Fluctuations of the critical Casimir force

The critical Casimir force (CCF) arises from confining fluctuations in a fluid and thus it is fluctuating quantity itself. While the mean CCF universal, its (static) variance has previously been found to depend on microscopic details of system which effectively set large-momentum cutoff underlying field theory, rendering potentially large. This raises question how properties are reflected experimentally observable quantities, such as thickness wetting film or position suspended colloidal particle. Here, based rigorous definition instantaneous force, we analyze static dynamic correlations for conserved geometry various boundary conditions within Gaussian approximation. We find that correlation function independent momentum decays algebraically time. Within approximation, associated exponent depends only universality class but not conditions. furthermore consider film, can fluctuate under influence time-dependent CCF. latter gives rise an effective non-Markovian noise equation motion induces distinct contribution variance. approximations used here, at short times, this grows time whereas, long saturates contributes steady-state thickness.