Abstract
We report high-resolution measurements at saturated vapor pressure of the thermal resistivity R of superfluid 4He over the reduced-temperature range 3×10−7<t≡1−T/T λ <3×10−5 (T λ is the transition temperature for Q=0) and heat-current-density range 4<Q<200 μW/cm2. For smaller Q and t, no thermal resistance was detectable below a transition at T c(Q)<T λ. For Q≳10 μW/cm2 we find that the results can be described well by R=(t/t 0)−2.8 K cm/W with t 0=(Q/Q 0)0.904 and Q 0=393 W/cm2. Thus R has an incipient divergence at T λ which is, however, supplanted by T c(Q) where R remains finite. The results imply R∝Q (m−1) with m=3.53±0.02. This differs from the original assumption m=3 of Gorter and Mellink, and from experimental results obtained well below T λ. However, it agrees with measurements by Leiderer and Pobell at larger currents and further below but still close to T λ. Our measurements could not resolve a critical heat current for the onset of resistance.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
L. D. Landau, J. Phys. USSR 5, 71 (1941) [English translation: Collected Papers of L. D. Landau, edited by D. ter Haar, Gordon and Breach, New York (1965), p. 301].
I. M. Khalatnikov, An Introduction to the Theory of Superfluidity, Benjamin, New York (1965).
D. F. Brewer, D. O. Edwards, and K. Mendelssohn, Phil. Mag. 1, 1130 (1956).
D. F. Brewer and D. O. Edwards, Phil. Mag. 6, 775 (1961).
J. R. Clow and J. D. Reppy, Phys. Rev. Lett. 19, 291 (1967); Phys. Rev. A 5, 424 (1972).
For a review, see for instance, J. T. Tough, Superfluid Turbulence, in Prog. Low Temp. Phys. VIII, edited by D. F. Brewer, North Holland, Amsterdam (1982), Ch. 3.
F. London and P. R. Zilsel, Phys. Rev. 74, 1148 (1948).
See also, for instance, J. Wilks, The Properties of Liquid and Solid Helium, Clarendon, Oxford (1967).
J. S. Langer and M. E. Fisher, Phys. Rev. Lett. 19, 560 (1967); J. S. Langer and J. D. Reppy, in Prog. Low Temp. Phys., edited by C. J. Gorter, North-Holland, Amsterdam (1970), Vol. VI, Ch. 1.
F. London, Superfluids, Dover, New York (1954), Vol. II, p. 150.
R. P. Feynman, Prog. Low Temp. Phys. I, edited by C. G. Gorter, North-Holland, Amsterdam (1955), Ch. 2.
A. Fetter, J. Low Temp. Phys. 16, 533 (1974).
K. DeConde and R. E. Packard, Phys. Rev. Lett. 35, 732 (1975).
D. J. Melotte and C. F. Barenghi, Phys. Rev. Lett. 80, 4181 (1998).
C. J. Gorter and J. H. Mellink, Physica 15, 285 (1949).
L. S. Goldner and G. Ahlers, Phys. Rev. B 45, 13129 (1992).
W. F. Vinen, Proc. Roy Soc. (London) A240, 114 (1957); A242, 493 (1957).
W. E. Keller and E. F. Hammel, Ann. Phys. (N.Y.) 10, 202 (1960).
V. P. Peshkov and V. B. Stryukov, Soviet Phys.-JETP 14, 1031 (1962).
C. E. Chase, Phys. Rev. 127, 361 (1962).
C. E. Chase, Phys. Rev. 131, 1898 (1963).
P. P. Craig, W. E. Keller, and E. F. Hammel, Ann. Phys. (N.Y.) 21, 72 (1963).
W. E. Keller and E. F. Hammel, Physics 2, 221 (1966).
P. R. Critchlow and H. A. Hemstreet, J. Appl. Phys. 40, 2675 (1969).
G. Ahlers, Phys. Rev. Lett. 22, 54 (1969).
P. Leiderer and F. Pobell, Z. Phys. 223, 378 (1969).
P. Leiderer and F. Pobell, J. Low Temp. Phys. 3, 577 (1970).
J. G. Daunt and R. S. Smith, Rev. Mod. Phys. 26, 172 (1954).
W. Y. Tam and G. Ahlers, Phys. Rev. B 32, 5932 (1985).
H. Fu, H. Baddar, K. Kuehn, M. Larson, N. Mulders, A. Schegolev, and G. Ahlers, J. Low Temp. Phys. (April 1998).
L. E. de Long, O. G. Symko, and J. C. Wheatley, Rev. Sci. Instrum. 42, 147 (1971).
G. Ahlers, Phys. Rev. 171, 275 (1968); J. Low Temp. Phys. 84, 173 (1991).
G. Ahlers, Phys. Rev. A 3, 696 (1971).
R. Haussmann and V. Dohm, Z. Phys. B (Condensed Matter) 87, 229 (1992).
R. Haussmann and V. Dohm, Phys. Rev. Lett. 72, 3060 (1994). See also D. Goodstein, T. Chui, and A. Harter, Phys. Rev. Lett. 77, 979 (1996); and R. Haussmann and V. Dohm, Phys. Rev. Lett. 77, 980 (1996); and T. C. P. Chui, D. L. Goodstein, A. W. Harter, and R. Mukhopadhyay, Phys. Rev. Lett. 77, 1793 (1996).
H. J. Mikeska, Phys. Rev. 179, 166 (1969); L. Kramer, Phys. Rev. 179, 149 (1969); V. L. Ginzburg and A. A. Sobyanin, Sov. Phys. Usp. 19, 773 (1976); J. Low Temp. Phys. 49, 507 (1982); A. Onuki, J. Low Temp. Phys. 50, 433 (1983); 55, 309 (1984).
R. V. Duncan, G. Ahlers, and V. Steinberg, Phys. Rev. Lett. 60, 1522 (1988).
W. A. Moeur, P. K. Day, F.-C. Liu, S. T. P. Boyd, M. J. Adriaans, and R. V. Duncan, Phys. Rev. Lett. 78, 2421 (1997).
R. Haussmann and V. Dohm, Phys. Rev. Lett. 67, 3404 (1991); Phys. Rev. B 46, 6361 (1992).
A. Singsaas and G. Ahlers, Phys. Rev. B 29, 4951 (1984).
R. Haussmann, Phys. Rev. B, in print.
C. F. Barenghi, R. J. Donnelly, and W. F. Vinen, J. Low Temp. Phys. 52, 189 (1983).
R. J. Donnelly, Quantized vortices in helium II, Cambridge University Press (1991).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Baddar, H., Ahlers, G., Kuehn, K. et al. Thermal Resistance of 4He Below but Very Near the Superfluid Transition. Journal of Low Temperature Physics 119, 1–26 (2000). https://doi.org/10.1023/A:1004683717235
Issue Date:
DOI: https://doi.org/10.1023/A:1004683717235