Abstract
A near-critical sample of superfluid 4He subjected to a combination of a heat current Q and a gravitational field g has recently been confirmed experimentally to exhibit a “self-organized critical” (SOC) state, in which the local temperature profile T(z) parallels the local superfluid transition temperature, T λ(z), so that T(z)−T λ(z) is independent of the vertical coordinate z. We show that there is a particular heat current Q 0(g)∝g such that the SOC state lies in the normal phase only when Q<Q 0(g). The SOC state is shown to be dynamically stable and, surprisingly, to possess a propagating mode in which perturbations travel “upstream” at a particular speed c SOC(Q). For Q>Q 0(g) the SOC state is pushed below the superfluid transition. We present a model based on the Model F equations that shows that the resulting superfluid state is intrinsically dynamical and supports an average temperature gradient by way of an approximately uniform density of recurring phase slips. The role of a certain local dynamical instability temperature, T c(Q, z), in the nucleation of the phase slips is emphasized.
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Weichman, P.B., Miller, J. Theory of the Self-Organized Critical State in Nonequilibrium 4He. Journal of Low Temperature Physics 119, 155–179 (2000). https://doi.org/10.1023/A:1004668820870
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DOI: https://doi.org/10.1023/A:1004668820870