Measurement of the SOC State Specific Heat in 4He

When a heat flux Q is applied downward through a sample of liquid 4He near the lambda transition, the helium self organizes such that the gradient in temperature matches the gravity induced gradient in T. All the helium in the sample is then at the same reduced temperature tSOC = and the helium is said to be in the Self-Organized Critical (SOC) state. We have made preliminary measurements of the 4He SOC state specific heat, CT(T(Q)). Despite having a cell height of 2.54 cm, our results show no difference between CT and the zero-gravity 4He 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 tSOC(Q). Closer to T the SOC specific heat falls slightly below LPE, reaching a maximum at approximately 50 nK below T, in agreement with theoretical predictions [R. Haussmann, Phys. Rev. B, 60, 12349 (1999)].