Fluctuations and Brownian Motion

L. H. Ford, G. O. Heymans, N. F. Svaiter

The fluctuations in the phonon vacuum state can lead to zero point density fluctuations in a material, which in turn lead to local zero point fluctuations of the dielectric properties of the material. We argue that the density fluctuations lead to a fluctuating force on a test charge, such as an electron, located a short distance outside of the material. This force is due to fluctuating dipole moments inside the material, and produces Brownian motion of the electron. We calculate the mean squared velocity of the electron in both the normal and transverse direction relative to the boundary of the material. The result is nonzero in both directions, but larger in the normal case. We estimate the magnitude of this quantum Brownian motion and find that, in some cases, it can exceed the effects of both thermal motion and quantum momentum uncertainty. This suggests that the effect may be observable, and could constitute a source of quantum noise in nanoscale devices. It also potentially offers a means to remotely sense zero point density fluctuations in a material.

Charlotte Bigg

Roumen Tsekov

A theoretical parallel between the classical Brownian motion and quantum mechanics is explored via two stochastic sources. It is shown that, in contrast to the classical Langevin force, quantum mechanics is driven by turbulent velocity fluctuations with diffusive behavior. In the case of simultaneous action of the thermal and quantum noises, the quantum Brownian motion is described as well.

John Maddox

Michael Stoeltzner

Explaining Brownian motion involved the combination of explorative experimentation with a theoretically sophisticated and philosophically informed understanding of statistical mechanics and probability. Only then was it possible to accept fluctuations as a lawful quantity and overcome a long tradition of visualization. In fluctuations experimenters possessed a stable signature of processes on the atomic scale producing a well-known phenomenon observable under the microscope. The paper shows that focusing on the concept of signature common in particle physics allows one to avoid certain traps of the realism-instrumentalism debate centering on Brownian motion and keep important lessons from the analyses about theory-mediated measurement and multiple determination.

Horacio M. Cataldo