Casimir effect for scalar fields under Robin boundary conditions on plates

Romeo, August; Saharian, Aram A.

doi:10.1088/0305-4470/35/5/312

Casimir effect for scalar fields under Robin boundary conditions on plates

August Romeo
(
- Barcelona, IEEC
)
,
Aram A. Saharian
(
- Yerevan State U.
)

Jul, 2000

20 pages

Published in:

J.Phys.A 35 (2002) 1297-1320

e-Print:

hep-th/0007242 [hep-th]

DOI:

10.1088/0305-4470/35/5/312

Report number:

YSU-0094

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Abstract:

We study the Casimir effect for scalar fields with general curvature coupling subject to mixed boundary conditions

(1+\beta_{m}n^{\mu}\partial_{\mu})\phi =0

at

x=a_{m}

on one (

m=1

) and two (

m=1,2

) parallel plates at a distance

a\equiv a_{2}-a_{1}

from each other. Making use of the generalized Abel-Plana formula previously established by one of the authors \cite{Sahrev}, the Casimir energy densities are obtained as functions of

\beta_{1}

and of

\beta_{1}

,

\beta_{2}

,

a

, respectively. In the case of two parallel plates, a decomposition of the total Casimir energy into volumic and superficial contributions is provided. The possibility of finding a vanishing energy for particular parameter choices is shown, and the existence of a minimum to the surface part is also observed. We show that there is a region in the space of parameters defining the boundary conditions in which the Casimir forces are repulsive for small distances and attractive for large distances. This yields to an interesting possibility for stabilizing the distance between the plates by using the vacuum forces.

Note:

21 pages, 8 figures, consideration of the contribution from complex eigenmodes added, possibility for the stabilization of the distance between the plates is discussed; accepted for publication in J. Phys. A Report-no: YSU-0094

field theory: scalar
boundary condition
energy: Casimir
invariance: conformal
regularization: zeta function
analytic properties
numerical calculations

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