By David A. Mazziotti
An up to date account of this state-of-the-art examine in a constant and comprehensible framework, of distinctive curiosity to specialists in different components of digital constitution and/or quantum many-body concept. it's going to serve both good as a self-contained consultant to studying approximately lowered density matrices both via self-study or in a school room in addition to a useful source for figuring out the severe developments within the box.
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Extra info for Advances in Chemical Physics, Reduced-Density-Matrix Mechanics: With Application to Many-Electron Atoms and Molecules (Volume 134)
60) may be expressed the Q- and the G-reduced Hamiltonians 2 K in terms of the usual D-representation of the reduced Hamiltonian: 2 " i;j K k;l ¼ 2 nq i;j i;j ðTr½2 K 2 Ik;l À ðr À NÞ L12 ½2 Kik ^ 1 Ilj þ 2 Kk;l Þ 2 nd ð66Þ and 2 ~ i;k K l; j ng ¼ nd 2 i;j Kk;l þ djk =ðr À N þ 1Þ X ! 2 i;m Kl;m ð67Þ m To the Q- and the G-reduced Hamiltonians, we may wish to afﬁx the name generalized reduced Hamiltonians. Just as the D-form of the reduced Hamiltonian may be lifted to an N-particle Hamiltonian, the Q-form of the reduced variational two-electron reduced-density-matrix theory 35 Hamiltonian may be lifted by Eq.
The three complementary representations of the reduced Hamiltonian offer a framework for understanding the D-, the Q-, and the G-positivity conditions for the 2-RDM. Each positivity condition, like the conditions in the one-particle case, correspond to including a different class of two-particle reduced Hamiltonians in the N-representability constraints of Eq. (50). The positivity of 2 D arises from employing all positive semideﬁnite 2 B in Eq. (50) while the Q- and the G" and 2 B ~ , respectively.
J. Coleman and R. M. ), Queen’s Press, Kingston, Ontario, 1969, p. 82. 11. M. Rosina, The characterization of collective states by means of density matrices, in Report of the Density Matrix Seminar (A. J. Coleman and R. M. ), Queen’s Press, Kingston, Ontario, 1969, p. 89. 12. C. Garrod and M. Rosina, The nonnegativity of the G-matrix and saturation, in Report of the Density Matrix Seminar (A. J. Coleman and R. M. ), Queen’s Press, Kingston, Ontario, 1969, p. 76. 13. R. M. Erdahl and M. Rosina, The B-condition is implied by the G-condition, in Reduced Density Operators with Applications to Physical and Chemical Systems—II (R.
Advances in Chemical Physics, Reduced-Density-Matrix Mechanics: With Application to Many-Electron Atoms and Molecules (Volume 134) by David A. Mazziotti