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Brownian motion7/6/2023 By analogy with microcantilever-based sensors 11, 12, our results reveal that the particle–fluid–trap system can be considered a nanomechanical resonator in which the intrinsic hydrodynamic backflow enhances resonance. Furthermore, we demonstrate different strategies to achieve peak amplification. We show that hydrodynamic correlations result in a resonant peak in the power spectral density of the sphere’s positional fluctuations, in strong contrast to overdamped systems. Here we measure the spectrum of thermal noise by confining the Brownian fluctuations of a microsphere in a strong optical trap. One hundred years after Perrin’s pioneering experiments on Brownian motion 7, 8, 9, direct experimental observation of this colour is still elusive 10. This hydrodynamic ‘memory’ translates to thermal forces, which have a coloured, that is, non-white, noise spectrum. The entrained fluid acts back on the particle and gives rise to long-range correlations 5, 6. However, as the particle receives momentum from the fluctuating fluid molecules, it also displaces the fluid in its immediate vicinity. The friction is assumed to be given by the Stokes drag, suggesting that motion is overdamped at long times in particle tracking experiments, when inertia becomes negligible. Conventionally, the thermal force is assumed to be random and characterized by a Gaussian white noise spectrum. Second, the friction between the particle and the viscous solvent damps its motion. First, the particle is driven by rapid collisions with the surrounding solvent molecules, referred to as thermal noise. Essentially, two counteracting forces govern the motion of the Brownian particle. Observation of the Brownian motion of a small probe interacting with its environment provides one of the main strategies for characterizing soft matter 1, 2, 3, 4.
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