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 The Casimir effect for pistons with transmittal boundary conditions

2017 ◽  
Vol 32 (31) ◽  
pp. 1750182 ◽  
Author(s):  
Guglielmo Fucci
Keyword(s):  
Boundary Conditions ◽  
Casimir Force ◽  
Compact Riemannian Manifold ◽  
Closed Interval ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Dimensional Sphere ◽  
Product Manifold ◽  
Regularization Technique ◽  
Spectral Zeta Function

This work focuses on the analysis of the Casimir effect for pistons subject to transmittal boundary conditions. In particular we consider, as piston configuration, a direct product manifold of the type [Formula: see text] where [Formula: see text] is a closed interval of the real line and [Formula: see text] is a smooth compact Riemannian manifold. By utilizing the spectral zeta function regularization technique, we compute the Casimir energy of the system and the Casimir force acting on the piston. Explicit results for the force are provided when the manifold [Formula: see text] is a [Formula: see text]-dimensional sphere.

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.

BEYOND PROXIMITY FORCE APPROXIMATION IN THE CASIMIR EFFECT

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1743-1747 ◽  
Author(s):  
M. BORDAG ◽  
V. NIKOLAEV
Keyword(s):  
Boundary Conditions ◽  
Casimir Force ◽  
Dirichlet Boundary ◽  
Casimir Effect ◽  
Neumann Boundary ◽  
Numerical Results ◽  
Dirichlet Boundary Conditions ◽  
Proximity Force Approximation ◽  
Interacting Surfaces ◽  
General Appearance

We compare the analytical and numerical results for the Casimir force for the configuration of a plane and a cylinder in front of a plane. While for Dirichlet boundary conditions on both, plane and sphere or cylinder, agreement is found, for Neumann boundary conditions on either the plane or one of the two, cylinder or sphere, disagreement is found. This holds, for a sphere, also for different boundary conditions on the interacting surfaces. From recent, new numerical results for the cylinder, a general appearance of logarithmic contributions beyond PFA can be predicted.

scholarly journals SCALAR CASIMIR EFFECT BETWEEN TWO CONCENTRIC D-DIMENSIONAL SPHERES

2012 ◽  
Vol 27 (18) ◽  
pp. 1250094 ◽  
Author(s):  
MUSTAFA ÖZCAN
Keyword(s):  
Scalar Field ◽  
Boundary Conditions ◽  
Complex Plane ◽  
Casimir Force ◽  
Dirichlet Boundary ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Dirichlet Boundary Conditions ◽  
Massless Scalar ◽  
Massless Scalar Field

The Casimir energy for a massless scalar field between the closely spaced two concentric D-dimensional (for D>3) spheres is calculated by using the mode summation with contour integration in the complex plane of eigenfrequencies and the generalized Abel–Plana formula for evenly spaced eigenfrequency at large argument. The sign of the Casimir energy between closely spaced two concentric D-dimensional spheres for a massless scalar field satisfying the Dirichlet boundary conditions is strictly negative. The Casimir energy between (D-1)-dimensional surfaces, close to each other is regarded as interesting both by itself and as the key to describing of stability of the attractive Casimir force.

scholarly journals BOUNDARY CONDITIONS IN THE DIRAC APPROACH TO GRAPHENE DEVICES

2012 ◽  
Vol 14 ◽  
pp. 240-249 ◽  
Author(s):  
C.G. BENEVENTANO ◽  
E.M. SANTANGELO
Keyword(s):  
Boundary Conditions ◽  
Zeta Function ◽  
Continuum Limit ◽  
Casimir Energy ◽  
Local Boundary ◽  
Graphene Devices ◽  
The Continuum

We study a family of local boundary conditions for the Dirac problem corresponding to the continuum limit of graphene, both for nanoribbons and nanodots. We show that, among the members of such family, MIT bag boundary conditions are the ones which are in closest agreement with available experiments. For nanotubes of arbitrary chirality satisfying these last boundary conditions, we evaluate the Casimir energy via zeta function regularization, in such a way that the limit of nanoribbons is clearly determined.

Chern-Simons boundary layers in the Casimir effect

2020 ◽  
Vol 35 (03) ◽  
pp. 2040015 ◽  
Author(s):  
Valery N. Marachevsky
Keyword(s):  
Boundary Layers ◽  
Casimir Force ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Energy Minimum ◽  
Strong Reduction ◽  
Si Substrates ◽  
Glass Substrates ◽  
Chern Simons ◽  
Substrate Influence

Casimir interaction of two SiO2 glass half spaces being substrates for Chern-Simons boundary layers is studied. The separation between two half spaces at which the Casimir energy minimum occurs is strongly increased for dielectric SiO2 glass substrates in comparison with previously considered metal Au and semiconductor Si substrates. Strong reduction in the Casimir force due to presence of Chern-Simons layers is found for SiO2 glass substrate. Influence of modification of the infrared absorption on the Casimir force is studied.

scholarly journals TRACE ANOMALY AND CASIMIR EFFECT

2000 ◽  
Vol 15 (35) ◽  
pp. 2159-2164 ◽  
Author(s):  
M. R. SETARE ◽  
A. H. REZAEIAN
Keyword(s):  
Boundary Conditions ◽  
Stress Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Casimir Energy ◽  
Two Dimensions ◽  
Dirichlet Boundary Conditions ◽  
Curved Space ◽  
Trace Anomaly ◽  
Dimensional Domain

The Casimir energy for scalar field of two parallel conductors in two-dimensional domain wall background, with Dirichlet boundary conditions, is calculated by making use of general properties of renormalized stress–tensor. We show that vacuum expectation values of stress–tensor contain two terms which come from the boundary conditions and the gravitational background. In two dimensions the minimal coupling reduces to the conformal coupling and stress–tensor can be obtained by the local and nonlocal contributions of the anomalous trace. This work shows that there exists a subtle and deep connection between Casimir effect and trace anomaly in curved space–time.

scholarly journals Algebraic Approach to Casimir Force Between Two $$\delta $$-like Potentials

2021 ◽  
Author(s):  
Kamil Ziemian
Keyword(s):  
Asymptotic Expansion ◽  
Casimir Force ◽  
Casimir Effect ◽  
Scaling Limit ◽  
Algebraic Approach ◽  
Casimir Energy ◽  
Universal Function ◽  
The Other ◽  
Three Space ◽  
Physical Quantities

AbstractWe analyse the Casimir effect of two nonsingular centers of interaction in three space dimensions, using the framework developed by Herdegen. Our model is mathematically well-defined and all physical quantities are finite. We also consider a scaling limit, in which the problem tends to that with two Dirac $$\delta $$ δ ’s. In this limit the global Casimir energy diverges, but we obtain its asymptotic expansion, which turns out to be model dependent. On the other hand, outside singular supports of $$\delta $$ δ ’s the limit of energy density is a finite universal function (independent of the details of the nonsingular model before scaling). These facts confirm the conclusions obtained earlier for other systems within the approach adopted here: the form of the global Casimir force is usually dominated by the modification of the quantum state in the vicinity of macroscopic bodies.

scholarly journals Casimir effect in Horava–Lifshitz-like theories

2015 ◽  
Vol 30 (36) ◽  
pp. 1550220 ◽  
Author(s):  
I. J. Morales Ulion ◽  
E. R. Bezerra de Mello ◽  
A. Yu. Petrov
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Casimir Force ◽  
Casimir Effect ◽  
Lorentz Symmetry ◽  
Space Time ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Scalar Field Theory

In this paper, we consider a Lorentz-breaking scalar field theory within the Horava–Lifshtz approach. We investigate the changes that a space–time anisotropy produces in the Casimir effect. A massless real quantum scalar field is considered in two distinct situations: between two parallel plates and inside a rectangular two-dimensional box. In both cases, we have adopted specific boundary conditions on the field at the boundary. As we shall see, the energy and the Casimir force strongly depends on the parameter associated with the breaking of Lorentz symmetry and also on the boundary conditions.

scholarly journals Equivalence of zeta function technique and Abel–Plana formula in regularizing the Casimir energy of hyper-rectangular cavities

2014 ◽  
Vol 29 (35) ◽  
pp. 1450181
Author(s):  
Rui-Hui Lin ◽  
Xiang-Hua Zhai
Keyword(s):  
Zeta Function ◽  
Regularization Method ◽  
Function Method ◽  
Casimir Energy ◽  
Function Technique ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Epstein Zeta Function ◽  
Formula Method ◽  
Reflection Formula

Zeta function regularization is an effective method to extract physical significant quantities from infinite ones. It is regarded as mathematically simple and elegant but the isolation of the physical divergency is hidden in its analytic continuation. By contrast, Abel–Plana formula method permits explicit separation of divergent terms. In regularizing the Casimir energy for a massless scalar field in a D-dimensional rectangular box, we give the rigorous proof of the equivalence of the two methods by deriving the reflection formula of Epstein zeta function from repeatedly application of Abel–Plana formula and giving the physical interpretation of the infinite integrals. Our study may help with the confidence of choosing any regularization method at convenience among the frequently used ones, especially the zeta function method, without the doubts of physical meanings or mathematical consistency.

Sign in / Sign up

Export Citation Format

Share Document