We present the first experimental evidence that the heat capacity of superfluid 4He, at temperatures very close to the lambda point T(lambda), is enhanced by a constant heat flux Q. The heat capacity at constant Q, C(Q), is predicted to diverge at a temperature T(c)(Q)

We have made heat capacity measurements of superfluid 4 He at temperatures very close to the lambda point, T λ , in a constant heat flux, Q, when the helium sample is heated from above. In this configuration the helium enters a self-organized (SOC) heat transport state [1] at a temperature T SOC (Q), which for Q ≥ 100 nW/cm 2 lies below T λ . At low Q we observe little or no deviation from the bulk Q = 0 heat capacity up to T SOC (Q); beyond this temperature the heat capacity appears to be sharply depressed, deviating dramatically from its bulk behaviour. This marks the formation and propagation of a SOC/superfluid two phase state, which we confirm with a simple model. The excellent agreement between data and model serves as an independent confirmation of the existence of the SOC state. As Q is increased (up to 6 µW/cm 2 ) we observe a Q dependant depression in the heat capacity that occurs just below T SOC (Q), when the entire sample is still superfluid. This is due to the emergence of a large thermal resistance in the sample, which we have measured and used to model the observed heat capacity depression. Our measurements of the superfluid thermal resistivity are a factor of ten larger than previous measurements by Baddar et al. [2].

AcknowledgementsThere are a number of people I would like to thank for their contributions to this thesis. My advisor David Goodstein was insightful, encouraging, and patient throughout the many challenges of performing a low-temperature experiment. Our conversations were always helpful because David has an extraordinary ability to make complicated concepts seem simple and intuitive. I had two mentors in the lab, Peter Day and Richard Lee, who taught me everything I know about performing experiments in low-temperature physics. My first lab experience was working with Peter. He provided me with the cryostat I used throughout my graduate career, answered hundreds of questions, and patiently showed me the techniques I needed. Richard returned to Caltech as my thesis experiment was taking shape. He was also an excellent resource for the tricks and techniques of low-temperature physics. (Plus, he made B.O.B.2, the electrical filtering system on this cryostat). However, what helped me most was that he patiently asked hundreds of questions, which forced me to think through all the details of my experiment. It is with his help that I avoided many pitfalls.There are a number of other physicists who made significant contributions to this work. Particularly helpful were the members of the DYNAMX team from the University of New Mexico (Rob Duncan, Dimitri Sergatskov, Alex Babkin, and Steve Boyd). They provided material help with the cryo-valve system and the construction of the experimental cell. In addition, they provided a lot of expertise on performing experiments on the SOC state of 4 He. In particular, I would like to thank Rob Duncan, who served as a secondary thesis advisor during a critical time in the experiment as David Goodstein recovered from an injury. Also helpful were discussions with two theorists, Peter Weichman and Rudolf Haussmann, who helped give meaning to my results.I would like to thank my parents for many many years of encouragement and support, and not asking me too often when I was going to get my degree.I would also like to thank my wife Avital, who provided an enormous amount of support and, through an intricate dance of prodding and patience, helped guide me through this endeavor. Lastly, I thank my son Jacob, whose arrival helped destroy the illusion that maybe, just maybe, I could be a graduate student forever. We report the first results of the heat capacity of the SOC state, C ∇T , for heat fluxes 60nW/cm 2 < Q < 13 µW/cm 2 and corresponding temperatures 9 nK > T SOC − T λ > −1.1 µK. We find that C ∇T tracks the static (i.e., zero heat flux) unrounded (i.e., in zero gravity) heat capacity C 0 with two exceptions. The first is that within 250 nK of T λ , C ∇T is depressed relative to C 0 and the maximum in C ∇T is shifted to 50 nK below T λ . The second difference is that at high heat flux, C ∇T is again depressed relative to C 0 with the departure starting at about 650 nK below T λ .We present the most extensive measurements of the speed and attenuation of the SOC wave to date. We report wav...

Abstract. When a heat flux Q is applied downward through a sample of liquid 4 He near the lambda transition, the helium self organizes such that the gradient in temperature matches the gravity induced gradient in 7\. All the helium in the sample is then at the same reduced temperature ^soc and the helium is said to be in the Self-Organized Critical (SOC) state. We have made preliminary measurements of the 4 He SOC state specific heat, Cy T (T(Q)). Despite having a cell height of 2.54 cm, our results show no difference between Cy T and the zero-gravity 4 He specific heat results of the Lambda Point Experiment (LPE) [J.A. Lipa et al., Phys. Rev. B, 68, 174518 (2003)] over the range 250 to 450 nK below the transition. There is no gravity rounding because the entire sample is at the same reduced temperature ^soc(2)-Closer to 7^, the SOC specific heat falls slightly below LPE, reaching a maximum at approximately 50 nK below 7\, in agreement with theoretical predictions [R. Haussmann, Phys. Rev. B, 60, 12349 (1999)].

Abstract. In 2000 Harter et al. reported the first measurements of the enhancement of the heat capacity ΔC Q ≡C(Q)-C(Q=0) of helium-II transporting a heat flux density Q near T λ . Surprisingly, their measured ΔC Q was ~7-12 times larger than predicted, depending on which theory was assumed. In this report we present a candidate explanation for this discrepancy: unintended heat flux inhomogeneity. Because C(Q) should diverge at a critical heat flux density Q c , homogeneous heat flow is required for an accurate measurement. We present results from numerical analysis of the heat flow in the Harter et al. cell indicating that substantial inhomogeneity occurred. We determine the effect of the inhomogeneity on ΔC Q and find rough agreement with the observed disparity between prediction and measurement.Keywords: helium, superfluid, heat capacity, lambda transition. PACS: 67.40. Kh, 67.40.Pm, 64.60.Ht In order to evaluate the idea that unintended inhomogeneity of the heat flow in the Harter et al. [1] experiment might account for the discrepancy between measurement and predictions [2,3] of ΔC Q , we must estimate the heat flow field Q(r) in the helium-II. It is not difficult to show [4] that thermal counterflow in helium-II can be solved simultaneously with the diffusive heat flow in the enclosing experimental cell using a standard finite-element solver [5], if the helium-II is nondissipative, nonvortical, nearly isothermal, and free of net mass flow (J=0). These conditions should have been well-approximated in the Harter et al. experiment. Such a numerical model has been constructed and solved for the Harter et al. cell. The model geometry is shown in Fig. 1. Not visible at this scale is the model for the Kapitza boundary resistance R K : an artificial thin envelope of thickness δ=25 μm and thermal conductivity κ RK =δ/R K interposed between the helium and the cell walls.For best accuracy, the helium-II diffusion coefficient should be modeled as κ He =α(ρ s /ρ n ), where α is a large constant required to reduce the variation of the scalar superfluid velocity potential function [4]. However, Harter et al. had a very short cell (0.64 mm) and did not approach closer to T λ than ~0.5×10 -6 K, limiting the maximum variation of ρ s /ρ n over the height of their cell to ~10%. To reduce the number of required computations we have approximated ρ s /ρ n as constant and set κ He =10 6 W/cmK. Test reductions of κ He to 10 5 W/cmK changed calculated enhancements by only ~0.01%, verifying that κ He is sufficiently large.To within their measurement noise, Harter et al. found that t -α ΔC Q was linear in (Q/Q c ) 2 , where t=(T λ -T)/T λ is the reduced temperature. Keeping only the Cell model geometry with heat flow streamlines.The model is axisymmetric about r=0. Streamlines show heat flowing from the primary heater to the cooled surface. The principal cause of inhomogeneity of the heat flow in the helium is the "well" cut into the upper endplate to accommodate the diaphragm valve.