Let g be a complex simple Lie algebra. Vogel derived a universal decomposition of S2g into (possibly virtual) Casimir eigenspaces, S2g = C⊕Y2 ⊕Y ′ 2 ⊕Y ′′ 2 which turns out to be a decomposition into irreducible modules. If we let 2t denote the Casimir eigenvalue of the adjoint representation (with respect to some invariant quadratic form), these modules respectively have Casimir eigenvalues 4t...

where ` is the area of each plate, a is the separation between them and the relation a ` is assumed in order to implement the condition of small separation. As a consequence of this shift there is an attractive force on the plates which was measured by Sparnaay in 1958 [2] and more recently with high accuracy by Lamoreaux [3] and by Mohideen and Roy [4, 5]. This shift in energy is known as the ...

Casimir effects have for many years been the subject of painstaking experiments and a variety of theoretical techniques, but it is only recently that they have attracted widespread attention. The surge of interest is attributable in large part to experimental developments. To the list of subtler reasons I would add one that can best be appreciated by the cognoscenti: Larry’s lapidary elucidatio...

The infinite-dimensional mechanics of fluids and plasmas can be formulated as “noncanonical” Hamiltonian systems on a phase space of Eulerian variables. Singularities of the Poisson bracket operator produce singular Casimir elements that foliate the phase space, imposing topological constraints on the dynamics. Here we proffer a physical interpretation of Casimir elements as adiabatic invariant...

Using field-theoretical methods and exploiting conformal invari-ance, we study Casimir forces at tricritical points exerted by long-range fluctuations of the order-parameter field. Special attention is paid to the situation where the symmetry is broken by the boundary conditions (extraordinary transition). Besides the parallel-plate configuration, we also discuss the geometries of two separate ...

" Screening " of universal van der Waals – Casimir terms by Coulomb gases in a fully-finite two-dimensional geometry Abstract. This paper is a continuation of a previous one [Jancovici B andŠamaj L, 2004 J. Stat. Mech. P08006] dealing with classical Casimir phenomena in semi-infinite wall geometries. In that paper, using microscopic Coulomb systems, the long-ranged Casimir force due to thermal ...

The critical Casimir force provides a thermodynamic analogue of the quantum mechanical Casimir force that arises from the confinement of electromagnetic field fluctuations. In its thermodynamic analogue, two surfaces immersed in a critical solvent mixture attract each other due to confinement of solvent concentration fluctuations. Here, we demonstrate the active assembly control of colloidal eq...

We review recent results obtained in the physics of the thermal Casimir force acting between two dielectrics, dielectric and metal, and between metal and semiconductor. The detailed derivation for the low-temperature behavior of the Casimir free energy, pressure and entropy in the configuration of two real dielectric plates is presented. For dielectrics with finite static dielectric permittivit...

In this paper we study the role of surface plasmon modes in the Casimir effect. First we write the Casimir energy as a sum over the modes of a real cavity. We may identify two sorts of modes, two evanescent surface plasmon modes and propagative modes. As one of the surface plasmon modes becomes propagative for some choice of parameters we adopt an adiabatic mode definition where we follow this ...

the natural frequency and pull-in instability of clamped-clamped nano-actuators in the presence of a dielectric layer are analyzed. the influence of the presence of casimir force, electrostatic force, fringing field effect, axial force, stretching effects and the size effect are taken into account. the governing equation of the dynamic response of the actuator is transformed in a non-dimensiona...