Skip to main content
SpringerLink
Log in

Joe Vinen and the Transverse Force on Vortex

  • Published:
Journal of Low Temperature Physics Aims and scope Submit manuscript

Abstract

The paper gives a glimpse on the problem of the transverse force on a vortex, its proper determination in general and the role in the process of quantum vortex nucleation. Investigation of this problem is an essential part of the scientific heritage of Joe Vinen as an experimentalist and a theoretician.

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

Similar content being viewed by others

Notes

  1. See discussion of vortex masses of various origins in the book [23].

References

  1. H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, 1997)

    MATH  Google Scholar 

  2. L.D. Landau, E.M. Lifshitz, Fluid Mechanics (Elsevier, Oxford, 1987)

    Google Scholar 

  3. H.E. Hall, W.F. Vinen, The rotation of liquid helium II The theory of mutual friction in uniformly rotating helium II. Proc. R Soc. London Ser. A. 238, 215–234 (1956)

    Article  ADS  MATH  Google Scholar 

  4. W.F. Vinen, The detection of single quanta of circulation in liquid helium II. Proc. Roy. Soc. London A 260, 218–236 (1961)

    Article  ADS  Google Scholar 

  5. P. Nozières, W.F. Vinen, The motion of flux lines in type II superconductors. Philos Magaz: J Theoret Exp Appl Phys 14(130), 667–688 (1966). https://doi.org/10.1080/14786436608211964

    Article  Google Scholar 

  6. E.M. Lifshitz, L.P. Pitaevskii, Absorption of second sound in rotating helium II. Zh. Eksp. Teor. Fiz. 33, 535–537 (1957). [Sov. Phys.–JETP, 6, 418–419 (1958)]

  7. S.V. Iordanskii, Mutual friction force in a rotating Bose gas. Zh. Eksp. Teor. Fiz. 49, 225–236 (1965). [Sov.Phys.- -JETP, 22, 160–167 (1966)]

  8. E.B. Sonin, Friction between the normal component and vortices in rotating superfluid helium. Zh. Eksp. Teor. Fiz. 69, 921–935 (1975). [Sov. Phys.–JETP, 42, 469–475 (1976)]

  9. E.B. Sonin, Magnus force in superfluids and superconductors. Phys. Rev. B 55, 485 (1997)

    Article  ADS  Google Scholar 

  10. E.B. Sonin, The Aharonov-Bohm effect in neutral liquids. J. Phys. A 43, 354003 (2010)

    Article  MATH  Google Scholar 

  11. Y. Aharonov, D. Bohm, Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485–491 (1959)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Y.M. Gal’perin, E.B. Sonin, Motion of vortices and electrical conductivity of pure type II supercomductors in weak magnetic fields. Fiz. Tverd. Tela (Leningrad) 18, 3034–3041 (1976). [Sov. Phys.–Solid State, 18, 1768–1772 (1976)]

  13. N.B. Kopnin, V.E. Kravtsov, Conductivity and Hall effect of pure type-II superconductors at low temperatures. Pis’ma Zh. Eksp. Teor. Fiz. 23, 631–634 (1976). [JETP Lett., 23, 578–581 (1976)]

  14. P. Ao, D.J. Thouless, Berry’s phase and the Magnus force for a vortex line in a superconductor. Phys. Rev. Lett. 70, 2158–2161 (1993)

    Article  ADS  Google Scholar 

  15. H.E. Hall, J.R. Hook, Comment on “Magnus and Iordanskii forces in superfluids". Phys. Rev. Lett. 80, 4356–4356 (1998). https://doi.org/10.1103/PhysRevLett.80.4356

    Article  ADS  Google Scholar 

  16. C. Wexler, D.J. Thouless, P. Ao, Q. Niu, Wexler et al. reply. Phys. Rev. Lett. 80, 4357–4357 (1998). https://doi.org/10.1103/PhysRevLett.80.4357

  17. E.B. Sonin, Comment on “Berry’s phase and the Magnus force for a vortex line in a superconductor," “Transverse force on a quantized vortex in a superfluid," and “Magnus and Iordanskii forces in superfluids.” Phys. Rev. Lett. 81, 4276–4276 (1998). https://doi.org/10.1103/PhysRevLett.81.4276

  18. C. Wexler, D.J. Thouless, P. Ao, Q. Niu, Wexler et al. reply. Phys. Rev. Lett. 81, 4277–4277 (1998). https://doi.org/10.1103/PhysRevLett.81.4277

  19. D.J. Thouless, M.R. Geller, W.F. Vinen, J.-Y. Fortin, S.W. Rhee, Vortex dynamics in the two-fluid model. Phys. Rev. B 63, 224504 (2001)

    Article  ADS  Google Scholar 

  20. E.B. Sonin, Magnus force and Aharonov-Bohm effect in superfluids, in Vortices in Unconventional Superconductors and Superfluids. ed. by R.P. Huebener, N. Schopohl, G.E. Volovik (Springer, Berlin, 2002), pp.119–145

    Chapter  Google Scholar 

  21. W.F. Vinen, Vortex lines in liquid helium II, in Progress in Low Temperature Physics, vol. 3, ed. by C.J. Gorter (North-Holand, Amsterdam, 1961), pp.1–57

    Chapter  Google Scholar 

  22. W.F. Vinen, Critical velocities in liquid helium II, in Liquid Helium: Proceeding of the International School of Physics “Enrico Fermi,” vol. XXI, ed. by G. Careri (Academic Press, New York, 1963), pp.336–355

  23. E.B. Sonin, Dynamics of Quantised Vortices in Superfluids (Cambridge University Press, Cambridge, 2016)

    MATH  Google Scholar 

  24. N.B. Kopnin, Theory of Nonequilibrium Superconductivity (Oxford University Press, Oxford, 2001)

    Book  Google Scholar 

  25. E.B. Sonin, Transverse forces on vortices in superfluids in a periodic potential. Phys. Rev. B 94, 054521 (2016). https://doi.org/10.1103/PhysRevB.94.054521

    Article  ADS  Google Scholar 

  26. M.R. Geller, C. Wexler, D.J. Thouless, Transverse force on a quantized vortex in a superconductor. Phys. Rev. B 57, 8119–8122 (1998)

    Article  ADS  Google Scholar 

  27. P. Matheiu, Y. Simon, Hydrodynamic theory of mutual friction in He II. Phys. Rev. Lett. 45, 1428–1431 (1980)

    Article  ADS  Google Scholar 

  28. C. Muirihead, W.F. Vinen, R.J., Donnelly, The nucleation of vorticity by ions in superfluid \(^4\)He. I. Basic theory. Phil. Trans. Roy. Soc. Lon. A 311, 433–487 (1984)

  29. J.C. Davis, J.D. Close, R. Zieve, R.E. Packard, Observation of quantized circulation in superfluid \(^3\)He-B. Phys. Rev. Lett. 66, 329–332 (1991)

    Article  ADS  Google Scholar 

  30. A.O. Caldeira, A.J. Leggett, Quantum tunneling in a dissipative system. Ann. Phys. (NY) 149, 374–456 (1983)

    Article  ADS  Google Scholar 

  31. L.D. Landau, E.M. Lifshitz, Quantum Mechanics (Pergamon Press, Oxford, 1982)

    MATH  Google Scholar 

  32. G. Blatter, M.V. Feigel’man, V.B. Geshkenbein, A.I. Larkin, V.M. Vinokur, Vortices in high-temperature superconductors. Rev. Mod. Phys. 66, 1125–1388 (1994)

    Article  ADS  Google Scholar 

  33. G.E. Volovik, Quantum-mechanical formation of vortices in a superfluid liquid. Pis’ma Zh. Eksp. Teor. Fiz. 15, 116–120 (1972). [JETP Lett., 15, 81–83 (1972)]

  34. E.B. Sonin, Nucleation and creep of vortices in superfluids and clean superconductors. Physica B 210, 234–250 (1995)

    Article  ADS  Google Scholar 

  35. E.B. Sonin, Critical velocities at very low temperatures and the vortices in a quantum Bose fluid. Zh. Eksp. Teor. Fiz. 64, 970–983 (1973). [Sov. Phys.–JETP, 37, 494–500 (1973)]

Download references

Acknowledgements

My numerous interactions and discussions with Joe Vinen during the Royal Society Kapitza fellowship in Birmingham and at other various occasions had a great impact on my research work.

Author information

Authors and Affiliations

  1. Racah Institute of Physics, Hebrew University of Jerusalem, Givat Ram, 9190401, Jerusalem, Israel

    Edouard Sonin

Authors
  1. Edouard Sonin
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

ES as the only author is responsible for the whole content of the paper.

Corresponding author

Correspondence to Edouard Sonin.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sonin, E. Joe Vinen and the Transverse Force on Vortex. J Low Temp Phys 212, 306–320 (2023). https://doi.org/10.1007/s10909-023-02977-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10909-023-02977-z

Keywords

Search

Navigation