Dynamical Casimir effect

It is clear that all results accumulated for several decades cannot be collected in one chapter. Therefore, in the following sections we have decided to emphasize mainly a detailed exposition of our own results concerning the analytical solutions for the cavities with resonantly oscillating boundaries, since we hope that these solutions could be important for further studies on the problem known as the nonstationary Casimir effect or the dynamical Casimir effect. 

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. 

Thermofield dynamics Generalized bogoliubov transormations and applications to Casimir effect... 

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. 

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). 

Casimir and Polder also showed that retardation effects weaken the dispersion force at separations of the order of the wavelength of the electronic absorption bands of the interacting molecules, which is typically 10 m. The retarded dispersion energy varies as R at large R and is determined by the static polarizabilities of the interacting molecules. At very large separations the forces between molecules are weak but for colloidal particles and macroscopic objects they may add and their effects are measurable. Fluctuations in particle position occur more slowly for nuclei than for electrons, so the intermolecular forces that are due to nuclear motion are effectively unretarded. A general theory of the interaction of macroscopic bodies in terms of the bulk static and dynamic dielectric properties... 

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