HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 54 (1975) > Number 2
| Next Article >

Prog. Theor. Phys. Vol. 54 No. 2 (1975) pp. 384-395

[ Full Text PDF : FREE ACCESS (1053K) ]

Ground-State Energy of a Many-Boson System

— Density and Phase Operator Approach —

Toshiyuki Nishiyama

Department of Physics, College of General Education, Osaka University, Toyonaka, Osaka 560

(Received December 19, 1974)

Abstract:

The density and phase operator approach is used for deriving the ground-state energy in a weakly interacting many-boson system up to the perturbation energy of order 1/N, the inverse total number of particles. An expression exactly the same as that of the method of correlated basis functions is obtained by summing up several perturbation terms neglected in the previous theories of the collective variable approach. Some remarks are made on the other related theories, in particular, the current algebra approach of Dashen and Sharp.


URL : http://ptp.ipap.jp/link?PTP/54/384/
DOI : 10.1143/PTP.54.384

[ Full Text PDF : FREE ACCESS (1053K) ] Citation:

References:

  1. E. Feenberg, Theory of Quantum Fluids (Academic Press, New York, 1969; Am. J. Phys. 38 (1970), 684.
  2. D. K. Lee, Phys. Rev. A 4 (1971), 1670[APS].
  3. N. N. Bogoliubov, J. of Phys. (USSR) 11 (1947), 23.
  4. P. Berdahl and D. K. Lee, Phys. Rev. A 7 (1973), 1376[APS].
  5. N. N. Bogoliubov and D. N. Zubarev, Zh. Eksp. i Teor. Fiz. 28 (1955), 129 [Sov. Phys.-JETP 1 (1955), 83].
  6. T. Tsuzuki, Prog. Theor. Phys. 52 (1974), 793[PTP].
  7. A. K. Rajagopal and G. S. Grest, Phys. Rev. A 10 (1974), 1837[APS].
  8. S. Sunakawa, S. Yamasaki and T. Kebukawa, Prog. Theor. Phys. 41 (1969), 919[PTP].
  9. H. M. Chan and J. G. Valatin, Nuovo Cim. (X) 19 (1961), 118.
  10. P. Berdahl, Ph. D. Thesis (Stanford Univ. 1972).
  11. T. Nishiyama, Prog. Theor. Phys. 7 (1952), 417[PTP]; ibid. 8 (1952), 655[PTP].
  12. M. Takahashi, Prog. Theor. Phys. 53 (1975), 386[PTP].
  13. E. H. Lieb and W. Liniger, Phys. Rev. 130 (1963), 1605[APS].
  14. K. Hiroike, private communication.
    See also, Prog. Theor. Phys. 21 (1959), 327[PTP].
  15. R. F. Dashen and D. H. Sharp, Phys. Rev. 165 (1968), 1867[APS].
  16. P. R. Zilzel, The Many-Body Problem, J. K. Percus, ed. (Interscience Pub., 1963).
  17. L. Landau, J. of Phys. (USSR) 5 (1941), 71.
  18. P. Carruthers and M. M. Nieto, Rev. Mod. Phys. 40 (1968), 411[APS].
  19. L. A. Turski, Physica 57 (1972), 432[CrossRef].
  20. H. Fröhlich, Physica 34 (1967), 47[CrossRef].
    See also S. Nakajima and D. Yoshioka, Prog. Theor. Phys. 52 (1974), 733[PTP].
  21. T. Nishiyama, Prog. Theor. Phys. 45 (1971), 730[PTP].
  22. G. S. Grest and A. K. Rajagopal, Prog. Theor. Phys. 52 (1974), 811[PTP].
  23. T. Nishiyama, Prog. Theor. Phys. 12 (1954), 265[PTP].
  24. A. Thellung, Physica 19 (1953), 217[CrossRef].
    See also J. M. Ziman, Proc. R. Soc. A 219 (1953), 257.
  25. H. Ito, Prog. Theor. Phys. 9 (1953), 117[PTP].
  26. S. Tomonaga, private communication. See loc. cit. (11).
  27. T. Nishiyama, Prog. Theor. Phys. 38 (1967), 1062[PTP].
  28. A. K. Rajagopal, Proceedings of the Symposium on Statistical Physics Celebrating the Discovery of the Bose Statistics, India (1974).
  29. S. Yamasaki, S. Sunakawa and T. Kebukawa, Prog. Theor. Phys. 54 (1975), 348[PTP].
  30. D. H. Kobe and G. C. Coomer, Phys. Rev. 7 (1973), 1312[APS].
  31. T. Tsuzuki, private communication.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 54 No. 2 (1975) pp. 597-599 :
    Momentum Distribution of an Interacting Many-Boson System
    Toshiyuki Nishiyama
  2. Progress of Theoretical Physics Vol. 55 No. 4 (1976) pp. 1330-1332 :
    Coherent State Approach to Many-Boson Problems
    Masakazu Tsujii
  3. Progress of Theoretical Physics Vol. 56 No. 1 (1976) pp. 16-30 :
    Momentum Distribution of an Interacting Many-Boson System at High Density
    Toshiyuki Nishiyama
  4. Progress of Theoretical Physics Vol. 56 No. 2 (1976) pp. 415-434 :
    Single Particle Aspects in a Collective Formalism for an Interacting Boson System
    Shuichiro Yamasaki, Takeji Kebukawa and Sigenobu Sunakawa
  5. Progress of Theoretical Physics Vol. 57 No. 1 (1977) pp. 12-27 :
    Use of a Coherent-State Representation for a Many-Boson System at High Density
    Masakazu Tsujii and Toshiyuki Nishiyama
  6. Progress of Theoretical Physics Vol. 57 No. 2 (1977) pp. 393-409 :
    Collective Variable Approach to Many-Boson Systems at High Density
    Toshiyuki Nishiyama and Masakazu Tsujii
  7. Progress of Theoretical Physics Vol. 64 No. 4 (1980) pp. 1248-1264 :
    Bose-Einstein Condensation and the Canonical Conjugates to the Density Fluctuations
    Shuichiro Yamasaki and Masahiko Hirooka
  8. Progress of Theoretical Physics Vol. 65 No. 4 (1981) pp. 1198-1216 :
    One-Dimensional Many Boson System. I
    Shosuke Sasaki and Takeji Kebukawa
  9. Progress of Theoretical Physics Vol. 68 No. 4 (1982) pp. 1050-1069 :
    Ground-State Energy of a System of Interacting Bose Particles
    Masahiko Hirooka and Shuichiro Yamasaki
  10. Progress of Theoretical Physics Vol. 68 No. 5 (1982) pp. 1482-1503 :
    Quasi-Particle Description of a Degenerate System of Bosons
    Masahiko Hirooka and Shuichiro Yamasaki

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.