Advertisement

Self-consistent RPA and the time-dependent density matrix approach

  • P. SchuckEmail author
  • M. Tohyama
Review
Part of the following topical collections:
  1. Finite range effective interactions and associated many-body methods - A tribute to Daniel Gogny

Abstract.

The time-dependent density matrix (TDDM) or BBGKY (Bogoliubov, Born, Green, Kirkwood, Yvon) approach is decoupled and closed at the three-body level in finding a natural representation of the latter in terms of a quadratic form of two-body correlation functions. In the small amplitude limit an extended RPA coupled to an also extended second RPA is obtained. Since including two-body correlations means that the ground state cannot be a Hartree-Fock state, naturally the corresponding RPA is upgraded to Self-Consistent RPA (SCRPA) which was introduced independently earlier and which is built on a correlated ground state. SCRPA conserves all the properties of standard RPA. Applications to the exactly solvable Lipkin and the 1D Hubbard models show good performances of SCRPA and TDDM.

References

  1. 1.
    M.P. Nightingale, C.J. Umrigar (Editors) Quantum Monte Carlo Methods in Physics and Chemistry (Springer, Berlin, 1999)Google Scholar
  2. 2.
    M. Holzmann, B. Bernu, C. Pierleoni, J. Mc Minis, D.M. Ceperly, V. Olevano, L. Delle Site, Phys. Rev. Lett. 107, 110402 (2011)ADSCrossRefGoogle Scholar
  3. 3.
    P.J. Knowles, C. Hampel, H.-J. Werner, J. Chem. Phys. 99, 5219 (1993)ADSCrossRefGoogle Scholar
  4. 4.
    R.F. Bishop, Theor. Chim. Acta 80, 95 (1991)CrossRefGoogle Scholar
  5. 5.
    I. Peschel, X. Wang, M. Kaulke, K. Hallberg (Editors), Density-Matrix Renormalisation, A New Numerical Method in Physics (Springer, Berlin, 1999). Google Scholar
  6. 6.
    U. Schollwoeck, Ann. Phys. 326, 96 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    U. Schollwoeck, Rev. Mod. Phys. 77, 259 (2005)ADSCrossRefGoogle Scholar
  8. 8.
    J.W. Clark, P. Westhaus, Phys. Rev. 141, 833 (1966)ADSCrossRefGoogle Scholar
  9. 9.
    G.E. Scuseria, C.L. Janssen, H.F. Schaefer, J. Chem. Phys. 89, 7382 (1988)ADSCrossRefGoogle Scholar
  10. 10.
    M. Tohyama, P. Schuck, Eur. Phys. J. A 50, 77 (2014)ADSCrossRefGoogle Scholar
  11. 11.
    S.J. Wang, W. Cassing, Ann. Phys. 159, 328 (1985)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, Berlin, 1980)Google Scholar
  13. 13.
    J. Dukelsky, P. Schuck, Nucl. Phys. A 512, 466 (1990)ADSCrossRefGoogle Scholar
  14. 14.
    P. Schuck, M. Tohyama, Phys. Rev. B 93, 165117 (2016)ADSCrossRefGoogle Scholar
  15. 15.
    M. Gong, M. Tohyama, Z. Phys. A 335, 153 (1990)ADSGoogle Scholar
  16. 16.
    J. Dukelsky, G. Roepke, P. Schuck, Nucl. Phys. A 628, 17 (1998)ADSCrossRefGoogle Scholar
  17. 17.
    M. Tohyama, P. Schuck, Eur. Phys. J. A 45, 257 (2010)ADSCrossRefGoogle Scholar
  18. 18.
    M. Tohyama, P. Schuck, Eur. Phys. J. A 19, 215 (2004)ADSCrossRefGoogle Scholar
  19. 19.
    M. Tohyama, S. Takahara, P. Schuck, Eur. Phys. J. A 21, 217 (2004)ADSCrossRefGoogle Scholar
  20. 20.
    M. Tohyama, P. Schuck, Eur. Phys. J. A 32, 139 (2007)ADSCrossRefGoogle Scholar
  21. 21.
    D.J. Rowe, Rev. Mod. Phys. 40, 153 (1968)ADSCrossRefGoogle Scholar
  22. 22.
    D.J. Rowe, Nuclear Collective Motion, Models and Theory (World Scientific, Singapore, 2010)Google Scholar
  23. 23.
    S. Takahara, M. Tohyama, P. Schuck, Phys. Rev. C 70, 057307 (2004)ADSCrossRefGoogle Scholar
  24. 24.
    M. Tohyama, Phys. Rev. C 75, 044310 (2007)ADSCrossRefGoogle Scholar
  25. 25.
    D.S. Delion, P. Schuck, J. Dukelsky, Phys. Rev. C 72, 064305 (2005)ADSCrossRefGoogle Scholar
  26. 26.
    M. Kirson, Ann. Phys. 66, 624 (1971)ADSCrossRefGoogle Scholar
  27. 27.
    F. Catara, G. Piccitto, M. Sambataro, N. Van Giai, Phys. Rev. B 54, 17536 (1996)ADSCrossRefGoogle Scholar
  28. 28.
    F. Catara, M. Grasso, G. Piccitto, M. Sambataro, Phys. Rev. B 58, 16070 (1998)ADSCrossRefGoogle Scholar
  29. 29.
    D. Delion, P. Schuck, M. Tohyama, Eur. Phys. J. B 89, 45 (2016)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    G. Feldman, T. Fulton, Ann. Phys. 152, 376 (1984)ADSCrossRefGoogle Scholar
  31. 31.
    M. Jemai, D.S. Delion, P. Schuck, Phys. Rev. C 88, 044004 (2013)ADSCrossRefGoogle Scholar
  32. 32.
    J.-P. Blaizot, G. Ripka, Quantum Theory of Finite Systems (The MIT Press, Cambridge, 1986)Google Scholar
  33. 33.
    J.G. Hirsch, A. Mariano, J. Dukelsky, P. Schuck, Ann. Phys. 296, 187 (2002)ADSCrossRefGoogle Scholar
  34. 34.
    A. Storozhenko, P. Schuck, J. Dukelsky, G. Roepke, A. Vdovin, Ann. Phys. 307, 308 (2003)ADSCrossRefGoogle Scholar
  35. 35.
    H.J. Lipkin, N. Meshkov, A.J. Glick, Nucl. Phys. 62, 188 (1965)MathSciNetCrossRefGoogle Scholar
  36. 36.
    D. Janssen, P. Schuck, Z. Physik A 339, 43 (1991)ADSCrossRefGoogle Scholar
  37. 37.
    M. Jemai, P. Schuck, J. Dukelsky, R. Bennaceur, Phys. Rev. B 71, 085115 (2005)ADSCrossRefGoogle Scholar
  38. 38.
    M. Tohyama, Phys. Rev. C 91, 017301 (2015)ADSCrossRefGoogle Scholar
  39. 39.
    D. Gambacurta, M. Grasso, J. Engel, Phys. Rev. C 92, 034303 (2015)ADSCrossRefGoogle Scholar
  40. 40.
    C. Robin, N. Pillet, D. Pena Arteaga, J.-F. Berger, Phys. Rev. C 93, 024302 (2016)ADSCrossRefGoogle Scholar
  41. 41.
    M. Tohyama, P. Schuck, Phys. Rev. C 87, 044316 (2013)ADSCrossRefGoogle Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institut de Physique NucléaireOrsay CEDEXFrance
  2. 2.Laboratoire de Physique et Modélisation des Milieux CondensésCNRS and Université Joseph FourierGrenoble Cédex 9France
  3. 3.Kyorin University School of MedicineMitaka, TokyoJapan

Personalised recommendations