Depression of the superfluid transition temperature inHe4by a heat current

Abstract

We report experimental results for the depression of the superfluid transition temperature 7\(g) in 4 He by a heat current Q. The data were obtained by use of thermometry with a resolution of 10 nK, and cover the range 0.4<g<10 fiW/cm 2 . They can be represented by 1 -7\(g)/7\(0) =(Q/Qo) x with go =568 ± 200 W/cm 2 and x =0.813 ± 0.012, and are in good agreement with theoretical predictions.

Liquid4Henear the superfluid transition in the presence of a heat current and gravity

“…From the slopes of the lines in the double-logarithmic plot we obtain effective power laws ∆T 1 (Q) ∼ −Q x and ∆T c (Q) ∼ −Q x with nearly the same exponent x, which varies between x ≈ 0.9 for 0.1 µW/cm 2 < ∼ Q < ∼ 1 µW/cm 2 and x ≈ 1.25 for Q > ∼ 10 µW/cm 2 . While our theoretical predictions for the dissipative region agree qualitatively with the experimental observations 5,6,8 , there are three major quantitative disagreements. First of all, the experimentally observed dissipation is much larger than the theoretically predicted, because for ∆T c (Q) < ∆T < ∆T λ (Q) the measured thermal resistivity ρ T = 1/λ T of Ref.…”

“…Then suddenly, when the temperature ∆T approaches and drops below the second transition temperature ∆T c (Q), the experimentally observed thermal resistivity is so small, that it was not detected any more in the experiment 6 . Our theory does not predict the second transition temperature ∆T c (Q), which has been found in the experiments 5,6,8 . While the solid line in Fig.…”

“…In the experiments 5,9-11 a depression ∆T c (Q) of the superfluid transition has been observed which agrees qualitatively with the theory, but not quantitatively. For small Q in the critical regime the shift ∆T c (Q) ∼ −Q 0.81 has been found 5 . While the exponents do not agree, the experimentally observed shift ∆T c (Q) is larger than the theoretically calculated ∆T λ (Q).…”

“…measured in the experiments 5,6,8 . We find that ∆T c (Q) obtained from our theory is close to ∆T 1 (Q) and located slightly above the solid line in Fig.…”

“…Liquid 4 He close to T λ in the presence of a heat current Q has been investigated theoretically [2][3][4] and experimentally [5][6][7][8] . In the ∆T -Q plane a line of critical temperatures is found which separates superfluid from normal-fluid helium.…”