ar X iv : c on d - m at / 9 60 90 53 v 1 5 S ep 1 99 6 Thermally assisted quantum cavitation in solutions of 3 He in 4 He

We have investigated the quantum-to-thermal crossover temperature T for cavitation in liquid helium mixtures up to 5% He concentrations. With respect to the pure He case, T is sizeably reduced, to a value below 50 mK for He concentrations above 2%. As in pure He, the homogeneous cavitation pressure is systematically found close to the spinodal pressure. 64.60.Qb, 64.60.My, 67.60.-g, 67.80.Gb Typeset using REVTEX 1 Quantum cavitation in superfluid liquid He has been experimentally observed by Balibar and coworkers [1]. They have used an ultrasound technique by means of which, a large pressure oscillation is created in a small bulk region of the experimental sample. This prevents cavitation on the walls of the experimental cell. Moreover, as superfluid He can be made perfectly pure, heterogeneous cavitation can be avoided. Due to the nature of these experiments, it is very difficult to determine the pressure (P) and temperature (T) at the cavitation site. Consequently, a quantitative analysis of the experimental results relies on theoretical estimates of the equation of state and cavitation barriers in the spinodal region [2,3]. Depending on these theoretical inputs and on experimental conditions, such as volume and observation time, it is inferred that quantum cavitation likely takes over thermal cavitation at a temperature in the 200-240 mK range. The agreement between experiment [1] and theory [2,3] can be considered as satisfactory given the inherent limitations of both. In this work we address the problem of thermally assisted quantum cavitation in low Heconcentration, liquid helium mixtures (up to 5%). The relevance of this problem is twofold. First, the planned experiments on quantum cavitation in these mixtures [4]. Second, the complexity introduced in the theoretical description of the still superfluid liquid He, when a small but sizeable He amount is present. To our knowledge, no investigation of this kind, either experimental or theoretical, exists in the literature. Some effort has been concentrated in the study of supersaturated He-He mixtures at positive pressures and low temperatures (see for example Refs. [5–8]), or near the tricritical point (see Ref. [9] and refs. therein). The method we use here is conceptually simple and technically workable. It is based, on the one hand, in using a density functional [10] that reproduces the thermodynamical properties of the He-He liquid mixture at zero temperature. This functional has been slightly modified to reproduce the surface properties of the He-He interface, and those of the mixture free-surface [11,12]. All these properties are relevant for a quantitative description of the cavitation process. On the other hand, we make use of a functional-integral approach especially well suited to find the crossover temperature T with the only further approximation of imposing irrotational motion for the growing of the critical bubbles. 2 Let us first generalize the functional-integral approach as used in [3], to the mixture case (see also [13] for another example of how it applies). We recall that above a crossover temperature T, the cavitation rate, i.e., the number of bubbles formed per unit time and volume, is given by JT = J0T e −∆Ωmax/T , (1) where ∆Ωmax is the barrier height for thermal activation. Below T , assuming ∆Ωmax >> T, one can write JQ = J0Q e −Smin , (2) being Smin the minimum of the imaginary-time action