<FONT FACE=Symbol>z</font>-function method for repulsive Casimir forces

Abstract

We compute the Casimir pressure between an unusual pair of parallel plates, namely, a perfectly conducting plate ! 1 and an in nitely permeable one ! 1 with the generalized -function method. The result for this problem, which has been rarely discussed in the literature, is a repulsive Casimir force. The -function method provides a very compact and economic way of obtaining the nal result.Since Casimir's paper 1 on the attraction of two neutral parallel perfectly conducting plates due to the vacuum uctuations of the electromagnetic eld, a considerable amount o f w ork has been done on this subject, varying from the application of alternative techniques to the exploration of new geometries and theories. Excellent reviews as well as a large list of relevant references on this subject can be found in the work of Plunien et al 2 and in the book by Mostepanenko and Trunov 3 .The rst experimental test of Casimir's prediction was made by Sparnaay 4 only in 1958. However, the accuracy of the results was far from being reasonable: approximately one hundred percent of error. Since then, experiments involving dielectrics have been done, but only four decades after Sparnaay's work an experiment of the Casimir force between metals was repeated: in 1997, Lamoreaux 5 made an experiment with a slightly di erent geometry a spherical metallic lens and a at metal plate where theory and the experimental data agree within a few percents. More recently, another experiment with metals was performed by U. Mohideen and A. Roy 6 . Using an atomic force microscope they measured the Casimir force between a metallized sphere of diameter equal to 196m and a at metal plate for separations from 0; 1m t o 0 ; 9m. They showed that the experimental data are in very good agreement with the theoretical predictions. May be this is one of the most striking results of quantum eld theory once it is a macroscopic measurable manifestation of the quantum vacuum. Instead of paying attention to the sources the perfect conducting plates, Casimir's approach for this problem consisted basically in computing the interacting energy between the plates as the regularized di erence between the zero point energies with and without the boundary conditions dictated by the physical situation perfectly conductor character of the plates. In fact, the great novelty of Casimir's paper of 1948 was not the fact that two neutral objects attracted each other 1 , but the simplicity of the method to do it in the context of quantum eld theory. However, since Casimir's work, many other techniques were developed which m a y be more appropriate depending on the physical situation under study. In particular, methods of computing e ective actions are in general very powerful for our purposes.We shall be concerned here with one of these methods, namely, the so called generalized -function method. In this communication we shall apply it to the unusual case of a pair of parallel plates, where one of them is perfectly conducting ! 1 , while the other is in nitely permeable ! 1 . This probl...

Casimir effect for a massive scalar field under mixed boundary conditions

“…The limits of small and large mass were taken and are in agreement with expected results. In fact, the zero mass limit coincides precisely with the results found in literature [8,10] and the first correction in the mass has opposite sign compared with the zero mass case. This means that the first correction weakens the Casimir energy.…”

“…On the other hand, for a small mass, we have the well known result for the corresponding massless case (first term of r.h.s. stands for − 7 8 times the standard result of the Casimir energy for a massless scalar field subjected to Dirichlet BC) [8,10] plus a small (negative) correction in m 2 .…”

“…Boyer [8] studied the Casimir force for electromagnetic field between two parallel plates where one of them was a perfectly conductor plate and the other was an infinitely permeable one. This result can be mimicked by a massless scalar field submitted to mixed BC [9,10]. Nowadays, the study of repulsive Casimir forces has attracted the attention of physicists, since the existence of paramagnetic material with non-trivial permeability may exist [11], though there is some controversy about it [12,13].…”

Thermofield dynamics and Casimir effect for fermions

“…The effect was an attractive force between the plates given by the negative pressure P = −π 2 /240L 4 (we use natural units: = c = 1) [15]. Over the decades, the Casimir effect has been applied to different geometries, fields and physical conditions, enjoying a remarkable popularity [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33] and raising interest, in particular, in the context of microelectronics [34,35] as a practical tool for switching devices.…”

Some developments of the Casimir effect in p-cavity of (D + 1)-dimensional space–time

“…[46][47][48][49][50][51][52][53][54][55][56] The zeta function technique, 46,47,50,51,53,54 which can be traced back to G. H. Hardy,57,58 is used to be regarded as an elegant and unique regularization method 59,60 different from other ones such as frequency cut-off method (see e.g. Ref.…”