Abstract
The shear viscosity η(T) in the Balian-Werthamer (BW) state of superfluid3He is calculated variationally throughout the region 0≤t≤ 1(t=T/T c) from the transport equation for Bogoliubov quasiparticles. Coherence factors are treated exactly in the calculation of the collision integral. The numerical result for\(\tilde \eta \)=ηs= ηs(T)/ηn(Tc) agree very well with experiment in the range 0.8≤t≤1.0. Analytic expressions\(\tilde \eta \) = 0.577 (1−1.0008t) and\(\tilde \eta \)=1−(23π/64)δ [δ=Δ(T)/k B T] are obtained in the low-temperature region and in the vicinity ofT c, respectively. From the numerical analysis it is shown that the latter equation is valid only in the temperature range 0.9997≤t≤1.0.
Similar content being viewed by others
References
J. C. Wheatley,Rev. Mod. Phys. 47, 415 (1975).
A. J. Leggett,Rev. Mod. Phys. 47, 331 (1975).
T. A. Alvesalo, Yu. D. Anufriyev, H. K. Collan, O. V. Lounasmaa, and P. Wennerström,Phys. Rev. Lett. 30, 962 (1973).
T. A. Alvesalo, H. K. Collan, M. T. Loponen, and M. C. Veuro,Phys. Rev. Lett. 32, 981 (1974).
T. A. Alvesalo, H. K. Collan, M. T. Loponen, O. V. Lounasmaa, and M. C. Veuro,J. Low Temp. Phys. 19, 1 (1975).
T. J. Greytak, R. T. Johnson, D. N. Paulson, and J. C. Wheatley,Phys. Rev. Lett. 31, 452 (1973).
R. T. Johnson, R. L. Kleinberg, R. A. Webb, and J. C. Wheatley,J. Low Temp. Phys. 18, 501 (1975).
C. W. Kiewiet, P. C. Main, and H. E. Hall, inProc. 14th Int. Conf. Low Temp. Phys. (North-Holland, Amsterdam, 1975), Vol. 5, p. 413; P. C. Main, C. W. Kiewiet, W. T. Band, J. R. Hook, D. J. Sandiford, and H. E. Hall,J. Phys. C 9, L397 (1976).
V. P. Galaxxxko,Zh. Eksp. Teor. Fiz. 61, 382 (1971) [Sov. Phys.—JETP 34, 203 (1972)].
V. S. Shumeiko,Zh. Eksp. Teor. Fiz. 63, 621 (1972) [Sov. Phys.—JETP 36, 330 (1973)].
J. Seiden,Compt. Rend. 276B, 905 (1973);277B, 115 (1973);278B, 1009 (1974);279B, 151, 487 (1974).
T. Soda and K. Fujiki,Prog. Theor. Phys. 52, 1405 (1974);53, 1218 (1975) (Erratum).
C. J. Pethick, H. Smith, and P. Bhattacharyya,Phys. Rev. Lett. 34, 643 (1975).
C. J. Pethick, H. Smith, and P. Bhattacharyya, inProc. 14th Int. Conf. Low Temp. Phys. (North-Holland, Amsterdam, 1975), Vol. 1, p. 5.
P. Bhattacharyya, C. J. Pethick, and H. Smith, inProc. 14th Int. Conf. Low Temp. Phys. (North-Holland, Amsterdam, 1975), Vol. 1, p. 9.
C. J. Pethick, H. Smith, and P. Bhattacharyya,J. Low Temp. Phys. 23, 225 (1976).
O. Valls and A. Houshton,Phys. Lett. 50A, 211 (1974).
M. A. Schazamanian,J. Low Temp. Phys. 21, 589 (1975).
M. Kohler,Z. Phys. 124, 772 (1948).
J. M. Ziman,Can. J. Phys. 34, 1256 (1956).
J. M. Ziman,Electrons and Phonons (Clarendon Press, Oxford, 1960), Chapter 7, p. 275.
H. Højgaad Jensen, H. Smith, and J. W. Wilkins,Phys. Rev. 185, 323 (1969).
R. Balian and N. R. Werthamer,Phys. Rev. 131, 1553 (1963).
A. A. Abrikosov and I. M. Khalatnikov,Rep. Prog. Phys. 22, 329 (1959).
P. Morel and P. Nozières,Phys. Rev. 126, 1909 (1962).
D. Pines and P. Nozières,The Theory of Quantum Liquids (Benjamin, New York, 1966), Vol. 1, Chapter 1.
A. Messiah,Quantum Mechanics (North-Holland, Amsterdam, 1964), Chapter XIII and Appendix C.
B. Mühlschlegel,Z. Phys. 155, 313 (1959).
M. Abramowitz and I. A. Segun, eds.,Handbook of Mathematical Functions (Dover, New York, 1965), Chapter 25.
P. Wölfle,Phys. Rev. B 14, 89 (1976).
B. T. Gexxxlikman and V. R. Chechetkin,Zh. Eksp. Teor. Fiz. 69, 286 (1975) [Sov. Phys.—JETP 42, 148 (1976)].
C. J. Pethick, H. Smith, and P. Bhattacharyya, submitted toPhys. Rev. B (October 1976).
Author information
Authors and Affiliations
Additional information
Supported by the Research Institute for Fundamental Physics, Kyoto University.
Rights and permissions
About this article
Cite this article
Ono, Y.A., Hara, J., Nagai, K. et al. Shear viscosity of the B phase of superfluid3He. J Low Temp Phys 27, 513–536 (1977). https://doi.org/10.1007/BF00655284
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00655284