By David A. Mazziotti
An updated account of this state-of-the-art examine in a constant and comprehensible framework, of precise curiosity to specialists in different components of digital constitution and/or quantum many-body thought. it is going to serve both good as a self-contained advisor to studying approximately diminished density matrices both via self-study or in a lecture room in addition to a useful source for knowing the severe developments within the box.
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Additional info for Advances in Chemical Physics, Reduced-Density-Matrix Mechanics: With Application to Many-Electron Atoms and Molecules (Volume 134
20. M. Rosina and C. Garrod, The particle–hole matrix: its connection with the symmetries and collective features of the ground state. J. Math. Phys. 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. Computational Phys. 18, 300–310 (1975). 23. M. Rosina, Direct variational calculation of the two-body density matrix, in The Nuclear ManyBody Problem (Proceedings of the Symposium on Present Status and Novel Developments in the Nuclear Many-Body Problem, Rome 1972, (F.
3. C. Garrod and J. K. Percus, J. Math. Phys. 5, 1756 (1964). 4. H. Kummer, N-Representability problem for reduced density matrices. J. Math. Phys. 8, 2063– 2081 (1967). 5. F. Bopp, Z. Phys. 56, 348 (1959). 6. R. L. Hall and H. R. Post, Proc. Phys. Soc. A69, 936 (1956); A79: 819 (1962); A90: 381 (1967); A91: 16 (1967). 7. M. V. Mihailovic´ and M. Rosina, Excitations as ground state variational parameters. Nucl. Phys. A130, 386–400 (1969). 8. M. Rosina, Transition amplitudes as ground state variational parameters, in Reduced Density Matrices with Applications to Physical and Chemical Systems (A.
Independent of the correlation present in the 1-RDM, an ensemble of the extreme elements in Eqs. (56) and (59) may generate any energy-shifted Hamiltonian 1 C—both the positive and the negative parts of its spectrum. Proof of this important idea was ﬁrst given by Coleman [6, 7]. From the formal deﬁnition of the N-representability constraints in Eq. (50), therefore, the positivity of the oneparticle and the one-hole RDMs is necessary and sufﬁcient for the ensemble N-representability of the 1-RDM .