Article

# The Casimir effect: some aspects

Brazilian Journal of Physics (Impact Factor: 0.6). 01/2007; DOI: 10.1590/S0103-97332006000700006

Source: arXiv

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**ABSTRACT:**This paper studies the Casimir effect due to fractional massless Klein-Gordon field confined to parallel plates. A new kind of boundary condition called fractional Neumann condition which involves vanishing fractional derivatives of the field is introduced. The fractional Neumann condition allows the interpolation of Dirichlet and Neumann conditions imposed on the two plates. There exists a transition value in the difference between the orders of the fractional Neumann conditions for which the Casimir force changes from attractive to repulsive. Low and high temperature limits of Casimir energy and pressure are obtained. For sufficiently high temperature, these quantities are dominated by terms independent of the boundary conditions. Finally, validity of the temperature inversion symmetry for various boundary conditions is discussed. Comment: 31 pagesJournal of Mathematical Physics 04/2008; · 1.30 Impact Factor -
##### Article: Image method in the calculation of the van der Waals force between an atom and a conducting surface

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**ABSTRACT:**Initially, we make a detailed historical survey of van der Waals forces, collecting the main references on the subject. Then, we review a method recently proposed by Eberlein and Zietal to compute the dispersion van der Waals interaction between a neutral but polarizable atom and a perfectly conducting surface of arbitrary shape. This method has the advantage of relating the quantum problem to a corresponding classical one in electrostatics so that all one needs is to compute an appropriate Green function. We show how the image method of electrostatics can be conveniently used together with the Eberlein and Zietal mehtod (when the problem admits an image solution). We then illustrate this method in a couple of simple but important cases, including the atom-sphere system. Particularly, in our last example, we present an original result, namely, the van der Waals force between an atom and a boss hat made of a grounded conducting material.American Journal of Physics 04/2012; · 0.78 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The zero-point radiation is an electromagnetic form of energy pervading the universe. Its existence is granted by standard quantum theories. We provide here an explanation based on deterministic classical electrodynamics, by associating to particles and nuclei a series of shells, made of constrained photons, with frequencies decaying with the distance. Such photons are part of a pre-existing background, evolving in vacuum even at zero temperature, and are captured by stable subatomic particles to form very distinctive quantized patterns. The evolving shells bring, for instance, to the creation of a fractal-type structure of electromagnetic layers around a conductive body. This property is then used to justify, both qualitatively and quantitatively, the attractive Casimir force of two metal plates. The analysis is carried out by standard arguments, except that here the surrounding zero-point energy is finite and, albeit with a very complicated appearance, very well-organized. Comment: 22 pages, 12 figures06/2009;

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