Truncation scheme of time-dependent density-matrix approach II

Regular Article - Theoretical Physics


A truncation scheme of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for reduced density matrices, where a three-body density matrix is approximated by two-body density matrices, is improved to take into account a normalization effect. The truncation scheme is tested for the Lipkin model. It is shown that the obtained results are in good agreement with the exact solutions.


  1. 1.
    M. Bonitz, Quantum Kinetic Theory, 2nd edition (Springer, 2015), and references thereinGoogle Scholar
  2. 2.
    S.J. Wang, W. Cassing, Ann. Phys. 159, 328 (1985)ADSCrossRefGoogle Scholar
  3. 3.
    M. Gong, M. Tohyama, Z. Phys. A 335, 153 (1990)ADSGoogle Scholar
  4. 4.
    S. Takahara, M. Tohyama, P. Schuck, Phys. Rev. C 70, 057307 (2004)ADSCrossRefGoogle Scholar
  5. 5.
    M. Tohyama, J. Phys. Soc. Jpn. 81, 054707 (2012)ADSCrossRefGoogle Scholar
  6. 6.
    K.-J. Schmitt, P.-G. Reinhard, C. Toepffer, Z. Phys. A 336, 123 (1990)ADSGoogle Scholar
  7. 7.
    T. Gherega, R. Krieg, P.-G. Reinhard, C. Toepffer, Nucl. Phys. A 560, 166 (1993)ADSCrossRefGoogle Scholar
  8. 8.
    M. Tohyama, P. Schuck, Eur. Phys. J. A 50, 7 (2014)CrossRefGoogle Scholar
  9. 9.
    I. Shavitt, R.J. Bartlett, Many-Body Methods in Chemistry and Physics (Cambridge University Press, 2009)Google Scholar
  10. 10.
    P. Schuck, M. Tohyama, Phys. Rev. B 93, 165117 (2016)ADSCrossRefGoogle Scholar
  11. 11.
    H.J. Lipkin, N. Meshkov, A.J. Glick, Nucl. Phys. 62, 188 (1965)CrossRefGoogle Scholar
  12. 12.
    M. Tohyama, Phys. Rev. A 71, 043613 (2005)ADSCrossRefGoogle Scholar
  13. 13.
    M. Tohyama, arXiv:1708.07219Google Scholar

Copyright information

© SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Kyorin University School of MedicineMitaka, TokyoJapan
  2. 2.Institut de Physique Nucléaire, IN2P3-CNRS, Université Paris-SudOrsay CedexFrance
  3. 3.Laboratoire de Physique et de Modélisation des Milieux Condensés, CNRS and Université Joseph FourierGrenoble Cedex 9France

Personalised recommendations