Necessary conditions for the N -representability of the second-order reduced density matrix: Upper bounds on the P and Q matrices

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 75, Issue 3, 2007, Pages

  Van Neck, Dimitri ^a   Ayers, Paul W ^b  

^a GHENT UNIVERSITY   (Belgium)

^b MCMASTER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINT THEORY; EIGENVALUES AND EIGENFUNCTIONS; HAMILTONIANS; MATRIX ALGEBRA; VARIATIONAL TECHNIQUES;

DENSITY MATRIX; SECOND ORDER REDUCED DENSITY MATRIX; UPPER BOUNDS;

GROUND STATE;

EID: 33847739357     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.75.032502     Document Type: Article

References (31)

1. M. Nakata, H. Nakatsuji, M. Ehara, M. Fukuda, K. Nakata, and K. Fujisawa, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1360199 114, 8282 (2001).
2. M. Nakata, M. Ehara, and H. Nakatsuji, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1453961 116, 5432 (2002).
3. Z. J. Zhao, B. J. Braams, M. Fukuda, M. L. Overton, and J. K. Percus, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1636721 120, 2095 (2004).
4. D. A. Mazziotti, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.062511 65, 062511 (2002).
5. D. A. Mazziotti, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 93.213001 93, 213001 (2004).
6. D. A. Mazziotti, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1810134 121, 10957 (2004).
7. G. Gidofalvi and D. A. Mazziotti, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1855885 122, 094107 (2005).
8. D. A. Mazziotti, Acc. Chem. Res. ACHRE4 0001-4842 10.1021/ar050029d 39, 207 (2006).
9. E. Cances, G. Stoltz, and M. Lewin, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2222358 125, 064101 (2006).
10. J. Coleman, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.35.668 35, 668 (1963).
11. A. J. Coleman and V. I. Yukalov, Reduced Density Matrices: Coulson's Challenge (Springer, Berlin, 2000).
12. C. Garrod and J. K. Percus, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1704098 5, 1756 (1964).
13. E. R. Davidson, Reduced Density Matrices in Quantum Chemistry (Academic, New York, 1976).
14. C. N. Yang, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.34.694 34, 694 (1962).
15. C. Bloch and A. Messiah, Nucl. Phys. NUPHA7 0029-5582 10.1016/0029-5582(62)90377-2 39, 95 (1962).
16. A. J. Coleman, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1704794 6, 1425 (1965).
17. R. W. Richardson and N. Sherman, Nucl. Phys. NUPHA7 0029-5582 10.1016/0029-5582(64)90687-X 52, 221 (1964).
18. R. W. Richardson, Phys. Lett. PHLTAM 0031-9163 3, 277 (1963).
19. M. Gaudin, J. Phys. Colloq. JPQCAK 0449-1947 37, 1087 (1976).
20. G. Ortiz, R. Somma, J. Dukelsky, and S. Rombouts, Nucl. Phys. B NUPBBO 0550-3213 10.1016/j.nuclphysb.2004.11.008 707, 421 (2005).
21. J. Dukelsky, S. Pittel, and G. Sierra, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.76.643 76, 643 (2004).
22. W. H. Dickhoff and D. Van Neck, Many-Body Theory Exposed! Propagator Descriptions of Quantum Mechanics in Many-Body Systems (World Scientific, Singapore, 2005).
23. D. Van Neck, Y. Dewulf, and M. Waroquier, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.062107 63, 062107 (2001).
24. F. Pan, J. P. Draayer, and W. E. Ormand, Phys. Lett. B PYLBAJ 0370-2693 10.1016/S0370-2693(98)00034-3 422, 1 (1998).
25. G. Racah, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.63.367 63, 367 (1943).
26. S. Rombouts, D. Van Neck, and J. Dukelsky, Phys. Rev. C PRVCAN 0556-2813 10.1103/PhysRevC.69.061303 69, 061303 (2004).
27. J. Nocedal and S. J. Wright, Numerical Optimization (Springer-Verlag, New York, 1999).
28. F. Sasaki, Phys. Rev. PRVBAK 0096-8269 10.1103/PhysRev.138.B1338 138, B1338 (1965).
29. A. J. Coleman, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/(SICI)1097-461X(1997)63:1<23::AID-QUA5>3.0.CO;2-4 63, 23 (1997).
30. R. Larsen, Functional Analysis: An Introduction (Dekker, New York, 1973).
31. P. W. Ayers, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.042502 74, 042502 (2006).