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

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Pressure and size dependence of roton emission and vortex creation by moving objects in He II in T→0 limit: Generalized nonlocal Gross-Pitaevskii model

Nicolás P. Müller1,*, Ladislav Skrbek2,†, Yuri A. Sergeev3,‡, and Giorgio Krstulovic4,§

  • *Contact author: nicolas.muller@lpp.polytechnique.fr
  • †Contact author: ladislav.skrbek@matfyz.cuni.cz
  • ‡Contact author: yuri.sergeev@newcastle.ac.uk
  • §Contact author: giorgio.krstulovic@univ-cotedazur.fr
PDF

Phys. Rev. Fluids 11, 104705 – Published 16 October, 2026

DOI: https://doi.org/10.1103/n4hm-rnpj

Abstract

In the framework of the generalized, nonlocal Gross-Pitaevskii (GP) model, we study numerically the pressure- and size-dependent mechanisms of roton emission and vortex nucleation by objects moving in superfluid He4. For each of several pressures in the range from 0 to the solidification pressure of ≈25bar, we chose the parameters of the interatomic interaction potential such that the resulting excitation spectrum for the generalized, nonlocal GP equation approximates fairly accurately the pressure-dependent dispersion curve determined experimentally by Godfrin et al. [Phys. Rev. B 103, 104516 (2021)]. In the two-dimensional approximation, for circular obstacles (disks) moving in quiescent He4, we calculated two critical velocities—one corresponding to the roton emission and the other to the nucleation of quantized vortices—as functions of pressure and the obstacle's size. We also comment briefly on three-dimensional simulations of the roton emission and vortex nucleation by moving spherical obstacles.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (80)

  1. P. Kapitza, Viscosity of liquid helium below the λ-point, Nature (London) 141, 74 (1938).
  2. J. F. Allen and A. D. Misener, Flow of liquid helium II, Nature (London) 141, 75 (1938).
  3. F. London, The λ-phenomenon of liquid helium and the Bose-Einstein degeneracy, Nature (London) 141, 643 (1938).
  4. E. Andronikashvilli, A direct observation of two kinds of motion in helium II, J. Phys. (USSR) 10, 201 (1946).
  5. L. Tisza, Transport phenomena in helium II, Nature (London) 141, 913 (1938); Sur la superconductibilité thermique de l'hélium II liquide et la statistique de Bose-Einstein, C. R. Acad. Sci. 207, 1035 (1938); La viscosité de l'hélium II liquide et la statistique de Bose–Einstein, 207, 1186 (1938).
  6. L. D. Landau, The theory of superfluidity of helium II, J. Phys. (USSR) 5, 71 (1941).
  7. L. D. Landau, On the theory of superfluidity of helium II, J. Phys. (USSR) 11, 91 (1947).
  8. V. Peshkov, Second sound in helium II, J. Phys. (USSR) 8, 381 (1944).
  9. V. P. Peshkov, Determination of the velocity of propagation of the second sound in helium II, J. Phys. (USSR) 10, 389 (1946).
  10. L. Onsager, Statistical hydrodynamics, Nuovo Cimento 6, 279 (1949).
  11. W. F. Vinen, Detection of single quanta of circulation in liquid helium II, Proc. R. Soc. London A 260, 218 (1961).
  12. R. P. Feynman, Application of quantum mechanics to liquid helium, in Progress in Low-Temperature Physics, edited by C. J. Gorter (North Holland, Amsterdam, 1955), Vol. 1, pp. 17–53.
  13. W. F. Vinen, Mutual friction in a heat current in liquid helium II, Proc. R. Soc. A 240, 114 (1957); 240, 128 (1957); 242, 493 (1957); 243, 400 (1958).
  14. R. P. Feynman and M. Cohen, Theory of inelastic scattering of cold neutrons from liquid helium, Phys. Rev. 102, 1189 (1956).
  15. H. Godfrin, K. Beauvois, A. Sultan, E. Krotscheck, J. Dawidowski, B. Fåk, and J. Ollivier, Dispersion relation of Landau elementary excitations and thermodynamic properties of superfluid He4, Phys. Rev. B 103, 104516 (2021).
  16. H. R. Glyde, Excitations in the quantum liquid He4: A review, Rep. Prog. Phys. 81, 014501 (2018).
  17. L. Meyer and F. Reif, Ion motion in superfluid liquid helium under pressure, Phys. Rev. 123, 727 (1961).
  18. G. W. Rayfield and F. Reif, Quantized vortex rings in superfluid helium, Phys. Rev. 136, A1194 (1964).
  19. G. W. Rayfield, Roton emission from negative ions in helium II, Phys. Rev. Lett. 16, 934 (1966).
  20. L. Skrbek and Y. A. Sergeev, Critical velocities in flows of superfluid He4, Phys. Fluids 37, 031305 (2025).
  21. A. Phillips and P. V. E. McClintock, Evidence for roton creation in a superfluid field emission diode near 0.5 K, Phys. Lett. A 46, 109 (1973).
  22. D. R. Allum, P. V. E. McClintock, A. Phillips, and R. M. Bowley, The breakdown of superfluidity in liquid He4: An experimental test of Landau's theory, Philos. Trans. R. Soc. London A 284, 179 (1977).
  23. P. C. E. Stamp, P. V. E. McClintock, and W. M. Fairbairn, Possible influence of thermal rotons on vortex nucleation by negative ions in pressurised He II below 1K, J. Phys. C: Solid State Phys. 12, L589 (1979).
  24. G. G. Nancolas and P. V. E. McClintock, Quenching of the ion/vortex-ring transition in He II by intense electric fields, Phys. Rev. Lett. 48, 1190 (1982).
  25. T. Ellis and P. V. E. McClintock, Effective mass of the normal negative-charge carrier in bulk He II, Phys. Rev. Lett. 48, 1834 (1982).
  26. R. M. Bowley, P. V. E. McClintock, F. E. Moss, G. G. Nancolas, and P. C. E. Stamp, The breakdown of superfluidity in liquid He4: III. Nucleation of quantized vortex rings, Philos. Trans. R. Soc. London A 307, 201 (1982).
  27. T. Ellis and P. V. E. McClintock, The breakdown of superfluidity in liquid He4. V. Measurement of the Landau critical velocity for roton creation, Philos. Trans. R. Soc. London A 315, 259 (1985).
  28. G. G. Nancolas, R. M. Bowley, and P. V. E. McClintock, The breakdown of superfluidity in liquid He4. IV. Influence of He3 isotopic impurities on the nucleation of quantized vortex rings, Philos. Trans. R. Soc. London A 313, 537 (1985).
  29. G. G. Nancolas, T. Ellis, P. V. E. McClintock, and R. M. Bowley, A new form of energy dissipation by a moving object in He II, Nature (London) 316, 797 (1985).
  30. P. C. Hendry, N. S. Lawson, P. V. E. McClintock, C. D. H. Williams, and R. M. Bowley, Macroscopic quantum tunneling of vortices in He II, Phys. Rev. Lett. 60, 604 (1988).
  31. P. C. Hendry, N. S. Lawson, P. V. E. McClintock, C. D. H. Williams, and R. M. Bowley, The breakdown of superfluidity in liquid He4. VI. Macroscopic quantum tunnelling by vortices in isotopically pure He II, Philos. Trans. R. Soc. London A 332, 387 (1990).
  32. P. V. E. McClintock and R. M. Bowley, The Landau critical velocity, in Progress in Low Temperature Physics, edited by W. P. Halperin (Elseivier, New York, 1995), Vol. XIV, pp. 1–68.
  33. R. M. Bowley and F. W. Sheard, Motion of negative ions at supercritical drift velocities in liquid He4 at low temperatures, Phys. Rev. B 16, 244 (1977).
  34. R. M. Bowley, Nucleation of vortex rings by negative ions in liquid helium at low temperatures, J. Phys. C: Solid State Phys. 17, 595 (1984).
  35. C. M. Muirhead, W. F. Vinen, R. J. Donnelly, C. M. Muirhead, W. F. Vinen, and R. J. Donnelly, The nucleation of vorticity in superfluid He4. I. Basic theory, Philos. Trans. R. Soc. Lond. A 311, 433 (1984).
  36. C. F. Barenghi, P. V. E. McClintock, and C. M. Muirhead, Vinen's energy barrier, J. Low Temp. Phys. 212, 185 (2023).
  37. S. V. Iordanskiĭ, Calculation of the critical current of extraneous particles in a Bose system, Sov. Phys. JETP 27, 793 (1968).
  38. G. E. Volovik, Calculation of the critical current for particles decaying into nonparallel excitations, Sov. Phys. JETP 31, 1106 (1970).
  39. J. S. Brooks and R. J. Donnelly, The calculated thermodynamic properties of superfluid helium-4, J. Phys. Chem. Ref. Data 6, 51 (1977).
  40. G. W. Rayfield, Study of the ion-vortex-ring transition, Phys. Rev. 168, 222 (1968).
  41. N. P. Müller and G. Krstulovic, Kolmogorov and Kelvin wave cascades in a generalized model for quantum turbulence, Phys. Rev. B 102, 134513 (2020).
  42. N. P. Müller and G. Krstulovic, Critical velocity for vortex nucleation and roton emission in a generalized model for superfluids, Phys. Rev. B 105, 014515 (2022).
  43. P. Nozières, Is the roton in superfluid He4 the ghost of a Bragg spot? J. Low Temp. Phys. 137, 45 (2004).
  44. S. Balibar, The discovery of superfluidity, J. Low Temp. Phys. 146, 441 (2007).
  45. L. P. Pitaevskiĭ, Properties of the spectrum of elementary excitations near the disintegration threshold of the excitations, Sov. Phys. JETP 36, 830 (1959).
  46. V. I. Marchenko and A. Ya Parshin, On the energy spectrum of helium II, JETP Lett. 87, 327 (2008).
  47. D. D. Awschalom and K. W. Schwarz, Observation of a remanent vortex-line density in superfluid helium, Phys. Rev. Lett. 52, 49 (1984).
  48. W. H. Zurek, Cosmological experiments in superfluid helium? Nature (London) 317, 505 (1985).
  49. W. F. Vinen and L. Skrbek, Quantum turbulence generated by oscillating structures, Proc. Natl. Acad. Sci. 111, 4699 (2014).
  50. R. Goto, S. Fujiyama, H. Yano, Y. Nago, N. Hashimoto, K. Obara, O. Ishikawa, M. Tsubota, and T. Hata, Turbulence in boundary flow of superfluid He4 triggered by free vortex rings, Phys. Rev. Lett. 100, 045301 (2008).
  51. H. J. Maris, Electrons in liquid helium, J. Phys. Soc. Jpn. 77, 111008 (2008).
  52. B. E. Springett and R. J. Donnelly, Pressure dependence of the radius of the negative ion in helium II, Phys. Rev. Lett. 17, 364 (1966).
  53. R. M. Ostermeier, Pressure dependence of charge carrier mobilities in superfluid helium, Phys. Rev. A 8, 514 (1973).
  54. P. V. E. McClintock, An apparatus for preparing isotopically pure He4, Cryogenics 18, 201 (1978).
  55. P. C. Hendry and P. V. E. McClintock, Continuous flow apparatus for preparing isotopically pure He4, Cryogenics 27, 131 (1987).
  56. Such a drag force can be interpreted as a classical viscous force exerted by the normal component of He4.
  57. A charged vortex ring is a structure consisting of a quantized vortex rings with an ion bubble trapped on the vortex core.
  58. N. G. Berloff and P. H. Roberts, Motions in a Bose condensate: VI. Vortices in a nonlocal model, J. Phys. A: Math. Gen. 32, 5611 (1999).
  59. C. Huepe and M.-É. Brachet, Solutions de nucléation tourbillonnaires dans un modele d'écoulement superfluide, C. R. Acad. Sci., Sér. II B 325, 195 (1997).
  60. S. Rica, A remark on the critical speed for vortex nucleation in the nonlinear Schrödinger equation, Physica D 148, 221 (2001).
  61. T. Winiecki, J. F. McCann, and C. S. Adams, Vortex structures in dilute quantum fluids, Europhys. Lett. 48, 475 (1999).
  62. T. Winiecki, B. Jackson, J. F. McCann, and C. S. Adams, Vortex shedding and drag in dilute Bose–Einstein condensates, J. Phys. B: At. Mol. Opt. Phys. 33, 4069 (2000).
  63. C.-T. Pham, C. Nore, and M.-E. Brachet, Boundary layers and emitted excitations in nonlinear Schrödinger superflow past a disk, Physica D 210, 203 (2005).
  64. G. W. Stagg, R. W. Pattinson, C. F. Barenghi, and N. G. Parker, Critical velocity for vortex nucleation in a finite-temperature Bose gas, Phys. Rev. A 93, 023640 (2016).
  65. G. W. Stagg, N. G. Parker, and C. F. Barenghi, Superfluid boundary layer, Phys. Rev. Lett. 118, 135301 (2017).
  66. T. Frisch, S. Nazarenko, and S. Rica, Superflow passing over a rough surface: Vortex nucleation, Phys. Rev. Fluids 9, 024701 (2024).
  67. A. Villois and H. Salman, Vortex nucleation limited mobility of free electron bubbles in the Gross-Pitaevskii model of a superfluid, Phys. Rev. B 97, 094507 (2018).
  68. E. P. Gross, Hydrodynamics of a superfluid condensate, J. Math. Phys. 4, 195 (1963).
  69. J. Dupont-Roc, M. Himbert, N. Pavloff, and J. Treiner, Inhomogeneous liquid He4: A density functional approach with a finite-range interaction, J. Low Temp. Phys. 81, 31 (1990).
  70. Y. Pomeau and S. Rica, Model of superflow with rotons, Phys. Rev. Lett. 71, 247 (1993).
  71. F. Dalfovo, A. Lastri, L. Pricaupenko, S. Stringari, and J. Treiner, Structural and dynamical properties of superfluid helium: A density-functional approach, Phys. Rev. B 52, 1193 (1995).
  72. N. G. Berloff, Nonlocal nonlinear Schrödinger equations as models of superfluidity, J. Low Temp. Phys. 116, 359 (1999).
  73. N. G. Berloff, M. Brachet, and N. P. Proukakis, Modeling quantum fluid dynamics at nonzero temperatures, Proc. Natl. Acad. Sci. USA 111, 4675 (2014).
  74. J. Reneuve, J. Salort, and L. Chevillard, Structure, dynamics, and reconnection of vortices in a nonlocal model of superfluids, Phys. Rev. Fluids 3, 114602 (2018).
  75. T. Lahaye, C. Menotti, L. Santos, M. Lewenstein, and T. Pfau, The physics of dipolar bosonic quantum gases, Rep. Prog. Phys. 72, 126401 (2009).
  76. N. G. Parker and D. H. J. O'Dell, Thomas–Fermi versus one- and two-dimensional regimes of a trapped dipolar Bose–Einstein condensate, Phys. Rev. A 78, 041601(R) (2008).
  77. A. Villois, M. Onorato, and D. Proment, Vortex to roton transition in dipolar Bose-Einstein condensates, Phys. Rev. Lett. 134, 253401 (2025).
  78. G. Krstulovic, A theoretical description of vortex dynamics in superfluids. Kelvin waves, reconnections and particle-vortex interaction, Habilitation à Diriger des Recherches (Université Côte d'Azur, Nice, 2020), https://hal.science/tel-03544830v1.
  79. L. Tuckerman, C. Huepe, and M.-E. Brachet, Instabilities and Nonequilibrium structures IX (Kluwer, Dordrecht, 2004), pp. 75–83.
  80. R. J. Donnelly, Quantized Vortices in Helium II (Cambridge University, Cambridge, 1991).

Outline

Information

Phys. Rev. Fluids 11, 104705– Published 16 October, 2026
  • Received 22 May 2026
  • Accepted 18 September 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation