Abstract
Griffin, Wu and Stringari have derived the hydrodynamic equations of a trapped dilute Bose gas above the Bose-Einstein transition temperature. We give the extension which includes hydrodynamic damping, following the classic work of Uehling and Uhlenbeck based on the Chapman-Enskog procedure. Our final result is a closed equation for the velocity fluctuations δ v which includes the hydrodynamic damping due to the shear viscosity θ and the thermal conductivity κ. Following Kavoulakis, Pethick and Smith, we introduce a spatial cutoff in our linearized equations when the density is so low that the hydrodynamic description breaks down. Explicit expressions are given for θ and κ, which are position-dependent through dependence on the local fugacity when one includes the effect of quantum degeneracy of the trapped gas. We also discuss a trapped Bose-condensed gas, generalizing the work of Zaremba, Griffin and Nikuni to include hydrodynamic damping due to the (non-condensate) normal fluid.
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REFERENCES
D. S. Jin et al., Phys. Rev. Lett. 77, 420 (1996); M.-O. Mewes et al., Phys. Rev. Lett. 77, 992 (1996).
D. S. Jin et al., Phys. Rev. Lett. 78, 764 (1997).
A. Griffin, W. C. Wu, and S. Stringari, Phys. Rev. Lett. 78, 1838 (1997).
E. Zaremba, A. Griffin, and T. Nikuni, Phys. Rev. A 57 (in press) cond-mat/9705134.
M. R. Andrews et al., Phys. Rev. Lett. 79, 553 (1997).
A useful discussion of the conditions which must be satisfied to probe the hydrodynamic region is given by G. M. Kavoulakis, C. J. Pethick, and H. Smith, Phys. Rev. A 57 (in press) cond-mat/9710130.
E. A. Uehling and G. E. Uhlenbeck, Phys. Rev. 43, 552 (1933).
E. A. Uehling, Phys. Rev. 46, 917 (1934).
G. M. Kavoulakis, C. J. Pethick, and H. Smith, private communication.
L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics, Benjamin, New York (1962), Chap. 6.
T. R. Kirkpatrick and J. R. Dorfman, J. Low Temp. Phys. 58, 304 (1985); ibid. 399 (1985).
For a detailed review of the Chapman-Enskog method as applied to classical gases, see J. H. Ferziger and H. G. Kaper, Mathematical Theory of Transport Processes in Gases, North-Holland, London (1972).
K. Huang, Statistical Mechanics, Wiley, New York (1987), 2nd ed., p. 113.
See L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Pergamon, Oxford (1959), p. 298.
At T BEC (when z = 1 and n c = 0), our integral equations (22) are equivalent to Eqs. (24) in the second paper in Ref. 11, and hence our results for κ and η should coincide at T BEC with Eqs. (26) of this reference. However, our numerical factors differ slightly.
S. Giorgini, L. P. Pitaevskii, and S. Stringari, J. Low Temp. Phys. 109, 309 (1997).
I. M. Khalatnikov, An Introduction to the Theory of Superfluidity, Benjamin, New York (1965).
N. N. Bogoliubov, Lectures on Quantum Statistics, Gordon and Breach, New York (1970), Vol. 2, p. 148.
For example, see P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics, Cambridge University Press, New York (1995), Chap. 8 and especially p. 460ff.
See, for example, T. L. Ho and V. B. Shenoy, J. Low Temp. Phys. 111, 937 (1998).
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Nikuni, T., Griffin, A. Hydrodynamic Damping in Trapped Bose Gases. Journal of Low Temperature Physics 111, 793–814 (1998). https://doi.org/10.1023/A:1022221123509
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DOI: https://doi.org/10.1023/A:1022221123509