Quantum Density Fluctuations in Classical Liquids

TL;DR

This paper explores quantum density fluctuations in classical liquids as an analog for relativistic quantum fields, calculating their effects on light scattering and estimating their observability.

Contribution

It introduces a model linking fluid density fluctuations to quantum field theory and derives the frequency-dependent scattering cross section due to zero point fluctuations.

Findings

Zero point density fluctuations can cause measurable light scattering.

The scattering cross section scales with the fifth power of light frequency.

Zero point scattering can be about 0.5% of thermal scattering in water at room temperature.

Abstract

We discuss the density fluctuations of a fluid due to zero point motion. These can be regarded as density fluctuations in the phonon vacuum state. We assume a linear dispersion relation with a fixed speed of sound and calculate the density correlation function. We note that this function has the same form as the correlation function for the time derivative of a relativistic massless scalar field, but with the speed of light replaced by the speed of sound. As a result, the study of density fluctuations in a fluid can be a useful analog model for better understanding fluctuations in relativistic quantum field theory. We next 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. This can be understood as the product of fourth power dependence of the usual Rayleigh cross section with the linear frequency dependence of the spectrum of zero point density fluctuations. 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 order 0.5% for water at room temperature and 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.