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By David A. Mazziotti
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10, 1855 (1969). 21. C. Garrod, M. V. Mihailovic´, and M. Rosina, The variational approach to the two body density matrix. J. Math. Phys. 16, 868 874 (1975). 22. M. Rosina and C. Garrod, The variational calculation of reduced density matrices. J. Computa tional Phys. 18, 300 310 (1975). 23. M. Rosina, Direct variational calculation of the two body density matrix, in The Nuclear Many Body Problem (Proceedings of the Symposium on Present Status and Novel Developments in the Nuclear Many Body Problem, Rome 1972, (F.
This interpretation allows us to demonstrate that the 2-positivity conditions are exact for certain classes of Hamiltonian operators for any interaction strength. In this section all of the RDMs are normalized to unity. Much of this discussion appeared originally in Refs. [21, 29]. 1. Convex Set of N-Representable 2-RDMs The energy for a system of N fermions with p-particle interactions may be written as a linear functional of the p-RDM: Â Ã E ¼ Tr H N D ¼ Tr½p K p D ð46Þ where p K is the p-particle reduced Hamiltonian matrix.
0. These conditions physically restrict the probability distributions for two particles, two holes, and one particle and one hole to be nonnegative with respect to all unitary transformations of the two-particle basis set. Collectively, the three restrictions are known as the 2-positivity conditions . Because 2 D ! 0 and 2 Q ! 0 imply 1 D ! 0 and 1 Q ! 0 by contraction 1 Dik ¼ 1 Qik ¼ 1 X 2 i;j Dk;j NÀ1 j X 1 rÀN À1 2 j ð16Þ Qi;j k;j ð17Þ 26 david a. mazziotti the 2-positivity conditions imply the 1-positivity conditions.
Advances in Chemical Physics, Special by David A. Mazziotti