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Europhysics Letters (EPL)

Thermal conductivity and viscosity of a Bose gas above superfluid transition

Wittaya Kanchanapusakit

Published Apr 1, 2010• 1 citation
Publisher

Abstract

The thermal fluctuations of the order parameter affect the transport of Bose gas above the superfluid transition. Using the time-dependent Ginzburg-Landau theory in the classical region, we calculate the fluctuation corrections to the coefficients of thermal conductivity and shear viscosity. Above the transition temperature T c , the fluctuation contribution to the thermal conductivity diverges as ( T − T c ) -2+ d /2 for dimensions d . The viscosity drops near T c since the fluctuation contributes a correction which varies as − ( T − T c ) −2+ d /2 . The calculations are conducted under the condition that the fluctuation corrections are small compared with the normal part of the transport coefficients.

DOI
10.1209/0295-5075/90/26004

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The contribution of order-parameter fluctuations to the static and dynamic properties of a weakly interacting Bose gas near the Bose-Einstein condensation temperature Tc{T}_{c}Tc​ is investigated via a novel approach. Self-consistent approximations for the propagator of order-parameter fluctuations GGG are generated in successive temperature ranges closer and closer to Tc{T}_{c}Tc​. Mean-field theory corresponds to assuming that the correlation of fluctuations G2{G}_{2}G2​ is given by G2(1)=GG{{G}_{2}}^{(1)}=GGG2​(1)=GG. This first approximation is valid in the range ${\ensuremath{\tau}}_{1}<\ensuremath{\tau}=\frac{(T\ensuremath{-}{T}_{c})}{{T}_{c}}<1$, where at $\ensuremath{\tau}={\ensuremath{\tau}}_{1}$ the neglected terms are comparable to those included. In this paper we consider the second approximation G2(2)=GGVGG{{G}_{2}}^{(2)}=GGVGGG2​(2)=GGVGG, which involves the first-order interaction between the fluctuations. Two independent criteria for the range of validity ${\ensuremath{\tau}}_{2}<\ensuremath{\tau}<{\ensuremath{\tau}}_{1}$ of the second approximation are established. It is conjectured that the qualitative results of the present model calculation are applicable to liquid helium in the presently accessible temperature range. The predicted temperature dependences of the specific heat, superfluid density, and fourth sound are in agreement with the scaling hypothesis and available experiments in helium. The condensate density is predicted to vanish linearly with $\ensuremath{\tau}$. It is shown that the contribution of order-parameter fluctuations to the thermal conductivity diverges as ${\ensuremath{\tau}}^{\frac{\ensuremath{-}1}{3}}$ above Tc{T}_{c}Tc​, and it is suggested that the absence of logarithmic factors is due to the inconsistent treatment of entropy fluctuations.
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