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Wick’s theorem and reconstruction schemes for reduced density matrices

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Abstract

We first obtained a closed form of the Wick’s theorem expressed in Grassman wedge product, which is similar to a binomial expansion. With this new expansion, new reconstruction schemes for reduced density matrices are derived rigorously. The higher order reduced density matrices are systematically decomposed into a sum of the lower order reduced density matrices which could be used to solve the contracted Schrödinger equation.

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References

  1. Davidson E R. Reduced Density Matrices in Quantum Chemistry. New York: Academic, 1976

    Google Scholar 

  2. Cioslowski J, ed. Many-Electron Densities and Reduced Density Matrices. Boston: Kluwer, 2000

    Google Scholar 

  3. Coleman A J. Structure of Fermion density matrices. Rev Mod Phys, 1963, 35: 668–687

    Article  Google Scholar 

  4. Sasaki F. Eigenvalues of Fermion density matrices. Phys Rev, 1965, 138: 1338–1342

    Article  CAS  Google Scholar 

  5. Weinhold F, Wilson E B. Reduced density matrices of atoms and molecules (II): On the N-representability problem. J Chem Phys, 1967, 47: 2298–2311

    Article  CAS  Google Scholar 

  6. Kummer H. N-representability problem for reduced density matrices. J Math Phys, 1967, 8: 2063–2081

    Article  Google Scholar 

  7. Davidson E R. Linear inequality for density matrices. J Math Phys, 1969, 10: 725–734

    Article  Google Scholar 

  8. McRae W B, Davidson E R. Linear inequality for density matrices (II). J Math Phys, 1972, 13: 1527–1538

    Article  Google Scholar 

  9. McRae W B, Davidso E R. An algorithm for the extreme rays of a pointed convex polyhedral cone. SIAM J Comput, 1973, 2: 281–293

    Article  Google Scholar 

  10. Yoseloff M L, Kuhn H W. Combinatorial approach to the N-representability of p-density matrices. J Math Phys, 1969, 10: 703–706

    Article  Google Scholar 

  11. Beste A, Runge K, Bartlett R. Ensuring N-representability: Coleman’s algorithm. Chem Phys Lett, 2002, 355: 263–269

    Article  CAS  Google Scholar 

  12. Cho S. Sci Rep Gumma Univ, 1962, 11: 1

    Google Scholar 

  13. Nakatsuji H. Equation for the direct determination of density matrix. Phys Rev A, 1976, 14: 41–50

    Article  CAS  Google Scholar 

  14. Cohen L, Frishberg C. Hierarchy equations for the density matrices. Phys Rev A, 1976, 13: 927–930

    Article  Google Scholar 

  15. Valdemore C. Approximating the second-order density matrix in terms of first-order one. Phys Rev A, 1992, 45: 4462–4467

    Article  Google Scholar 

  16. Colmenero F, Pérez del Valle C, Valdemore C. Approximating the q-order density matrix in terms of lower-order ones (I): General relations. Phys Rev A, 1993, 47: 971–978

    Article  CAS  Google Scholar 

  17. Colmenero F, Valdemore C. Approximating the q-order density matrix in terms of lower-order ones (II): Applications. Phys Rev A, 1993, 47: 979–985

    Article  CAS  Google Scholar 

  18. Nakatsuji H, Yasuda K. Direct determination of the quantum-mechanical density matrix using the density equation. Phys Rev Lett, 1996, 76: 1039–1042

    Article  CAS  Google Scholar 

  19. Yasuda K, Nakatsuji H. Direct determination of the quantum-mechanical density matrix using the density equation (II). Phys Rev A, 1997, 56: 2648–2657

    Article  CAS  Google Scholar 

  20. Mazziotti D A. Contracted Schrödinger equation: Determing quantum energies and two particle density matrices without wave functions. Phys Rev A, 1998, 57: 4219–4234

    Article  CAS  Google Scholar 

  21. Mazziotti D A. Approximate solution for electron correlation through the use of Schwinger Prober. Chem Phys Lett, 1998, 289: 419–427

    Article  CAS  Google Scholar 

  22. Kubo R. Generalized cumulant expansion method. J Phys Soc Jpn, 1962, 17: 1100–1120

    Article  Google Scholar 

  23. Wick G C. The valuation of the collision matrix. Phys Rev, 1950, 80: 268–272

    Article  Google Scholar 

  24. March N H, Young W H, Sampanthar S. The Many Body Problem in Quantum Mechanics. London and New York: Cambridge University Press, 1967

    Google Scholar 

  25. Coleman A J, Absar I. Reduced Hamiltonian orbitals (III): Unitarily invariant decomposition of Hermitian operators. Int J Quantum Chem, 1980, 18: 1279–1307

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Department of Chemistry, University of Science and Technology Beijing, Beijing, 100083, China

    Chen Feiwu

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  1. Chen Feiwu
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Chen, F. Wick’s theorem and reconstruction schemes for reduced density matrices. SCI CHINA SER B 49, 402–406 (2006). https://doi.org/10.1007/s11426-006-0402-9

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  • DOI: https://doi.org/10.1007/s11426-006-0402-9

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