Casimir forces can appear between intrusions placed in different media driven by several fluctuation mechanisms, either in equilibrium or out of it. Herein, we develop a general formalism to obtain such forces from the dynamical equations of the fluctuating medium, the statistical properties of the driving noise, and the boundary conditions of the intrusions (which simulate the interaction betw...

Recent progress in the simulation of Casimir forces between various objects has allowed traditional computational electromagnetic solvers to be used to find Casimir forces in arbitrary three-dimensional objects. The underlying theory to these approaches requires knowledge and manipulation of quantum field theory and statistical physics. We present a calculation of the Casimir force using the me...

The lateral Casimir force between a sinusoidally corrugated gold coated plate and large sphere was measured for surface separations between 0.2 to 0.3 microm using an atomic force microscope. The measured force shows the required periodicity corresponding to the corrugations. It also exhibits the necessary inverse fourth power distance dependence. The obtained results are shown to be in good ag...

We consider the three-dimensional Ising model in a L(⊥)×L(∥)×L(∥) cuboid geometry with a finite aspect ratio ρ=L(⊥)/L(∥) and periodic boundary conditions along all directions. For this model the finite-size scaling functions of the excess free energy and thermodynamic Casimir force are evaluated numerically by means of Monte Carlo simulations. The Monte Carlo results compare well with recent fi...

We report measurements of the Casimir force between a gold sphere and a silicon surface with an array of nanoscale, rectangular corrugations using a micromechanical torsional oscillator. At distances between 150 and 500 nm, the measured force shows significant deviations from the pairwise additive formulism, demonstrating the strong dependence of the Casimir force on the shape of the interactin...