Self-organization inH4enear the superfluid transition in heat flow and gravity

Abstract

We investigate the nonlinear dynamics of 4 He slightly below the superfluid transition by integrating model F equations in three dimensions. When a superfluid is heated from above under gravity, a vortex tangle and sheetlike phase slips both appear near the bottom plate. Then a self-organized superfluid containing high-density vortices and phase slips grows upward, where high-amplitude second sounds are emitted from the self-organized to the ordinary superfluid region. A phase slip sheet often changes into a vortex aggregate and vice versa. The thermal resistance due to these defects produces a constant temperature gradient equal to the gradient of the pressure-dependent transition temperature T λ (p). In this self-organized region, the temperature deviation T − T λ (p) consists of a negative constant determined by the heat flux Q and time-dependent fluctuations. Its time-average is calculated to be 155 nK for Q = 11.2 erg/cm 2 s in good agreement with the experiment (W.A. Moeur et al., Phys. Rev. Lett. 78, 2421(1997).

Renormalization-group calculation of the superfluid/normal-fluid interface of liquid4He in gravity nearTλ

“…In this way they obtain a temperature gradient ∇T which on average equals the gradient ∇T λ as required for the self-organized critical state. More recently Yabunaka and Onuki [30] performed a three-dimensional numerical simulation based on model F in order to investigate the selforganized critical state and the superfluid/normal-fluid interface. They observed the formation and motion of vortices and phase slips which produce a nonzero temperature gradient ∇T on average in the superfluid region which compensates ∇T λ .…”