Skip to main content
SpringerLink
Log in

Astrophysical quantum matter: spinless charged particles on a magnetic dipole sphere

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

We consider the quantum mechanics of a spinless charged particle on a 2-dimensional sphere. When threaded with a magnetic monopole field, this is the well-known Haldane sphere that furnishes a translationally-invariant, incompressible quantum fluid state of a gas of electrons confined to the sphere. This letter presents the results of a novel variant of the Haldane solution where the monopole field is replaced by that of a dipole. We argue that this system is relevant to the physics on the surface of compact astrophysical objects like neutron stars.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. While \(\sim 10^{14}\)T magnetic fields are achievable in heavy-ion collisions at, for example the LHC, these are out of equilibrium and too short-lived to be relevant for our purposes.

  2. Although it must be pointed out that it is likely not pure dipole. Like the sun, there are multipole moments that decay rapidly with radius. We thank Bryan Gaensler for reminding us of this.

References

  1. Wright, E. et al.: Ant-Man, Marvel Cinematic Universe (2015)

  2. Haldane, F.D.M.: Phys. Rev. Lett. 51, 605 (1983). https://doi.org/10.1103/PhysRevLett.51.605

    Article  ADS  MathSciNet  Google Scholar 

  3. Jain, J.: Composite Fermions. Cambridge University Press, Cambridge (2007). https://doi.org/10.1017/CBO9780511607561

    Book  MATH  Google Scholar 

  4. Haldane, F., Rezayi, E.: Phys. Rev. B 31(4), 2529 (1985). https://doi.org/10.1103/PhysRevB.31.2529

    Article  ADS  Google Scholar 

  5. Bellucci, S., Onorato, P.: Phys. Rev. B 82, 205305 (2010). https://doi.org/10.1103/PhysRevB.82.205305

    Article  ADS  Google Scholar 

  6. Wen, X.G., Niu, Q.: Phys. Rev. B 41, 9377 (1990). https://doi.org/10.1103/PhysRevB.41.9377

    Article  ADS  Google Scholar 

  7. https://tinyurl.com/y78w9xw3

  8. Heyl, J., Caiazzo, I.: Galaxies 6(3), 76 (2018). https://doi.org/10.3390/galaxies6030076

  9. Störmer, C.: Arch. Sci. Phys. Nat 24, (1907)

  10. Dragt, A.J.: Rev. Geophys. 3, 2 (1965). https://doi.org/10.1029/RG003i002p00255

    Article  Google Scholar 

  11. Grosse, H., Martin, A., Stubbe, J.: Phys. Lett. A 181, 7 (1993). https://doi.org/10.1016/0375-9601(93)91115-L

    Article  ADS  MathSciNet  Google Scholar 

  12. Fano, G., Ortolani, F., Colombo, E.: Phys. Rev. B 34, 2670 (1986). https://doi.org/10.1103/PhysRevB.34.2670

    Article  ADS  Google Scholar 

  13. Morse, P.M., Feshbach, H.: McGraw-Hill Book Co. Inc, New York NY (1953)

  14. Murugan, J., Shock ,J.P., Slayen, R.P.: In preparation

  15. E. Berti, V. Cardoso and M. Casals, Phys. Rev. D 73, 024013 (2006) Erratum: [Phys. Rev. D 73, 109902 (2006)] https://doi.org/10.1103/PhysRevD.73.109902

  16. Hod, S.: Phys. Lett. B 746, 365 (2015). https://doi.org/10.1016/j.physletb.2015.05.036

  17. Kramer, M., Strappers, B.: [arXiv:1507.04423 [astro-ph.IM]]

  18. Can, T., Laskin, M., Wiegmann, P.: Ann. Phys. 362, 752 (2015). https://doi.org/10.1016/j.aop.2015.02.013

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We would like to thank Bryan Gaensler for very useful comments on the manuscript. JM is supported by the NRF of South Africa under Grant CSUR 114599. RPS is supported by a graduate fellowship from the National Institute for Theoretical Physics.

Author information

Authors and Affiliations

  1. The Laboratory for Quantum Gravity and Strings and, Department of Mathematics and Applied Mathematics, Univeristy of Cape Town, Rondebosch, 7700, South Africa

    Jeff Murugan, Jonathan P. Shock & Ruach Pillay Slayen

  2. National Institute for Theoretical, Physics, Stellenbosch University, Stellenbosch Institute of Advanced Study, Private Bag X1, Matieland, 7602, South Africa

    Jonathan P. Shock

Authors
  1. Jeff Murugan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jonathan P. Shock
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ruach Pillay Slayen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jeff Murugan.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Murugan, J., Shock, J.P. & Slayen, R.P. Astrophysical quantum matter: spinless charged particles on a magnetic dipole sphere. Gen Relativ Gravit 53, 29 (2021). https://doi.org/10.1007/s10714-020-02783-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-020-02783-y

Keywords

Search

Navigation