Physics of Atomic Nuclei

, Volume 77, Issue 3, pp 336–343 | Cite as

Higher-order Brunnian structures and possible physical realizations

  • N. A. Baas
  • D. V. Fedorov
  • A. S. Jensen
  • K. Riisager
  • A. G. Volosniev
  • N. T. Zinner
Nuclei Theory

Abstract

We consider few-body bound state systems and provide precise definitions of Borromean and Brunnian systems. The initial concepts are more than a hundred years old and originated in mathematical knot-theory as purely geometric considerations. About thirty years ago they were generalized and applied to the binding of systems in nature. It now appears that recent generalization to higher-order Brunnian structures may potentially be realized as laboratory-made or naturally occurring systems. With the binding energy as measure, we discuss possibilities of physical realization in nuclei, cold atoms, and condensedmatter systems. Appearance is not excluded. However, both the form and the strengths of the interactions must be rather special. The most promising subfields for present searches would be in cold atoms because of external control of effective interactions, or perhaps in condensed-matter systems with nonlocal interactions. In nuclei, it would only be by sheer luck due to a lack of tunability.

Keywords

Atomic Nucleus Polar Molecule Cold Atom Feshbach Resonance Neutron Dripline 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    P.G. Tait, Trans. R. Soc. Edinburgh 28, 145 (1876).Google Scholar
  2. 2.
    H. Brunn, Sitz. Bayer. Akad. Wiss. Math.-Phys. Klasse 22, 77 (1892).Google Scholar
  3. 3.
    H. Debrunner, Duke Math. J. 28, 17 (1961).CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    D. E. Penney, Duke Math. J. 36, 31 (1969).CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    N. A. Baas, Int. J. Gen. Syst. 42, 137 (2013); arXiv: 1012.2698 [cond-mat.quant-gas].CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    N. A. Baas and N. C. Seeman, J. Math. Chem. 50, 220 (2012).CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    C. Liang and K. Mislow, J. Math. Chem. 16, 27 (1994).CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    N. A. Baas, Eur. Phys. J. Spec. Top. 178, 25 (2009).CrossRefGoogle Scholar
  9. 9.
    N. A. Baas, Int. J. Gen. Syst. 42, 170 (2013); arXiv: 1201.6228 [math.GM].CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    H. L. Frisch and E. Wassermann, J. Am. Chem. Soc. 83, 3789 (1961).CrossRefGoogle Scholar
  11. 11.
    C.Mao,W. Sun, and N. C. Seeman, Nature 386, 137 (1997).ADSGoogle Scholar
  12. 12.
    M. V. Zhukov, D. V. Fedorov, B. V. Danilin, et al., Nucl. Phys. A 539, 177 (1992).ADSCrossRefGoogle Scholar
  13. 13.
    F. Ferlaino and R. Grimm, Physics 3, 9 (2010).CrossRefGoogle Scholar
  14. 14.
    A. S. Jensen, K. Riisager, D. V. Fedorov, and E. Garrido, Rev. Mod. Phys. 76, 215 (2004).ADSCrossRefGoogle Scholar
  15. 15.
    M. Lewenstein et al., Adv. Phys. 56, 243 (2007).ADSCrossRefGoogle Scholar
  16. 16.
    I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80, 885 (2008).ADSCrossRefGoogle Scholar
  17. 17.
    C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Rev. Mod. Phys. 82, 1225 (2010).ADSCrossRefGoogle Scholar
  18. 18.
    T. Lahaye, C. Menotti, L. Santos, et al., Rep. Prog. Phys. 72, 126401 (2009).ADSCrossRefGoogle Scholar
  19. 19.
    L. D. Carr, D. DeMille, R. V. Krems, and J. Ye, New J. Phys. 11, 055049 (2009).ADSCrossRefGoogle Scholar
  20. 20.
    M.-S. Chang, Q. Qin, W. Zhang, et al., Nature Phys. 1, 111 (2005).ADSCrossRefGoogle Scholar
  21. 21.
    L. E. Sadler, J. M. Higbie, S. R. Leslie, et al., Nature 443, 312 (2006).ADSCrossRefGoogle Scholar
  22. 22.
    A. Micheli, G. Pupillo, H. P. Büchler, and P. Zoller,, Phys. Rev. A 76, 043604 (2007).ADSCrossRefGoogle Scholar
  23. 23.
    M. H. G. de Miranda et al., Nature Phys. 7, 502 (2011).ADSCrossRefGoogle Scholar
  24. 24.
    E. Nielsen, D. V. Fedorov, and A. S. Jensen, Phys. Rev. A 56, 3287 (1997).ADSCrossRefGoogle Scholar
  25. 25.
    S.-J. Huang et al., Phys. Rev. A 85, 055601 (2012); arXiv: 1112.2035v1 [cond-mat.quant-gas].ADSCrossRefGoogle Scholar
  26. 26.
    A. G. Volosniev et al., in preparation.Google Scholar
  27. 27.
    J. R. Armstrong, N. T. Zinner, D. V. Fedorov, and A. S. Jensen, Europhys. Lett. 91, 16001 (2010).ADSCrossRefGoogle Scholar
  28. 28.
    A. G. Volosniev, N. T. Zinner, D. V. Fedorov, et al., J. Phys. B 44, 125301 (2011).ADSCrossRefGoogle Scholar
  29. 29.
    A. G. Volosniev, D. V. Fedorov, A. S. Jensen, and N. T. Zinner, Phys. Rev. Lett. 106, 250401 (2011).ADSCrossRefGoogle Scholar
  30. 30.
    W. Ketterle and M.W. Zwierlein, Riv. Nuovo Cimento 31, 247 (2008).Google Scholar
  31. 31.
    T. Lompe, T. B. Ottenstein, F. Serwane, et al., Science 330, 940 (2010).ADSCrossRefGoogle Scholar
  32. 32.
    S. Nakajima, M. Horikoshi, T. Mukaiyama, et al., Phys. Rev. Lett. 106, 143201 (2011).ADSCrossRefGoogle Scholar
  33. 33.
    O. Sørensen, D. V. Fedorov, and A. S. Jensen, Phys. Rev. Lett. 89, 173002 (2002).ADSCrossRefGoogle Scholar
  34. 34.
    R. G. Dall et al., Nature Commun. 2, 291 (2011).ADSCrossRefGoogle Scholar
  35. 35.
    S. Tan, Ann. Phys. (N.Y.) 323, 2952 (2008); Ann. Phys. (N.Y.) 323, 2971 (2008); Ann. Phys. (N.Y.) 323, 2987 (2008).ADSCrossRefMATHGoogle Scholar
  36. 36.
    P. A. Lee, N. Nagaosa, and X.-G. Wen, Rev. Mod. Phys. 78, 17 (2006).ADSCrossRefGoogle Scholar
  37. 37.
    J. T. Stewart, J. P. Gaebler, T. E. Drake, and D.S. Jin, Phys. Rev. Lett. 104, 235301 (2010).ADSCrossRefGoogle Scholar
  38. 38.
    E. D. Kuhnle, H. Hu, X.-J. Liu, et al., Phys. Rev. Lett. 105, 070402 (2010).ADSCrossRefGoogle Scholar
  39. 39.
    E. Braaten, D. Kang, and L. Platter, Phys. Rev. Lett. 106, 153005 (2011).ADSCrossRefGoogle Scholar
  40. 40.
    Y. Castin and F. Werner, Phys. Rev. A 83, 063614 (2011).ADSCrossRefGoogle Scholar
  41. 41.
    R. J. Wild, P. Makotyn, J. M. Pino, et al., Phys. Rev. Lett. 108, 145305 (2012).ADSCrossRefGoogle Scholar
  42. 42.
    A. Altland and B. Simons, Condensed Matter Field Theory, 2nd ed. (Cambridge Univ. Press, 2010).CrossRefMATHGoogle Scholar
  43. 43.
    J. E. Moore, Nature 464, 194 (2010).ADSCrossRefGoogle Scholar
  44. 44.
    M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).ADSCrossRefGoogle Scholar
  45. 45.
    X.-L. Qi and S.-C. Zhang, Rev.Mod. Phys. 83, 1057 (2011).ADSCrossRefGoogle Scholar
  46. 46.
    Z. F. Ezawa, Quantum Hall Effects, 2nd ed. (World Scientific, Singapore, 2008).CrossRefGoogle Scholar
  47. 47.
    N. Curtis et al., Phys. Rev. C 77, 021301 (2008).ADSCrossRefGoogle Scholar
  48. 48.
    K. Ikeda, N. Tagikawa and H. Horiuchi, Prog. Theor. Phys. Suppl., Extra Number, 464 (1968).Google Scholar
  49. 49.
    W. von Oertzen, M. Freer, and Y. Kanada-En’yo, Phys. Rep. 432, 43 (2006).ADSCrossRefGoogle Scholar
  50. 50.
    A. S. Jensen and K. Riisager, Phys. Lett. B 480, 39 (2000).ADSCrossRefGoogle Scholar
  51. 51.
    M. Freer, Rep. Prog. Phys. 70, 2149 (2007).ADSCrossRefGoogle Scholar
  52. 52.
    D. H. Wilkinson, Nucl. Phys. A 452, 296 (1986).ADSCrossRefGoogle Scholar
  53. 53.
    A. S. Jensen and K. Riisager, Nucl. Phys. A 537, 45 (1992).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  • N. A. Baas
    • 1
  • D. V. Fedorov
    • 2
  • A. S. Jensen
    • 2
  • K. Riisager
    • 2
  • A. G. Volosniev
    • 2
  • N. T. Zinner
    • 2
  1. 1.Department of Mathematical SciencesNTNUTrondheimNorway
  2. 2.Department of Physics and AstronomyAarhus UniversityAarhusDenmark

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