scholarly journals Magnetic field corrections to the repulsive Casimir effect at finite temperature

2016 ◽  
Vol 31 (07) ◽  
pp. 1650018 ◽  
Author(s):  
Andrea Erdas
Keyword(s):  
Magnetic Field ◽  
Free Energy ◽  
High Temperature ◽  
Finite Temperature ◽  
Casimir Effect ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Parallel Plates ◽  
The Magnetic Field ◽  
Plate Distance

I investigate the finite temperature Casimir effect for a charged and massless scalar field satisfying mixed (Dirichlet–Neumann) boundary conditions on a pair of plane parallel plates of infinite size. The effect of a uniform magnetic field, perpendicular to the plates, on the Helmholtz free energy and Casimir pressure is studied. The [Formula: see text]-function regularization technique is used to obtain finite results. Simple analytic expressions are obtained for the zeta function and the free energy, in the limits of small plate distance, high temperature and strong magnetic field. The Casimir pressure is obtained in each of the three limits and the situation of a magnetic field present between and outside the plates, as well as that of a magnetic field present only between the plates is examined. It is discovered that, in the small plate distance and high temperature limits, the repulsive pressure is less when the magnetic field is present between the plates but not outside, than it is when the magnetic field is present between and outside the plates.

scholarly journals Finite temperature Casimir effect for massive scalars in a magnetic field

2014 ◽  
Vol 29 (17) ◽  
pp. 1450091 ◽  
Author(s):  
Andrea Erdas ◽  
Kevin P. Seltzer
Keyword(s):  
Magnetic Field ◽  
Free Energy ◽  
Scalar Field ◽  
Zeta Function ◽  
Finite Temperature ◽  
Casimir Effect ◽  
Dirichlet Boundary Conditions ◽  
Parallel Plates ◽  
Massive Scalar Field ◽  
Plate Distance

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.

scholarly journals Casimir Effect in Domain Wall Formation

2003 ◽  
Vol 18 (23) ◽  
pp. 4285-4293 ◽  
Author(s):  
M. R. Setare
Keyword(s):  
Domain Wall ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Casimir Effect ◽  
Mixed Boundary Conditions ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Parallel Plates ◽  
De Sitter ◽  
Casimir Forces

The Casimir forces on two parallel plates in conformally flat de Sitter background due to conformally coupled massless scalar field satisfying mixed boundary conditions on the plates is investigated. In the general case of mixed boundary conditions formulae are derived for the vacuum expectation values of the energy–momentum tensor and vacuum forces acting on boundaries. Different cosmological constants are assumed for the space between and outside of the plates to have general results applicable to the case of domain wall formations in the early universe.

scholarly journals Influence of quantized massive matter fields on the Casimir effect

2015 ◽  
Vol 30 (20) ◽  
pp. 1550099
Author(s):  
Yu. A. Sitenko
Keyword(s):  
Magnetic Field ◽  
Casimir Effect ◽  
Hamiltonian Operator ◽  
Matter Field ◽  
Parallel Plates ◽  
Vacuum Fluctuations ◽  
New Type ◽  
The Magnetic Field ◽  
External Uniform Magnetic Field ◽  
Matter Fields

Charged massive matter fields of spin-0 and spin-[Formula: see text] are quantized in the presence of an external uniform magnetic field in a spatial region bounded by two parallel plates. The most general set of boundary conditions at the plates, that is required by mathematical consistency and the self-adjointness of the Hamiltonian operator, is employed. The vacuum fluctuations of the matter field in the case of the magnetic field orthogonal to the plates are analyzed, and it is shown that the pressure from the vacuum onto the plates is positive and independent of the boundary condition, as well as of the distance between the plates. Possibilities of the detection of this new-type Casimir effect are discussed.

scholarly journals SCALAR CASIMIR EFFECT BETWEEN TWO CONCENTRIC SPHERES

2012 ◽  
Vol 27 (16) ◽  
pp. 1250082 ◽  
Author(s):  
MUSTAFA ÖZCAN
Keyword(s):  
Scalar Field ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Outer Radius ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Parallel Plates ◽  
New Approach ◽  
Concentric Spheres ◽  
Spherical Boundary

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.

scholarly journals THEORY OF THE CASIMIR EFFECT FOR GRAPHENE AT FINITE TEMPERATURE

2012 ◽  
Vol 14 ◽  
pp. 435-444 ◽  
Author(s):  
VALERY N. MARACHEVSKY
Keyword(s):  
Free Energy ◽  
High Temperature ◽  
Finite Temperature ◽  
Graphene Layer ◽  
Casimir Effect ◽  
Temperature Behavior ◽  
Metal System ◽  
High Temperature Behavior ◽  
Metal Metal

Theory of the Casimir effect for a flat graphene layer interacting with a parallel flat material is presented in detail. The high-temperature asymptotics of a free energy in a graphene-metal system coincides with a Drude high-temperature asymptotics of the metal-metal system. High-temperature behavior in the graphene-metal system is expected at separations of the order of 100 nm at temperature T = 300 K .

scholarly journals Casimir effect in an axially symmetric spacetime with unparticles

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
V. B. Bezerra ◽  
C. R. Muniz ◽  
H. S. Vieira
Keyword(s):  
Energy Density ◽  
Characteristic Length ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Einstein Equations ◽  
Kerr Solution ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Parallel Plates ◽  
Axially Symmetric

Abstract We investigate the Casimir effect of the massless scalar field in a cavity formed by ideal parallel plates in the spacetime generated by a rotating axially symmetric distribution of vector or scalar (tensor) unparticles, around which the plates orbit. The presence of the unparticles is incorporated to the background by means of a correction to the Kerr solution of the Einstein equations, in which the characteristic length and the scale dimension associated to the unparticle theory are taken into account. We show that the Casimir energy density depends also on these parameters. The analysis of the “ungravity” limit for the Casimir energy density, in which the characteristic length is very large in comparison to the horizon radius, is made, too. At zero temperature, we show that such a limit implies the instability of the system, since the Casimir energy density becomes an imaginary quantity. The general result is compared to the current terrestrial experiments of the Casimir effect. Thermal corrections also are investigated and the ungravity limit again examined, with the aforementioned instability disappearing at high temperatures.

scholarly journals Casimir effect in the Kerr spacetime with quintessence

2016 ◽  
Vol 32 (01) ◽  
pp. 1750005 ◽  
Author(s):  
V. B. Bezerra ◽  
M. S. Cunha ◽  
L. F. F. Freitas ◽  
C. R. Muniz ◽  
M. O. Tahim
Keyword(s):  
Casimir Effect ◽  
Polar Angle ◽  
State Parameter ◽  
Spherical Body ◽  
Casimir Energy ◽  
Radial Coordinate ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Parallel Plates ◽  
Kerr Spacetime

We calculate the Casimir energy of a massless scalar field in a cavity formed by nearby parallel plates orbiting a rotating spherical body surrounded by quintessence, investigating the influence of the gravitational field on that energy, at zero temperature. This influence includes the effects due to the spacetime dragging caused by the source rotation as well as those ones due to the quintessence. We show that the energy depends on all the involved parameters, as source mass, angular momentum and quintessence state parameter, for any radial coordinate and polar angle. We show that at the north pole the Casimir energy is not influenced by the quintessential matter. At the equatorial plane, when the quintessence is canceled, the result obtained in the literature is recovered. Finally, constraints in the quintessence parameters are obtained from the uncertainty in the current measurements of Casimir effect.

FINITE TEMPERATURE CASIMIR EFFECT FOR PERFECTLY CONDUCTING PARALLEL PLATES IN (D + 1)-DIMENSIONAL SPACETIME

2012 ◽  
Vol 07 ◽  
pp. 202-208
Author(s):  
XIANG-HUA ZHAI ◽  
YANG YANG ◽  
JIE LAI
Keyword(s):  
Free Energy ◽  
Zeta Function ◽  
Finite Temperature ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Parallel Plates ◽  
Regularization Technique ◽  
Asymptotic Expressions ◽  
Dimensional Spacetime ◽  
Riemann Zeta

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.

scholarly journals On finite temperature Casimir effect for Dirac lattices

2020 ◽  
Vol 35 (03) ◽  
pp. 2040019
Author(s):  
Irina Pirozhenko
Keyword(s):  
Free Energy ◽  
High Temperature ◽  
Heat Kernel ◽  
Finite Temperature ◽  
Casimir Effect ◽  
Delta Function ◽  
Nonzero Temperature ◽  
Heat Kernel Expansion

We consider polarizable sheets modeled by a lattice of delta function potentials. The Casimir interaction of two such lattices is calculated at nonzero temperature. The heat kernel expansion for periodic singular background is discussed in relation with the high temperature asymptote of the free energy.

scholarly journals Casimir effect in space-times of rotating wormholes

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
C. R Muniz ◽  
V. B. Bezerra ◽  
J. M. Toledo
Keyword(s):  
Black Hole ◽  
Energy Density ◽  
Casimir Effect ◽  
Kerr Black Hole ◽  
Casimir Energy ◽  
Vacuum Energy Density ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Thermodynamic Quantities ◽  
Parallel Plates

AbstractWe investigate the Casimir effect between parallel plates placed along a circular trajectory around the rotating Damour–Solodkhin (D–S) and Teo wormholes. This is made through the calculation of the renormalized quantum vacuum energy density of a massless scalar field obeying the Dirichlet boundary conditions, initially at zero temperature. We use the zero tidal approximation inside the cavity. Then, we compare our results with those ones previously obtained in the literature with respect to the Kerr black hole. We also compare the computed Casimir energy density in a static D–S wormhole spacetime with that one recently found for a static Ellis wormhole. In what follows, we investigate the effect around the rotating Teo wormhole by calculating the Casimir energy density between the plates, and compare it with the same quantities obtained previously. Finally, we investigate the phenomenon at finite temperature, obtaining some Casimir thermodynamic quantities in the rotating D–S wormhole spacetime, comparing them with the ones valid in the Kerr black hole spacetime. With this, the ways as gravito-inertial and frame dragging effects influence the vacuum quantum fluctuations inside the Casimir apparatus allows to distinct among the different types of rotating wormholes and black holes.

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