The appearance of oscillating second sound induced patterns on the free surface of He II. A nonequilibrium phase transition with critical slowing down

In the system under consideration second sound generates surface patterns on He II. Some years ago it was found that at small excitations the spatially periodic surface structures are immobile, whereas at higher excitations a variety of harmonic and chaotic oscillations occur. A transcription of the corresponding Hamilton function in terms of Green's functions suggests that the observed phenomena are manifestations of a nonequilibrium phase transition and reveals an analogy between the building up of oscillating surface patterns on He II and the ordering of antiferromagnetic systems in thermodynamic equilibrium. The critical excitation, where the stationary surface becomes unstable, has now been studied extensively. In this context the transition times between the stable stationary and the stable oscillating states and the corresponding relaxation times have been investigated experimentally. In the vicinity of the critical Landau number, a dynamical critical slowing down phenomenon has been observed.