Casimir pressure

Abstract. Within the context of the Thermofield Dynamics, we introduce generalized Bogoliubov transformations which accounts simultaneously for spatial com-pactification and thermal effects. As a specific application of such a formalism, we consider the Casimir effect for Maxwell and Dirac fields at finite temperature. Particularly, we determine the temperature at which the Casimir pressure for a massless fermionic field in a cubic box changes its nature from attractive to repulsive. This critical temperature is approximately 100 MeV when the edge of the cube is of the order of the confining length ( 1 fm) for baryons. 

It is interesting to note that we have calculated the casimir pressure at finite temperature for parallel plates, a square wave-guide and a cubic box. For a fermion field in a cubic box with an edge of 1.0 fm, which is of the order of the nuclear dimensions, the critical temperature is 100 MeV. Such a result will have implications for confinement of quarks in nucleons. However such an analysis will require a realistic calculation, a spherical geometry, with full account of color and flavor degrees of freedom of quarks and gluons. 

The Casimir effect for the electromagnetic field between parallel metallic plates can be obtained from Eq. (23) the Casimir energy and pressure are... 

Similarly, from Eq. (24), we find the Casimir energy and pressure for the Dirac field confined between parallel plates, with anti-periodic boundary conditions, as ... 

The vdW force is always attractive between any two materials in a vacuum. This is because there is no interaction between a dielectric material and a vacuum. However, in the Casimir effect, the spatial restriction of vacuum quantum fluctuations when two metal plates are placed in close proximity, creates an attractive pressure on them, in addition to the vdw force. 

In the case in which the intermediate m is a vacuum, sm = Mm = 1, GAmB(/, T -> 0) coincides with the Casimir interaction energy whose derivative pressure between metallic plates is... 

Figure 18 Schematics of electro-optical potential including the Casimir-Polder attraction of Eq. (48) for 87Rb atom between leads. The evanescent field, that decreases exponentially on it half wave-length expels atoms away of the surface to the location where attractive forces balance the light pressure. The line in the well cartoons the trap occupation.

Another term, nonstationary Casimir effect (NSCE), was introduced earlier [116] for the class of phenomena caused by the reconstruction of the quantum state of field due to a time dependence of the geometric configuration [149— 152]. Its synonym is the term dynamical Casimir effect, which became popular after the series of articles by Schwinger [153-157] who tried to explain the phenomenon of sonoluminescence by the creation of photons in bubbles with time-dependent radii, oscillating under the action of acoustic pressure in the liquids (see a brief discussion of this subject in Section X). 

One of the reasons for the studies on the dynamical Casimir effect was Schwinger s hypothesis [153-157] that this effect could explain the sonolumi-nescence phenomenon, specifically, the emission of bright short pulses of the visible light from the gas bubbles in the water, when the bubbles pulsate because of the pressure oscillations in a strong standing acoustic wave. (Several reviews and numerous references related to this effect are available, [121,326-328].) There are several publications [329-331], whose authors considered the models giving tremendous numbers of photons that could be produced even in the visible range as a result of the fast motion of the boundaries. However, analysis of these models shows that they are based on such laws of motion of the boundaries that imply the superluminal velocities, so they are not realistic. 

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. 

Here the first equation is the usual Fourier law, the second relates the viscous pressure tensor to the internal variable W, and the last is the evolution of the internal variable. The matrix of the transport coefficients Ly is positive definite with L q = —Lq due to Onsager-Casimir reciprocal rules. 

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