Quantum Density Fluctuations in Classical Liquids

We discuss the density fluctuations of a fluid due to zero point motion, assuming a linear dispersion relation. We argue that density fluctuations in a fluid can be a useful analog model for better understanding fluctuations in relativistic quantum field theory. We calculate the differential cross section for light scattering by the zero point density fluctuations, and find a result proportional to the fifth power of the light frequency. We give some estimates of the relative magnitude of this effect compared to the scattering by thermal density fluctuations, and find that it can be of the order 13% for liquid neon at optical frequencies. This relative magnitude is proportional to frequency and inversely proportional to temperature. Although the scattering by zero point density fluctuation is small, it may be observable.