  We consider the stochastic dynamics of an array of two closely spaced atomic
force microscope cantilevers in a viscous fluid for use as a possible
biomolecule sensor. The cantilevers are not driven externally, as is common in
applications of atomic force microscopy, and we explore the stochastic
cantilever dynamics due to the constant buffeting of fluid particles by
Brownian motion. The stochastic dynamics of two adjacent cantilevers are
correlated due to long range effects of the viscous fluid. Using a recently
proposed thermodynamic approach the hydrodynamic correlations are quantified
for precise experimental conditions through deterministic numerical
simulations. Results are presented for an array of two readily available atomic
force microscope cantilevers. It is shown that the force on a cantilever due to
the fluid correlations with an adjacent cantilever is more than 3 times smaller
than the Brownian force on an individual cantilever. Our results indicate that
measurements of the correlations in the displacement of an array of atomic
force microscopes can detect piconewton forces with microsecond time
resolution.
