An experimental set-up for the measurement of the Casimir effect at separations larger than a few microns is presented. The apparatus is based on a mechanical resonator and uses a homodyne detection technique to sense the Casimir force in the plane-parallel configuration. First measurements in the 3-10 micrometer range show an unexpected large force probably due to patch effects.

The dynamics of an ideal fluid or plasma is constrained by topological invariants such as the circulation of (canonical) momentum or, equivalently, the flux of the vorticity or magnetic fields. In the Hamiltonian formalism, topological invariants restrict the orbits to submanifolds of the phase space. While the coadjoint orbits have a natural symplectic structure, the global geometry of the deg...

The Casimir force between metallic plates made of realistic materials is evaluated for distances in the nanometer range. A spectrum over real frequencies is introduced and shows narrow peaks due to surface resonances (plasmon polaritons or phonon polaritons) that are coupled across the vacuum gap. We demonstrate that the Casimir force originates from the attraction (repulsion) due to the corres...

The Casimir effect giving rise to an attractive or repulsive force between the configuration boundaries that confine the massless scalar field is reexamined for one to three-dimensional pistons in this paper. Especially, we consider Casimir pistons with hybrid boundary conditions, where the boundary condition on the piston is Neumann and those on other surfaces are Dirichlet. We show that the C...

The chain rule for functionals is used to reduce the noncanonical Poisson bracket for magnetohydrodynamics (MHD) to one for axisymmetric and translationally symmetric MHD and hydrodynamics. The procedure for obtaining Casimir invariants from noncanonical Poisson brackets is reviewed and then used to obtain the Casimir invariants for the considered symmetrical theories. It is shown why extrema o...

The Casimir force is one of the most accessible experimental consequences of vacuum fluctuations in the macroscopic world. It is the most significant force between neutral, non-magnetic objects at distances on the micrometer scale and below. For many experiments searching for novel short-range forces predicted by unification models, theoretical calculations of the Casimir force are crucial and ...

In this Letter, we consider the fluctuation-induced force exerted between two plates separated by a distance L in a fluid with a temperature gradient. We predict that for a range of distances L, this nonequilibrium force is anomalously large compared to other Casimir forces. The physical reason is that correlations in a nonequilibrium fluid are generally of longer range than other correlations,...

The scaling properties of the free energy and some of universal amplitudes of a group of models belonging to the universality class of the quantum nonlinear sigma model and the O(n) quantum φ4 model in the limit n → ∞ as well as the quantum spherical model, with nearest-neighbor and long-range interactions (decreasing at long distances r as 1/rd+σ) is presented. For temperature driven phase tra...

Results of lattice analysis indicate that the static potential in SU(3) gauge theory is proportional to eigenvalue of quadratic Casimir operator for the corresponding representation with a good accuracy. We discuss the pattern of deviation from this Casimir scaling in gluodynamics in terms of correlators of path-ordered gauge-invariant operators defined on the worldsheet of the confining string.