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 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.

Electromagnetic thermal corrections to Casimir energy

2016 ◽  
Vol 31 (22) ◽  
pp. 1650127 ◽  
Author(s):  
Borzoo Nazari
Keyword(s):  
Electromagnetic Field ◽  
Gravitational Field ◽  
Scalar Field ◽  
Finite Temperature ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Parallel Plates ◽  
Weak Gravitational Field

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.

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 CASIMIR ENERGY OF A DILUTE DIELECTRIC BALL AT ZERO AND FINITE TEMPERATURE

2002 ◽  
Vol 17 (06n07) ◽  
pp. 790-793 ◽  
Author(s):  
V. V. NESTERENKO ◽  
G. LAMBIASE ◽  
G. SCARPETTA
Keyword(s):  
Free Energy ◽  
Electromagnetic Field ◽  
Angular Momentum ◽  
High Temperature ◽  
Finite Temperature ◽  
Bessel Functions ◽  
Thermodynamic Characteristics ◽  
Casimir Energy ◽  
Addition Theorem ◽  
Temperature Expansion

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).

scholarly journals Fermionic Casimir effect in Horava–Lifshitz theories

2019 ◽  
Vol 34 (20) ◽  
pp. 1950107
Author(s):  
Dêivid R. da Silva ◽  
M. B. Cruz ◽  
E. R. Bezerra de Mello
Keyword(s):  
Boundary Condition ◽  
Casimir Effect ◽  
Lorentz Symmetry ◽  
Casimir Energy ◽  
Quantum Field ◽  
Parallel Plates ◽  
Symmetry Violation ◽  
Massless Quantum

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.

REGULARIZATION OF GENERAL MULTIDIMENSIONAL EPSTEIN ZETA-FUNCTIONS

1989 ◽  
Vol 01 (01) ◽  
pp. 113-128 ◽  
Author(s):  
E. ELIZALDE ◽  
A. ROMEO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Partition Function ◽  
Zeta Function ◽  
Finite Temperature ◽  
Casimir Effect ◽  
Zeta Functions ◽  
Quantum Field ◽  
Type Formula

We study expressions for the regularization of general multidimensional Epstein zeta-functions of the type [Formula: see text] After reviewing some classical results in the light of the extended proof of zeta-function regularization recently obtained by the authors, approximate but very quickly convergent expressions for these functions are derived. This type of analysis has many interesting applications, e.g. in any quantum field theory defined in a partially compactified Euclidean spacetime or at finite temperature. As an example, we obtain the partition function for the Casimir effect at finite temperature.

scholarly journals The Casimir effect for thick pistons

2016 ◽  
Vol 31 (06) ◽  
pp. 1650012
Author(s):  
Guglielmo Fucci
Keyword(s):  
Boundary Conditions ◽  
Zeta Function ◽  
Regularization Method ◽  
Casimir Force ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Numerical Results ◽  
Spectral Zeta Function

In this work, we analyze the Casimir energy and force for a thick piston configuration. This study is performed by utilizing the spectral zeta function regularization method. The results we obtain for the Casimir energy and force depend explicitly on the parameters that describe the general self-adjoint boundary conditions imposed. Numerical results for the Casimir force are provided for specific types of boundary conditions and are also compared to the corresponding force on an infinitely thin piston.

scholarly journals CASIMIR EFFECT WITH A HELIX TORUS BOUNDARY CONDITION

2011 ◽  
Vol 26 (26) ◽  
pp. 1953-1964 ◽  
Author(s):  
XIANG-HUA ZHAI ◽  
XIN-ZHOU LI ◽  
CHAO-JUN FENG
Keyword(s):  
Boundary Condition ◽  
Casimir Effect ◽  
Scalar Fields ◽  
Critical Value ◽  
Casimir Energy ◽  
Critical Ratio ◽  
Massive Scalar ◽  
Massless Field ◽  
Dimensional Spacetime ◽  
Pressure Changes

We use the generalized Chowla–Selberg formula to consider the Casimir effect of a scalar field with a helix torus boundary condition in the flat (D + 1)-dimensional spacetime. We obtain the exact results of the Casimir energy density and pressure for any D for both massless and massive scalar fields. The numerical calculation indicates that once the topology of spacetime is fixed, the ratio of the sizes of the helix will be a decisive factor. There is a critical value r c of the ratio r of the lengths at which the pressure vanishes. The pressure changes from negative to positive as the ratio r passes through r c increasingly. In the massive case, we find the pressure tends to the result of massless field when the mass approaches zero. Furthermore, there is another critical ratio of the lengths [Formula: see text] and the pressure is independent of the mass at [Formula: see text] in the D = 3 case.

scholarly journals Casimir Energy in a Bounded Gross-Neveu model

2018 ◽  
Vol 64 (6) ◽  
pp. 577
Author(s):  
Juan Cristóbal Rojas
Keyword(s):  
Boundary Conditions ◽  
Zeta Function ◽  
Casimir Effect ◽  
Beta Function ◽  
Spatial Dimension ◽  
Casimir Energy ◽  
The Other ◽  
Effective Theory ◽  
Different Boundary Conditions ◽  
Complex Picture

In this letter, we study some relevant parameters of the massless Gross-Neveu (GN) model in afinite spatial dimension for different boundary conditions. It is considered the standard homogeneousHartree-Fock solution using zeta function regularization for the study the mass dynamically generated and its respective beta function. It is found that the beta function does not depend on the boundary conditions. On the other hand, it was considered the Casimir effect of the resulting effective theory. There appears a complex picture where the sign of the generated forces depends on the parameters used in the study.

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