Electromagnetic thermal corrections to Casimir energy

2016 ◽  
Vol 31 (22) ◽  
pp. 1650127 ◽  
Author(s):  
Borzoo Nazari

In [B. Nazari, Mod. Phys. Lett. A 31, 1650007 (2016)], we calculated finite temperature corrections to the energy of the Casimir effect of two conducting parallel plates in a general weak gravitational field. The calculations was done for the case a scalar field was present between the plates. Here we find the same results in the presence of an electromagnetic field.

2016 ◽  
Vol 31 (02) ◽  
pp. 1650007 ◽  
Author(s):  
Borzoo Nazari

We calculate finite temperature corrections to the energy of the Casimir effect of a two conducting parallel plates in a general weak gravitational field. After solving the Klein–Gordon equation inside the apparatus, mode frequencies inside the apparatus are obtained in terms of the parameters of the weak background. Using Matsubara’s approach to quantum statistical mechanics gravity-induced thermal corrections of the energy density are obtained. Well-known weak static and stationary gravitational fields are analyzed and it is found that in the low temperature limit the energy of the system increases compared to that in the zero temperature case.


2012 ◽  
Vol 27 (16) ◽  
pp. 1250082 ◽  
Author(s):  
MUSTAFA ÖZCAN

The Casimir effect giving rise to an attractive force between the closely spaced two concentric spheres that confine the massless scalar field is calculated by using a direct mode summation with contour integration in the complex plane of eigenfrequencies. We developed a new approach appropriate for the calculation of the Casimir energy for spherical boundary conditions. The Casimir energy for a massless scalar field between the closely spaced two concentric spheres coincides with the Casimir energy of the parallel plates for a massless scalar field in the limit when the dimensionless parameter η, ([Formula: see text] where a(b) is inner (outer) radius of sphere), goes to zero. The efficiency of new approach is demonstrated by calculation of the Casimir energy for a massless scalar field between the closely spaced two concentric half spheres.


2020 ◽  
Vol 35 (31) ◽  
pp. 2050209
Author(s):  
Andrea Erdas

In this paper, I study the Casimir effect caused by a charged and massive scalar field that breaks Lorentz invariance in a CPT-even, aether-like manner. I investigate the case of a scalar field that satisfies Dirichlet or mixed (Dirichlet–Neumann) boundary conditions on a pair of very large plane parallel plates. The case of Neumann boundary conditions is straightforward and will not be examined in detail. I use the [Formula: see text]-function regularization technique to study the effect of a constant magnetic field, orthogonal to the plates, on the Casimir energy and pressure. I investigate the cases of a timelike Lorentz asymmetry, a spacelike Lorentz asymmetry in the direction perpendicular to the plates, and a spacelike asymmetry in the plane of the plates and, in all those cases, derive simple analytic expressions for the zeta function, Casimir energy and pressure in the limits of small plate distance, strong magnetic field and large scalar field mass. I discover that the Casimir energy and pressure, and their magnetic corrections, all strongly depend on the direction of the unit vector that implements the breaking of the Lorentz symmetry.


Author(s):  
Andrea Erdas

In this work, I study the Casimir effect of a massive complex scalar field in the presence of one large compactified extra dimension. I investigate the case of a scalar field confined between two parallel plates in the macroscopic three dimensions, and examine the cases of Dirichlet and mixed (Dirichlet–Neumann) boundary conditions on the plates. The case of Neumann boundary conditions is uninteresting, since it yields the same result as the case of Dirichlet boundary conditions. The scalar field also permeates a fourth compactified dimension of a size that could be comparable to the distance between the plates. This investigation is carried out using the [Formula: see text]-function regularization technique that allows me to obtain exact expressions for the Casimir energy and pressure. I discover that when the compactified length of the extra dimension is similar to the plate distance, or slightly larger, the Casimir energy and pressure become significantly different than their standard three-dimensional values, for either Dirichlet or mixed boundary conditions. Therefore, the Casimir effect of a quantum field that permeates a compactified fourth dimension could be used as an effective tool to explore the existence of large compactified extra dimensions.


2002 ◽  
Vol 17 (29) ◽  
pp. 4385-4392 ◽  
Author(s):  
DANIEL MÜLLER ◽  
HELIO V. FAGUNDES

The original Casimir effect results from the difference in the vacuum energies of the electromagnetic field, between that in a region of space with boundary conditions and that in the same region without boundary conditions. In this paper we develop the theory of a similar situation, involving a scalar field in spacetimes with closed spatial sections of negative curvature.


2012 ◽  
Vol 07 ◽  
pp. 202-208
Author(s):  
XIANG-HUA ZHAI ◽  
YANG YANG ◽  
JIE LAI

We study the finite temperature Casimir effect between perfectly conducting parallel plates in (D + 1)-dimensional spacetime by using zeta-function regularization technique. We get the analytical results for Casimir energy, Casimir free energy, Casimir entropy and Casimir pressure expressed by Riemann zeta function and Bessel function and give the asymptotic expressions for low and high temperature limits. In the case of D = 3, through mathematic transformation, we reproduce the standard results in the literature which is in most times obtained by using Green's function regularization technique.


2014 ◽  
Vol 29 (17) ◽  
pp. 1450091 ◽  
Author(s):  
Andrea Erdas ◽  
Kevin P. Seltzer

The finite temperature Casimir effect for a charged, massive scalar field confined between very large, perfectly conducting parallel plates is studied using the zeta function regularization technique. The scalar field satisfies Dirichlet boundary conditions at the plates and a magnetic field perpendicular to the plates is present. Four equivalent expressions for the zeta function are obtained, which are exact to all orders in the magnetic field strength, temperature, scalar field mass and plate distance. The zeta function is used to calculate the Helmholtz free energy of the scalar field and the Casimir pressure on the plates, in the case of high temperature, small plate distance, strong magnetic field and large scalar mass. In all cases, simple analytic expressions of the zeta function, free energy and pressure are obtained, which are very accurate and valid for practically all values of temperature, plate distance, magnetic field and mass.


2002 ◽  
Vol 17 (06n07) ◽  
pp. 790-793 ◽  
Author(s):  
V. V. NESTERENKO ◽  
G. LAMBIASE ◽  
G. SCARPETTA

The basic results in calculations of the thermodynamic functions of electromagnetic field in the background of a dilute dielectric ball at zero and finite temperature are presented. Summation over the angular momentum values is accomplished in a closed form by making use of the addition theorem for the relevant Bessel functions. The behavior of the thermodynamic characteristics in the low and high temperature limits is investigated. The T3-term in the low temperature expansion of the free energy is recovered (this term has been lost in our previous calculations).


2019 ◽  
Vol 34 (20) ◽  
pp. 1950107
Author(s):  
Dêivid R. da Silva ◽  
M. B. Cruz ◽  
E. R. Bezerra de Mello

In this paper, we analyze the fermionic Casimir effects associated with a massless quantum field in the context of Lorentz symmetry violation approach based on Horava–Lifshitz methodology. In order to obtain these observables, we impose the standard MIT bag boundary condition on the fields on two large and parallel plates. Our main objectives are to investigate how the Casimir energy and pressure depend on the parameter associated with the breaking of Lorentz symmetry.


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