Abstract
We present a renormalization-group calculation based on model F for the thermal conductivity λT(T, Q) in the presence of a homogeneous heat current Q and gravity. For temperatures below T λ we obtain a large but finite thermal conductivity corresponding to superfluid 4 He with dissipation. Furthermore, we consider the self-organized critical state where the effects of gravity and heat current cancel each other so that the distance from criticality ΔT = T(z) − T λ(z) is constant in space and a function of Q. We compare our theoretical results with recent experiments.
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REFERENCES
A. Onuki, J. Low Temp. Phys. 50, 433 (1983); 55, 309 (1984).
R. Haussmann and V. Dohm, Phys. Rev. B 46, 6361 (1992).
R. V. Duncan, G. Ahlers, and V. Steinberg, Phys. Rev. Lett. 60, 1522 (1988).
F. C. Liu and G. Ahlers, Phys. Rev. Lett. 76, 1300 (1996).
D. Murphy and H. Meyer, Phys. Rev. B 57, 536 (1998).
R. Haussmann and V. Dohm, Phys. Rev. Lett. 67, 3404 (1991); Z. Phys. B 87, 229 (1992).
G. Ahlers, Phys. Rev. 171, 275 (1968).
A. Onuki, Jnp. J. Apl. Phys. 26, 365 (1987); J. Low Temp. Phys. 104, 133 (1996).
G. Ahlers and F. C. Liu, J. Low Temp. Phys. 105, 255 (1996).
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).
B. I. Halperin, P. C. Hohenberg, and E. D. Siggia, Phys. Rev. Lett. 32, 1289 (1974); Phys. Rev. B 13 1299 (1976).
V. Dohm, Z. Phys. B 60, 61 (1985); Z. Phys. B 61, 193 (1985); Phys. Rev. B 44, 2697 (1991).
D. J. Amit, Field theory, the renormalization group, and critical phenomena (McGraw-Hill, New York 1978).
The same idea has been used independently for investigating finite-size effects in O (n) symmetric models where also [ø]-o; see: X. S. Chen and V. Dohm, Eur. Phys. J. B (1998), in press.
R. Haussmann, to be published.
W. Y. Tam and G. Ahlers, Phys. Rev. B 32, 5932 (1985).
J. A. Lipa, D. R. Swanson, J. A. Nissen, T. C. P. Chui, and U. E. Israelsson, Phys. Rev. Lett. 76, 944 (1996).
P. K. Day, W. A. Moeur, S. S. McCready, D. A. Sergatskov, F. C. Liu, and R. V. Duncan, Phys. Rev. Lett. 81, 2474 (1998).
G. Ahlers, private communication.
R. Haussmann and V. Dohm, Phys. Rev. Lett. 72, 3060 (1994); Czech. J. Phys. 46 S1, 171 (1996); J. Low Temp. Phys. 107, 21 (1997).
T. C. P. Chui, D. L. Goodstein, A. W. Harter, and R. Mukhopadhyay, Phys. Rev. Lett. 77, 1793 (1996).
R. Haussmann, to be published.
H. E. Hall and W. F. Vinen, Proc. R. Soc. (London) Ser. A 238, 204 and 215 (1956).
R. Haussmann, Z. Phys. B 87, 247 (1992).
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Haussmann, R. Heat transport and self-organized criticality in liquid 4He close to T λ . Journal of Low Temperature Physics 114, 1–10 (1999). https://doi.org/10.1023/A:1021845718982
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DOI: https://doi.org/10.1023/A:1021845718982