Journal o[ Low TemperaturePhysics, Vol.42, Nos. 1/2, 1981 Fluctuations in Small Volumes of Liquid 3He K. B. Efetov* and M. M. Salomaat Research Institute for Theoretical Physics, University of Helsinki, Helsinki, Finland (Received June 24, 1980) We calculate fluctuation contributions to the thermodynamic properties in a small volume of liquid 3He. Functional integration techniques are employed to derive the fluctuation free-energy functional for temperatures just above the superfluid transition temperature and for zero temperature. Due to finite-size effects, the critical regime is estimated to be large enough to warrant an experimental observation of fluctuations. At zero temperature we find two kinds of quasicollective gapless excitations, which correspond to fluctuations of phase and rotations of the order parameter in spin space, respectively. These excitations result in a periodic time dependence of the pair correlation function. Finally, the experimental observability of the effects considered are contem- plated. 1. INTRODUCTION Fluctuation effects in liquid 3He in the vicinity of the superfluid phase transition temperature are very small under most experimental circum- stances. There have recently appeared, however, several experimental investigations1-3 in which 3He has been enclosed into a small volume ~ with a typical diameter ranging between 100 and 10,000 ~. Under such condi- tions it is important to consider fluctuation phenomena. Spin triplet pairing does not occur in volumes with characteristic dimensions d << ~0, the superfluid coherence length, as was shown by Larkin. 4 Limited size effects in 3He have previously been considered by Kj[ildman et al., 5 but they were involved with determining the critical length dc at which superfluidity first occurs in two special geometries--a capillary tube and a slab. Triplet pairing is possible, on the other hand, in volumes with d > ~o, and in this case fluctuations around the phase transition temperature are strongly enhanced by the finite-size effects, as discussed in detail below. *Permanent address: L. D. Landau Institute for Theoretical Physics, Academy of Sciences, Moscow, USSR. tPresent address: Departmentof Physics,University of California, Los Angeles,California. 35 0022-2291/81/0100-0035503.00/0 9 1981 Plenum Publishing Corporation