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Vortex Dynamics: Quantum Versus Classical Regimes

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Abstract

For many years the classical Hall-Vinen-Iordanski (HVI) equation has been used to analyse vortex dynamics in superfluids. Here we discuss the extension of the theory of vortex dynamics to the quantum regime, in which the characteristic vortex frequency is higher than the temperature. At the same time we justify, in the low-frequency classical regime, the use of the HVI equation, provided an inertial mass term and a noise fluctuation term are added to it. The crossover to the quantum regime is discussed, and an intuitive picture is given of the vortex dynamics, which in general is described by 2 equations (one for the vortex coordinate, and one for its quantum fluctuations); we also discuss the simple equation of motion found in the extreme quantum regime.

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Notes

  1. Another example of a higher-dimensional quantum soliton system in which quasiparticle-soliton interactions have been treated (in this case using semi-classical methods) is the Skyrme model—see, e.g. [19–21].

  2. For a vortex near the centre of a circular cylinder of radius R o , we have a hydrodynamic vortex mass \(M_{v} = \pi\rho_{s} a_{o}^{2} [ \ln(R_{o}/a_{o}) + \gamma_{E} + 1/4]\).

References

  1. W.F. Vinen, Nature 181, 1524 (1958)

    Article  ADS  Google Scholar 

  2. H.E. Hall, W.F. Vinen, Proc. R. Soc. A 238, 204, 215 (1956)

    Google Scholar 

  3. S.V. Iordanskii, Ann. Phys. 29, 335 (1964)

    Article  ADS  Google Scholar 

  4. D.J. Thouless, J.R. Anglin, Phys. Rev. Lett. 99, 105301 (2007)

    Article  ADS  Google Scholar 

  5. D.J. Thouless, P. Ao, Q. Niu, Phys. Rev. Lett. 76, 3758 (1996)

    Article  ADS  Google Scholar 

  6. E.B. Sonin, Phys. Rev. B 55, 485 (1997)

    Article  ADS  Google Scholar 

  7. A.L. Fetter, Phys. Rev. 136, A1488 (1964)

    Article  MathSciNet  ADS  Google Scholar 

  8. C. Wexler, D.J. Thouless, Phys. Rev. B 58, R8897 (1998)

    Article  ADS  Google Scholar 

  9. M. Stone, Phys. Rev. B 61, 11780 (2000)

    Article  ADS  Google Scholar 

  10. L. Thompson, P.C.E. Stamp, Phys. Rev. Lett. 108, 184501 (2012)

    Article  ADS  Google Scholar 

  11. D.J. Thouless et al., Phys. Rev. B 63, 224504 (2001)

    Article  ADS  Google Scholar 

  12. L. Thompson, P.C.E. Stamp, in preparation

  13. L. Thompson, PhD thesis, University of British Columbia (2011)

  14. R. Rajaraman, Solitons and Instantons (Elsevier, Amsterdam, 1987)

    MATH  Google Scholar 

  15. T.D. Lee, Particle Physics and Introduction to Field Theory (Harwood Academic, Reading, 1981). Ch. 7

    Google Scholar 

  16. O. Penrose, L. Onsager, Phys. Rev. 104, 576 (1956)

    Article  ADS  MATH  Google Scholar 

  17. C.N. Yang, Rev. Mod. Phys. 34, 694 (1962)

    Article  ADS  Google Scholar 

  18. J.S. Langer, Phys. Rev. 167, 183 (1968)

    Article  ADS  Google Scholar 

  19. M.P. Mattis, M. Karliner, Phys. Rev. D 31, 2833 (1985)

    Article  ADS  Google Scholar 

  20. N. Dorey, J. Hughes, M.P. Mattis, Phys. Rev. D 49, 3598 (1994)

    Article  ADS  Google Scholar 

  21. B.M.A.G. Piette, B.J. Schroers, W.J. Zakrzevski, Nucl. Phys. B 439, 205 (1995)

    Article  ADS  MATH  Google Scholar 

  22. A.L. Fetter, Phys. Rev. 186, 128 (1969)

    Article  ADS  Google Scholar 

  23. P. Ao, D.J. Thouless, Phys. Rev. Lett. 72, 132 (1994)

    Article  ADS  Google Scholar 

  24. Q. Niu, P. Ao, D.J. Thouless, Phys. Rev. Lett. 72, 1706 (1994)

    Article  ADS  Google Scholar 

  25. R.P. Feynman, F.L. Vernon, Ann. Phys. 24, 118 (1963)

    Article  MathSciNet  ADS  Google Scholar 

  26. A.O. Caldeira, A.J. Leggett, Ann. Phys. 149, 374 (1983)

    Article  ADS  Google Scholar 

  27. T. Cox, P.C.E. Stamp, J. Low Temp. Phys. (2012). doi:10.1007/s10909-012-0731-3 this issue

Download references

Acknowledgements

This work was supported by funding from NSERC, from PITP, and from CIFAR. The work benefited greatly from discussions at various times with (and encouragement from) David Thouless; we also thank Bill Unruh and Gordon Semenoff for useful comments.

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Authors and Affiliations

  1. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    L. Thompson

  2. Department of Physics and Astronomy, Pacific Institute of Theoretical Physics, University of British Columbia, 6224 Agricultural Rd., Vancouver, BC, Canada, V6T 1Z1

    P. C. E. Stamp

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  1. L. Thompson
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  2. P. C. E. Stamp
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Correspondence to P. C. E. Stamp.

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Thompson, L., Stamp, P.C.E. Vortex Dynamics: Quantum Versus Classical Regimes. J Low Temp Phys 171, 526–538 (2013). https://doi.org/10.1007/s10909-012-0727-z

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