Casimir forces

Erom the qualitative analysis in this section, we tentatively conclude that there are several contributions of comparable magnitude to the thermal expansion at low temperatures. Higher order effects may also be present. In this case, it may be more straightforward to estimate the interaction between ripplons as extended membranes without using a multipole expansion, as indeed is done when computing the regular Casimir force between extended plates. 

Note that the Casimir force does not depend on any material constants, but is solely formulated in terms of fundamental constants, namely the velocity of... 

G.W.F. Drake High-Precision Calculations for the Rydberg States of Helium in Long Range Casimir Forces Theory and Recent Experiments in Atomic Systems, ed. by F.S. Levin, D.A. Micha (Plenum Press, New York, 1993), pp. 107-217... 

The Derjaguin idea, a mainstay in colloid science since its 1934 publication, was rediscovered by nuclear physicists in the 1970s. In the physics literature one speaks of "proximity forces," surface forces that fit the criteria already given. The "Derjaguin transformation" or "Derjaguin approximation" of colloid science, to convert parallel-surface interaction into that between oppositely curved surfaces, becomes the physicists "proximity force theorem" used in nuclear physics and in the transformation of Casimir forces.23... 

Source From T. Emig, A. Hanke, R. Golestanian, and M. Kardar, "Normal and lateral Casimir forces between deformed plates," Phys. Rev. A 67, 022114 (2003) numbers in [ ] are equation numbers in this source paper. Separation H in that paper is replaced here with Z period of corrugation k with kc energy with E. Symbols Gtm, Gte, Li , a, x, z, u, and n here as in source article. 

The interaction of real metal plates is in fact far more complicated than what is derived assuming ideal infinite conductance. See B. W. Ninham and J. Daicic, "Lifshitz theory of Casimir forces at finite temperature," Phys. Rev. A, 57, 1870-80 (1998), for an instructive essay that includes the effects of finite temperature, finite conductance, and electron-plasma properties. The nub of the matter is that the Casimir result is strictly correct only at zero temperature. 

H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and F. Capasso, "Quantum mechanical actuation of microelectro mechanical systems by the Casimir force," Science, 291, 1941-4 (2001) "Nonlinear micromechanical Casimir oscillator," Phys. Rev. Lett., 87, 211801 (2001). 

The attractive Casimir force between two plates of area A can be calculated approximately using the formula F = (phcA)/(480r4), where h is Planck constant, c is the speed of light, and r is the distance between the plates. 

Casimir force was predicted by H.B.G. Casimir in 1948. The first experimental confirmation came in 1958, and it was rigorously described in 1997 [ii]. 

P.W. MHonni, Casimir forces without the vacuum radiation field. Phys. Rev. A 25 (1982) 1315. 

PW Milonni, M.-L. Shih, Source theory of the Casimir force. Phys. Rev. A 45 (1992) 4241. R.R. McLone, E.A. Power, On the Interaction Between Two Identical Neutral Dipole Systems, One in an Excited State and the Other in the Ground State. Mathematika 11 (1964) 91. 

Various quantum effects arising due to the motion of dielectric boundaries, including the modification of the Casimir force and creation of photons, in both one and three dimensions, and for different orientations of the velocity vector with respect to the surface, have been studied in detail in the series of papers by Barton and his collaborators [142-148]. In one paper [142] the term mirror-induced radiation (MIR) was introduced. 

A possibility of generating the nonclassical (in particular, squeezed) states of the electromagnetic field in the cavity with moving walls was pointed out in several studies in [106,114,124,158-161], The dynamical Casimir force has been interpreted as a mechanical signature of the squeezing effect associated with the mirror s motion [123,125] (see also Ref. 162). 

It is not heretical to consider the electromagnetic vacuum as a physical system. In fact, it manifests some physical properties and is responsible for a number of important effects. For example, the field amplitudes continue to oscillate in the vacuum state. These zero-point oscillations cause the spontaneous emission [1], the natural linebreadth [5], the Lamb shift [6], the Casimir force between conductors [7], and the quantum beats [8]. It is also possible to generate quantum states of electromagnetic field in which the amplitude fluctuations are reduced below the symmetric quantum limit of zero-point oscillations in one quadrature component [9]. 

Modern sensors are remarkable in many ways. Their small dimensions open up new areas of mechanics, flow control, friction, and oscillation. Force measurements are just one example. The once somewhat obscure classical Coriolis force is now the principle means of sensing rotation. And the even more obscure miniscale quantum-mechanical Casimir force, arising between two close interfaces, is now also accessible to sensor structures. Sensitivities are astonishing even now, but will most probably continue to be enhanced. Very many external parameters, such as temperature, pressure, and electromagnetic fields, can be accurately and quickly measured. What a wonderful area of activity for physicists, chemists, engineers - and salespeople alike The prospect of protecting humankind as well as the environment is gratifying. 

The pseudo-Casimir force in a heterophase system wiU be illustrated with the example of a thin nematogenic film with order-inducing wetting layers on both confining surfaces discussed before. The resulting fluctuation force can be interpreted in terms of two contributions (i) the interaction between the substrates and the phase boundaries and (ii) the interaction between the two phase boundaries. 

Experimental Evidence of Structural and Pseudo-Casimir Forces in Liquid Crystals... 

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