Testing the Maxwell-Boltzmann distribution using Brownian particles

Abstract

We report on shot-noise limited measurements of the instantaneous velocity distribution of a Brownian particle. Our system consists of a single micron-sized glass sphere held in an optical tweezer in a liquid in equilibrium at room temperature. We provide a direct verification of a modified Maxwell-Boltzmann velocity distribution and modified energy equipartition theorem that account for the kinetic energy of the liquid displaced by the particle. Our measurements confirm the distribution over a dynamic range of more than six orders of magnitude in count-rate and five standard deviations in velocity.