Long-Range Order in Superfluid Helium

J. W. Kane; L. P. Kadanoff

doi:10.1103/PhysRev.155.80

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Long-Range Order in Superfluid Helium

J. W. Kane^*

L. P. Kadanoff^†

Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York

Department of Physics, University of Illinois, Urbana, Illinois

^*Parts of this paper are based on a thesis submitted to the University of Illinois in partial fulfillment of the requirements of the Ph.D. degree.
^†A. P. Sloan Foundation Fellow.

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Phys. Rev. 155, 80 – Published 5 March, 1967

DOI: https://doi.org/10.1103/PhysRev.155.80

Abstract

Fluctuations in the phase of the condensate wave function appearing in the single-particle Green's function for a condensed Bose system are examined in one, two, and three dimensions. The results indicate that at nonzero temperatures, long-range order will appear only in three dimensions.

References (18)

C. N. Yang, Rev. Mod. Phys. 34, 694 (1962)
T. M. Rice [Phys. Rev. 140, A1889 (1965)]
L. P. Kadanoff and P. C. Martin, Ann. Phys. (N. Y.) 24, 419 (1963)
L. Tisza, Nature 141, 913 (1938)
L. Landau, J. Phys. USSR 5, 71 (1941) I. M. Khalatnikov, Introduction to the Theory of Superfluidity (W. A. Benjamin, Inc., New York, 1965)
P. C. Hohenberg and P. C. Martin, Phys. Rev. Letters 12, 69 (1964) Ann. Phys. (N. Y.) 34, 291 (1965)
O. Penrose and L. Onsager, Phys. Rev. 104, 576 (1956)
J. W. Kane and L. P. Kadanoff, J. Math. Phys. 6, 1902 (1965)
B. Ambegaokar and L. P. Kadanoff, Nuovo Cimento 22, 914 (1961)
R. Kubo, J. Phys. Soc. Japan 17, 1100 (1962)
Omitted endnote
N. Bogoliubov, Hydrodynamics of the Superfluid Liquid (Dubna, USSR, 1963)
Omitted endnote
D. Pines, in Many-Body Theory, 1965 Tokyo Summer Lectures in Theoretical Physics, edited by R. Kubo (W. A. Benjamin, Inc., New York, 1966)
[5]
L. D. Landau and E. M. Lifshitz, Statistical Physics (Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1958)
G. V. Chester and L. Reatto (to be published)
F. Dyson (private communication)

[c1] C. N. Yang, Rev. Mod. Phys. 34, 694 (1962)

[c2] T. M. Rice [Phys. Rev. 140, A1889 (1965)]

[c3] L. P. Kadanoff and P. C. Martin, Ann. Phys. (N. Y.) 24, 419 (1963)

[c4] L. Tisza, Nature 141, 913 (1938)

[c5] L. Landau, J. Phys. USSR 5, 71 (1941) I. M. Khalatnikov, Introduction to the Theory of Superfluidity (W. A. Benjamin, Inc., New York, 1965)

[c6] P. C. Hohenberg and P. C. Martin, Phys. Rev. Letters 12, 69 (1964) Ann. Phys. (N. Y.) 34, 291 (1965)

[c7] O. Penrose and L. Onsager, Phys. Rev. 104, 576 (1956)

[c8] J. W. Kane and L. P. Kadanoff, J. Math. Phys. 6, 1902 (1965)

[c9] B. Ambegaokar and L. P. Kadanoff, Nuovo Cimento 22, 914 (1961)

[c10] R. Kubo, J. Phys. Soc. Japan 17, 1100 (1962)

[c11] Omitted endnote

[c12] N. Bogoliubov, Hydrodynamics of the Superfluid Liquid (Dubna, USSR, 1963)

[c13] Omitted endnote

[c14] D. Pines, in Many-Body Theory, 1965 Tokyo Summer Lectures in Theoretical Physics, edited by R. Kubo (W. A. Benjamin, Inc., New York, 1966)

[c15] [5]

[c16] L. D. Landau and E. M. Lifshitz, Statistical Physics (Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1958)

[c17] G. V. Chester and L. Reatto (to be published)

[c18] F. Dyson (private communication)

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Long-Range Order in Superfluid Helium

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