Abstract
In 1938 London [1,2] offered an explanation of the observation earlier that year of superfluid behavior in liquid 4He when it is cooled below a critical temperature of 2.17 °K. He argued that the superfluid transition was analogous to the Bose condensation of an (ideal) gas of non-interacting atoms obeying the same Bose-Einstein spin-statistics relation as 4He atoms. This relation requires the many-atom wave function to be completely symmetric in the atomic coordinates, resulting in a preference for the atoms to occupy the same single-particle states. For a finite system of atoms the momenta are quantized in spacings proportional to the inverse of the system size. At high temperatures the fraction of atoms occupying any one of the momentum states also scales as the inverse of the size. However, as the temperature is reduced below a critical Bose condensation temperature a significant fraction of the atoms, independent of the system size, begins to occupy the zero-momentum state. The Bose condensate fraction of an ideal gas approaches one at zero temperature. For 4He, by analogy, at high temperatures in the normal fluid the condensate fraction should be zero, but as temperatures are reduced below the superfluid transition temperature the condensate fraction should rise to a non-zero value. The effect of the strong interactions among the (non-ideal) 4He atoms is to deplete the zero temperature condensate fraction from one in an ideal gas to a value much less than one for 4He. While the analogy between superfluidity and Bose condensation is imperfect, the concept of a Bose condensate in the superfluid phase has survived. A variety of increasingly sophisticated many-body calculations have predicted a condensate fraction of about 10 % at zero temperature in superfluid 4He at SVP. Because of the importance of superfluidity and the related phenomenon of superconductivity to condensed matter physics, this simple prediction has motivated a more than twenty year effort involving up to one hundred scientists to measure the Bose condensate fraction in 4He.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
F. London, Nature 141, 643 (1938).
For a tutorial discussion of the relation beween Bose condensation and superfluidity see D. R. Tilley, J. Tilley, Superfluidity and Superconductivity-2nd edition, Adam Hilger Ltd., 1986.
For a complete review of the current state of the art, see Momentum Distributions, R. N. Silver, P. E. Sokol, eds., Plenum Press, 1989. For an introductory survey of momentum distribution studies across all of physics, see the article by P. E. Sokol, R. N. Silver, J. W. Clark, p. 1-38.
P. C. Hohenberg, P. M. Platzman, Phys. Rev. 152, 198 (1966); see also A. Miller, D. Pines, P. Nozieres, Phys. Rev. 127, 1452 (1962).
G. B. West, Physics Reports 18C, 263 (1975); see also G. B. West, in ref. [3], p. 95-110.
J. W. Clark, R. N. Silver, Proceedings of the Third International Conference on Nuclear Reaction Mechanisms, Varenna, Italy, June 13-18, 1988, E. Gadioli, ed. (Ricerca Scientifica ed Educazione Permanente, Universita degli Studi di Milano), Supplemento 66, p. 531-540(1988).
W. G. Stirling, E. F. Talbot, B. Tanatar, H. R. Glyde, J. Low Temperature Physics, 73, 33 (1988)
T. R. Sosnick, W. M. Snow, P. E. Sokol, R. N. Silver, Europhysics Letters 9, 707 (1989).
P. Whitlock, R. M. Panoff, Can. J. Phys. 65, 1409 (1987).
D. M. Ceperley, E. L. Pollock, Can. J. Phys. 65, 1416 (1987); see also D. M. Ceperley, in ref. [3], p. 71-80.
For reviews, see H. R. Glyde, E. C. Svensson, in Methods of Experimental Physics, V. 23B, D. L. Price, K. Skold, eds., Academic Press, 1987, p. 303-404; E. C. Svensson, V. F. Sears, Physica 137B, 126-140 (1986).
V. F. Sears, E. C. Svensson, P. Martel, A. D. B. Woods, Phys. Rev. Lett. 49, 279 (1982).
P. Martel, E. C. Svensson, A. D. B. Woods, V. F. Sears, R. A. Cowley, J. Low Temp. Phys. 23, 285 (1976).
J. Gavoret, P. Nozieres, Ann. Phys. (N.Y.) 28, 349 (1964); P. C. Hohenberg, P. C. Martin, Ann. Phys. (N. Y.) 34, 291 (1965).
A. Griffin, Phys. Rev. B32, 3289 (1985).
R. K. B. Helbing, J. Chem. Phys. 50, 493 (1969).
H. A. Gersch, L. J. Rodriguez, Phys. Rev. A8, 905 (1973).
L. J. Rodriguez, H. A. Gersch, H. A. Mook, Phys. Rev. A9, 2085 (1974).
P. Martel, E. C. Svensson, A. D. B. Woods, V. F. Sears, R. A. Cowley, J. Low Temp. Phys. 23, 285(1986).
See also H. R. Glyde, W. G. Stirling, in ref. [3], p. 111-122.
R. N. Silver in Condensed Matter Theories V. 3, J. S. Arponen, R. F. Bishop, M. Manninen, eds., p. 131–142, Plenum Press, 1988.
R. N. Silver, Phys. Rev. B37, 3794 (1988); ibid B38, 2283 (1988). The latter paper contains a rather complete list of theoretical papers on final state effects in deep inelastic neutron scattering.
A. Rinat, M. Butler, to be published.
R. W. Zwanzig, Physica (Utrecht) 30, 1109 (1964); see also P. N. Argyres, J. L. Sigel, Phys. Rev. Letts. 31, 1397 (1973); Phys. Rev. B9, 3197 (1974).
R. K. B. Helbing, J. Chem. Phys. 50, 493 (1969).
R. N. Silver, Phys. Rev. B39, 4022 (1989).
M. L. Ristig, J. W. Clark, in ref. [3], p. 365-370; M. L. Ristig, J. W. Clark, Phys. Rev. B40, 4355 (1989).
P. E. Sokol, T. R. Sosnick, W. M. Snow, in ref. [3], p. 139-158.
K. Herwig, W. M. Snow, P. E. Sokol, to be published.
E. Manousakis, V. R. Pandharipande, Q. N. Usmani, Phys. Rev. B31, 7022 (1985); E. Manousakis, V. R. Pandharipande, ibid., 7029; see also, E. Manousakis, in ref. [3], 81-94.
D. S. Sivia, R. N. Silver, in ref. [3], p. 377-380.
P. E. Sokol, R. N. Silver, T. R. Sosnick, W. M. Snow, in ref. [3], 385-392; W. M. Snow, T. R. Sosnick, P. E. Sokol, R. N. Silver, to be published.
This is essentially the same as P. M. Platzman, N. Tzoar, Phys. Rev. B30, 6397 (1984).
We thank Prof. Gersch for coming out of retirement to perform these calculations.
R. N. Silver, to be published.
R. Feltgen, H. Kirst, K. A. Koehler, F. Torello, J. Chem. Phys. 26, 2360 (1982).
P. Whitlock, R. M. Panoff, Can. J. Phys. 65, 1409 (1987); see also R. M. Panoff, P. A. Whitlock, in ref. [3], p. 59-70.
E. Manousakis, S. Fantoni, V. R. Pandharipande, Phys. Rev. B28, 3370 (1983).
J. P. Bouchaud, C. Lhuillier, Europhys. Lett. 3, 1273 (1987); J. P. Bouchaud, C. Lhuillier, Z. Phys. B75, 283 (1989).
For an experimental review, see I. Sick, in ref. [3], p. 175-186; D. Day, in ref. [3], p. 319-332.
For a theoretical discussion, see O.Benhar, A. Fabrocini, S.Fantoni, in ref. [3], p. 187-202.
V. R. Pandharipande, R. B. Wiringa, B. D. Day, Phys. Lett. 57B, 205 (1975).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer Science+Business Media New York
About this chapter
Cite this chapter
Silver, R.N., Sokol, P.E. (1990). Bose Condensate in Superfluid 4He and Momentum Distributions by Deep Inelastic Scattering. In: Avishai, Y. (eds) Recent Progress in Many-Body Theories. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3798-4_20
Download citation
DOI: https://doi.org/10.1007/978-1-4615-3798-4_20
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6693-5
Online ISBN: 978-1-4615-3798-4
eBook Packages: Springer Book Archive