On the Absence of Moderate-Velocity Persistent Currents in He II Films Adsorbed on Large Cylinders

  • T. Wang
  • I. Rudnick


Consider a glass cylinder approximately 1 in. in diameter as shown in Fig. 1, and suppose there is an adsorbed film of helium on the outer surface. Suppose this film is rotating about the axis of the cylinder. Then the superfluid velocity v s must obey the Onsager-Feynman relation
$$\int {{\upsilon _s}} \cdot dl = nh/m$$
where h is Planck’s constant, n is an integer, and m is the mass of the helium atom. Moreover, if the speed is not great, it is energetically unfavorable to have vortex lines (parallel to the axis of the cylinder), and the circulation given by Eq. (1) is the same along any path lying in the film and encircling the cylinder. The helium is in a unique quantum state and one which may be characterized by a very high quantum number (if v s ≃ 10 cm sec−1 then n ≃ 105). The velocity v s must vary as r −1, where r is the radius, if the circulation is to be a constant, but since the films we are concerned with are always significantly thinner than 102 Å, the velocity should be sensibly constant throughout the film.


Saturated Vapor Pressure Helium Atom Vortex Line Glass Cylinder Adsorbed Film 
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Copyright information

© Springer Science+Business Media New York 1974

Authors and Affiliations

  • T. Wang
    • 1
  • I. Rudnick
    • 1
  1. 1.Physics DepartmentUniversity of CaliforniaLos AngelesUSA

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