Vortices in an Imperfect Bose Gas. IV. Translational Velocity

Alexander L. Fetter

doi:10.1103/PhysRev.151.100

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Vortices in an Imperfect Bose Gas. IV. Translational Velocity

Alexander L. Fetter

Institute of Theoretical Physics, Department of Physics, Stanford University, Stanford, California

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Phys. Rev. 151, 100 – Published 4 November, 1966

DOI: https://doi.org/10.1103/PhysRev.151.100

Abstract

The translational velocity of a vortex with circulation $\frac{h}{m}$ in an imperfect Bose gas is calculated by considering the time dependence of the condensate wave function corresponding to a given initial configuration of vortices. Each vortex in a system of rectilinear vortices is shown to move with the local fluid velocity at its core; a vortex ring of radius $R$ is shown to move with velocity $(\frac{h}{4 π mR}) \ln (\frac{8 R}{α})$ , where $α$ is a length the order of the core size. Both results agree with the predictions of classical hydrodynamics.

References (17)

A. Sommerfeld, Mechanics of Deformable Bodies (Academic Press Inc., New York, 1950), p. 132
[1], pp. 154-155
[1], pp. 165-167
G. W. Rayfield and F. Reif, Phys. Rev. 136, A1194 (1964)
A. L. Fetter, Phys. Rev. 138, A429 (1965)
K. Huang and A. C. Olinto, Phys. Rev. 139, A1441 (1965)
D. Amit and E. P. Gross, Phys. Rev. 145, 130 (1966)
E. P. Gross, Nuovo Cimento 20, 454 (1961)
L. P. Pitaevskii, Zh. Eksperim. i Teor. Fiz. 40, 646 (1961)
P. C. Hohenberg and P. C. Martin, Ann. Phys. (N. Y.) 34, 291 (1965)
[7]
H. Lamb, Hydrodynamics (Dover Publications, Inc., New York, 1945), 6th ed., p. 237
H. B. Dwight, Tables of Integrals and Other Mathematical Data (The Macmillan Company, New York, 1957), 3rd ed., pp. 170-173
Omitted endnote
E. P. Gross, J. Math. Phys. 4, 195 (1963)
P. H. Borcherds, C. E. Gough, W. F. Vinen, and A. C. Warren, Phil. Mag. 10, 349 (1964) Y. B. Kim, C. F. Hempstead, and A. R. Strnad, Phys. Rev. 139, A1163 (1965)
J. Bardeen and M. J. Stephen, Phys. Rev. 140, A1197 (1965)

[c1] A. Sommerfeld, Mechanics of Deformable Bodies (Academic Press Inc., New York, 1950), p. 132

[c2] [1], pp. 154-155

[c3] [1], pp. 165-167

[c4] G. W. Rayfield and F. Reif, Phys. Rev. 136, A1194 (1964)

[c5] A. L. Fetter, Phys. Rev. 138, A429 (1965)

[c6] K. Huang and A. C. Olinto, Phys. Rev. 139, A1441 (1965)

[c7] D. Amit and E. P. Gross, Phys. Rev. 145, 130 (1966)

[c8] E. P. Gross, Nuovo Cimento 20, 454 (1961)

[c9] L. P. Pitaevskii, Zh. Eksperim. i Teor. Fiz. 40, 646 (1961)

[c10] P. C. Hohenberg and P. C. Martin, Ann. Phys. (N. Y.) 34, 291 (1965)

[c11] [7]

[c12] H. Lamb, Hydrodynamics (Dover Publications, Inc., New York, 1945), 6th ed., p. 237

[c13] H. B. Dwight, Tables of Integrals and Other Mathematical Data (The Macmillan Company, New York, 1957), 3rd ed., pp. 170-173

[c14] Omitted endnote

[c15] E. P. Gross, J. Math. Phys. 4, 195 (1963)

[c16] P. H. Borcherds, C. E. Gough, W. F. Vinen, and A. C. Warren, Phil. Mag. 10, 349 (1964) Y. B. Kim, C. F. Hempstead, and A. R. Strnad, Phys. Rev. 139, A1163 (1965)

[c17] J. Bardeen and M. J. Stephen, Phys. Rev. 140, A1197 (1965)

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Vortices in an Imperfect Bose Gas. IV. Translational Velocity

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Vortices in an Imperfect Bose Gas. I. The Condensate

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