Experiments on the Self-Organized Critical State of ^4He

Abstract

When a heat flux Q is applied downward through a sample of ^4He near the lambda transition, the helium self organizes such that the gradient in temperature matches the gravity-induced gradient in T_λ. All the helium in the sample is then at the same reduced temperature ϵ=T−T_λ_T_λ and the helium is said to be in the Self-Organized Critical (SOC) state. We have made the first measurements of the ^4He SOC state specific heat, C_(∇T) (T(Q)). There is no measurable difference between C_(∇T) and the static zero-gravity 4He specific heat for temperatures between 650 and 250 nK below T_λ. Closer to T_λ , the specific heat is depressed and reaches a maximum value at 50 nK below T_λ. This depression is similar to that predicted theoretically as reported by R. Haussmann (Phys. Rev. B 60, 12349, 1999). Contrary to the expectations of theory, however, we see another depression far below T_λ. In addition, over the heat flux range of 30 nW/cm^2 to 13 μW/cm^2, we have made improved measurements of the speed of a recently discovered propagating thermal mode, which travels only upstream against the nominal heat flux of the SOC state. We are able to accurately predict the speed of this wave by treating the helium of SOC state as a traditional fluid with a temperature dependent thermal conductivity.

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