scholarly journals Inhibition of the dynamical Casimir effect with Robin boundary conditions

2013 ◽  
Vol 87 (4) ◽  
Author(s):  
Andreson L. C. Rego ◽  
B. W. Mintz ◽  
C. Farina ◽  
Danilo T. Alves
Keyword(s):  
Boundary Conditions ◽  
Casimir Effect ◽  
Robin Boundary Conditions ◽  
Dynamical Casimir Effect ◽  
Robin Boundary

scholarly journals CASIMIR EFFECT FOR SCALAR FIELDS WITH ROBIN BOUNDARY CONDITIONS IN SCHWARZSCHILD BACKGROUND

2005 ◽  
Vol 20 (06) ◽  
pp. 441-450 ◽  
Author(s):  
M. R. SETARE
Keyword(s):  
Boundary Conditions ◽  
Stress Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Scalar Fields ◽  
Massless Scalar ◽  
Robin Boundary Conditions ◽  
Massless Scalar Field ◽  
Robin Boundary ◽  
Schwarzschild Background

The stress–tensor of a massless scalar field satisfying Robin boundary conditions on two one-dimensional wall in two-dimensional Schwarzschild background is calculated. We show that vacuum expectation value of stress–tensor can be obtained explicitly by Casimir effect, trace anomaly and Hawking radiation.

scholarly journals MODE SUMMATION APPROACH TO CASIMIR EFFECT BETWEEN TWO OBJECTS

2012 ◽  
Vol 27 (25) ◽  
pp. 1230021 ◽  
Author(s):  
L. P. TEO
Keyword(s):  
Boundary Conditions ◽  
Functional Form ◽  
Casimir Effect ◽  
Scalar Fields ◽  
Equation Of Motion ◽  
The Other ◽  
Robin Boundary Conditions ◽  
Operator Approach ◽  
The One ◽  
Robin Boundary

In the last few years, several approaches have been developed to compute the exact Casimir interaction energy between two nonplanar objects, all lead to the same functional form, which is called the TGTG formula. In this paper, we explore the TGTG formula from the perspective of mode summation approach. Both scalar fields and electromagnetic fields are considered. In this approach, one has to first solve the equation of motion to find a wave basis for each object. The two T's in the TGTG formula are [Formula: see text]-matrices representing the Lippmann–Schwinger T-operators, one for each of the objects. Each [Formula: see text]-matrix can be found by matching the boundary conditions imposed on the object, and it is independent of the other object. However, it depends on whether the object is interacting with an object outside it, or an object inside it. The two G's in the TGTG formula are the translation matrices, relating the wave basis of an object to the wave basis of the other object. These translation matrices only depend on the wave basis chosen for each object, and they are independent of the boundary conditions on the objects. After discussing the general theory, we apply the prescription to derive the explicit formulas for the Casimir energies for the sphere–sphere, sphere–plane, cylinder–cylinder and cylinder–plane interactions. First the [Formula: see text]-matrices for a plane, a sphere and a cylinder are derived for the following cases: the object is imposed with Dirichlet, Neumann or general Robin boundary conditions; the object is semitransparent; and the object is a magnetodielectric object immersed in a magnetodielectric media. Then the operator approach developed by R. C. Wittman [IEEE Trans. Antennas Propag.36, 1078 (1988)] is used to derive the translation matrices. From these, the explicit TGTG formula for each of the scenarios can be written down. On the one hand, we have summarized all the TGTG formulas that have been derived so far for the sphere–sphere, cylinder–cylinder, sphere–plane and cylinder–plane configurations. On the other hand, we provide the TGTG formulas for some scenarios that have not been considered before.

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