337-347
Author(s):  
XIAO-HONG WANG ◽  
SHAO-MING FEI ◽  
ZHI-XI WANG ◽  
KE WU
Keyword(s):  
Canonical Form ◽  
General Expression ◽  
Quantum Systems ◽  
Canonical Forms ◽  
Density Matrices ◽  
Partial Transposition ◽  
Separability Condition ◽  
Ppt States

We investigate the canonical forms of positive partial transposition (PPT) density matrices in [Formula: see text] composite quantum systems with rank N. A general expression for these PPT states are explicitly obtained. From this canonical form a sufficient separability condition is presented.

scholarly journals Separable approximations of density matrices of composite quantum systems

2001 ◽  
Vol 34 (35) ◽  
pp. 6919-6937 ◽  
Author(s):  
Sinisa Karnas ◽  
Maciej Lewenstein
Keyword(s):  
Quantum Systems ◽  
Density Matrices
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