Fluctuations in small volumes of liquid 3He

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 contemplated.