scholarly journals THE CASIMIR EFFECT BETWEEN NON-PARALLEL PLATES BY GEOMETRIC OPTICS

2005 ◽  
Vol 17 (08) ◽  
pp. 859-880
Author(s):  
BRENDAN GUILFOYLE ◽  
WILHELM KLINGENBERG ◽  
SIDDHARTHA SEN
Keyword(s):  
Closed Form ◽  
Parallel Plate ◽  
Casimir Force ◽  
Complex Geometry ◽  
Casimir Effect ◽  
Parallel Plates ◽  
Parametric Approach ◽  
Geometric Optics ◽  
Original Result

The first two authors have developed a technique which uses the complex geometry of the space of oriented affine lines in ℝ3 to describe the reflection of rays off a surface. This can be viewed as a parametric approach to geometric optics which has many possible applications. Recently, Jaffe and Scardicchio have developed a geometric optics approximation to the Casimir effect and the main purpose of this paper is to show that the quantities involved can be easily computed by this complex formalism. To illustrate this, we determine explicitly and in closed form the geometric optics approximation of the Casimir force between two non-parallel plates. By making one of the plates finite, we regularize the divergence that is caused by the intersection of the planes. In the parallel plate limit, we prove that our expression reduces to Casimir's original result.

scholarly journals ON THE CASIMIR EFFECT FOR PARALLEL PLATES IN THE SPACETIME WITH ONE EXTRA COMPACTIFIED DIMENSION

2006 ◽  
Vol 21 (25) ◽  
pp. 1957-1963 ◽  
Author(s):  
HONGBO CHENG
Keyword(s):  
Extra Dimension ◽  
Casimir Force ◽  
Casimir Effect ◽  
Universal Extra Dimension ◽  
Parallel Plates

In this paper, the Casimir effect for parallel plates in the presence of one compactified universal extra dimension is re-examined in detail. Having regularized the expressions of Casimir force, we show that the nature of Casimir force is repulsive if the distance between the plates is large enough, which does not agree with the experimental phenomena.

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 A system for probing Casimir energy corrections to the condensation energy

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Diego Pérez-Morelo ◽  
Alexander Stange ◽  
Richard W. Lally ◽  
Lawrence K. Barrett ◽  
Matthias Imboden ◽  
...  
Keyword(s):  
Transition Temperature ◽  
Casimir Force ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Superconducting Film ◽  
Superconducting Transition ◽  
Parallel Plates ◽  
Condensation Energy ◽  
Conducting Plate

AbstractIn this article, we present a nanoelectromechanical system (NEMS) designed to detect changes in the Casimir energy. The Casimir effect is a result of the appearance of quantum fluctuations in an electromagnetic vacuum. Previous experiments have used nano- or microscale parallel plate capacitors to detect the Casimir force by measuring the small attractive force these fluctuations exert between the two surfaces. In this new set of experiments, we aim to directly detect the shifts in the Casimir energy in a vacuum due to the presence of the metallic parallel plates, one of which is a superconductor. A change in the Casimir energy of this configuration is predicted to shift the superconducting transition temperature (Tc) because of the interaction between it and the superconducting condensation energy. In our experiment, we take a superconducting film, carefully measure its transition temperature, bring a conducting plate close to the film, create a Casimir cavity, and then measure the transition temperature again. The expected shifts are smaller than the normal shifts one sees in cycling superconducting films to cryogenic temperatures, so using a NEMS resonator in situ is the only practical way to obtain accurate, reproducible data. Using a thin Pb film and opposing Au surface, we observe no shift in Tc >12 µK down to a minimum spacing of ~70 nm at zero applied magnetic field.

scholarly journals CASIMIR EFFECT AS A TEST FOR THERMAL CORRECTIONS AND HYPOTHETICAL LONG-RANGE INTERACTIONS

2005 ◽  
Vol 20 (11) ◽  
pp. 2205-2221 ◽  
Author(s):  
G. L. KLIMCHITSKAYA ◽  
R. S. DECCA ◽  
E. FISCHBACH ◽  
D. E. KRAUSE ◽  
D. LÓPEZ ◽  
...  
Keyword(s):  
Long Range ◽  
Casimir Force ◽  
Casimir Effect ◽  
Newtonian Gravity ◽  
Parallel Plates ◽  
Interaction Range ◽  
Rigorous Approach ◽  
Long Range Interactions ◽  
The Standard Model

We have performed a precise experimental determination of the Casimir pressure between two gold-coated parallel plates by means of a micromachined oscillator. In contrast to all previous experiments on the Casimir effect, where a small relative error (varying from 1% to 15%) was achieved only at the shortest separation, our smallest experimental error (~ 0.5%) is achieved over a wide separation range from 170 nm to 300 nm at 95% confidence. We have formulated a rigorous metrological procedure for the comparison of experiment and theory without resorting to the previously used root-mean-square deviation, which has been criticized in the literature. This enables us to discriminate among different competing theories of the thermal Casimir force, and to resolve a thermodynamic puzzle arising from the application of Lifshitz theory to real metals. Our results lead to a more rigorous approach for obtaining constraints on hypothetical long-range interactions predicted by extra-dimensional physics and other extensions of the Standard Model. In particular, the constraints on non-Newtonian gravity are strengthened by up to a factor of 20 in a wide interaction range at 95% confidence.

scholarly journals HOŘAVA–LIFSHITZ MODIFICATIONS OF THE CASIMIR EFFECT

2013 ◽  
Vol 28 (12) ◽  
pp. 1350052 ◽  
Author(s):  
A. F. FERRARI ◽  
H. O. GIROTTI ◽  
M. GOMES ◽  
A. YU. PETROV ◽  
A. J. DA SILVA
Keyword(s):  
Casimir Force ◽  
Casimir Effect ◽  
The Other ◽  
Parallel Plates ◽  
Other Hand ◽  
First Case

We study the modifications induced by spacetime anisotropy on the Casimir effect in the case of two parallel plates. Non-perturbative and perturbative regimes are analyzed. In the first case, the Casimir force either vanishes or it reverses its direction which, in any case, makes the proposal untenable. On the other hand, the perturbative model enables us to incorporate appropriately the effects of spacetime anisotropy.

scholarly journals Modular invariance in finite temperature Casimir effect

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Francesco Alessio ◽  
Glenn Barnich
Keyword(s):  
Partition Function ◽  
Chemical Potential ◽  
Casimir Effect ◽  
Temperature Inversion ◽  
Massless Scalar ◽  
Partition Functions ◽  
Parallel Plates ◽  
Modular Transformations ◽  
Real Analytic ◽  
Set Up

Abstract The temperature inversion symmetry of the partition function of the electromagnetic field in the set-up of the Casimir effect is extended to full modular transformations by turning on a purely imaginary chemical potential for adapted spin angular momentum. The extended partition function is expressed in terms of a real analytic Eisenstein series. These results become transparent after explicitly showing equivalence of the partition functions for Maxwell’s theory between perfectly conducting parallel plates and for a massless scalar with periodic boundary conditions.

scholarly journals Thermal Casimir effect with general boundary conditions

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
J. M. Muñoz-Castañeda ◽  
L. Santamaría-Sanz ◽  
M. Donaire ◽  
M. Tello-Fraile
Keyword(s):  
Boundary Conditions ◽  
Vacuum Energy ◽  
Casimir Effect ◽  
Quantum Field ◽  
Quantum Vacuum ◽  
Parallel Plates ◽  
Casimir Forces ◽  
Thermal Correction ◽  
Frequency Independent ◽  
Scalar Quantum

Abstract In this paper we study the system of a scalar quantum field confined between two plane, isotropic, and homogeneous parallel plates at thermal equilibrium. We represent the plates by the most general lossless and frequency-independent boundary conditions that satisfy the conditions of isotropy and homogeneity and are compatible with the unitarity of the quantum field theory. Under these conditions we compute the thermal correction to the quantum vacuum energy as a function of the temperature and the parameters encoding the boundary condition. The latter enables us to obtain similar results for the pressure between plates and the quantum thermal correction to the entropy. We find out that our system is thermodynamically stable for any boundary conditions, and we identify a critical temperature below which certain boundary conditions yield attractive, repulsive, and null Casimir forces.

scholarly journals Influence of Parallel Plate Stack Spacing on the Temperature Difference of Thermoacoustic Refrigerator by using Helium as a Working Medium

2019 ◽  
Vol 8 (4) ◽  
pp. 2704-2712
Keyword(s):  
Heat Exchanger ◽  
Temperature Difference ◽  
Parallel Plate ◽  
Sheet Material ◽  
Maximum Temperature ◽  
Working Fluid ◽  
Operating Pressure ◽  
Parallel Plates ◽  
Refrigeration System ◽  
Thermoacoustic Refrigerator

The refrigerants are usually provided in the conventional refrigeration system despite the fact that, they produce CFCs and HCFCs, which are hazardous to the environment. However, these disadvantages can be overcome using air or inert gas in the thermoacoustic refrigeration system. The present research involves the effect of spacing of parallel plate stack on the performance of thermoacoustic refrigerator (TAR) in terms of temperature difference (∆T). The entire resonator system as well as other structural parts of the refrigerator are fabricated by using PVC to reduce conduction heat loss. Three parallel plate stacks have been used to study the performance of TAR considering different porosity ratios by varying the gap between the parallel plates (0.28 mm, 0.33 mm and 0.38 mm). The parallel plate stacks are fabricated by using aluminium and mylar sheet material and the working fluid used for the experimental study is helium. The experiments have been carried out with different drive ratios ranging from 0.6% to 1.6% with operating frequencies of 200 – 600 Hz. Also the mean operating pressure used for the experiment is 2 to 10 bar and cooling load of 2 to 10W are considered. The ∆T between the hot heat exchanger and cold heat exchanger is recorded using RTDs and Bruel and Kjaer data acquisition system. Experimental results shows that the lowest temperature measured at cold heat exchanger is -2.1 oC by maintaining the hot heat exchanger temperature at about 32 oC. The maximum temperature difference of 32.90 oC is achieved.

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.

scholarly journals Heuristic derivation of Casimir effect in minimal length theories

2020 ◽  
Vol 29 (02) ◽  
pp. 2050011 ◽  
Author(s):  
Massimo Blasone ◽  
Gaetano Lambiase ◽  
Giuseppe Gaetano Luciano ◽  
Luciano Petruzziello ◽  
Fabio Scardigli
Keyword(s):  
Field Theory ◽  
Parallel Plate ◽  
Casimir Effect ◽  
Generalized Uncertainty Principle ◽  
Casimir Energy ◽  
Minimal Length ◽  
Quadratic Term ◽  
Quantum Field ◽  
The One ◽  
Plate Geometry

We propose a heuristic derivation of Casimir effect in the context of minimal length theories based on a Generalized Uncertainty Principle (GUP). By considering a GUP with only a quadratic term in the momentum, we compute corrections to the standard formula of Casimir energy for the parallel-plate geometry, the sphere and the cylindrical shell. For the first configuration, we show that our result is consistent with the one obtained via more rigorous calculations in Quantum Field Theory (QFT). Experimental developments are finally discussed.

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