scholarly journals THE CASIMIR EFFECT IN THE SPHERE-PLANE GEOMETRY

2012 ◽  
Vol 14 ◽  
pp. 250-259 ◽  
Author(s):  
ANTOINE CANAGUIER-DURAND ◽  
ROMAIN GUÉROUT ◽  
PAULO A. MAIA NETO ◽  
ASTRID LAMBRECHT ◽  
SERGE REYNAUD
Keyword(s):  
Ambient Temperature ◽  
Casimir Force ◽  
Casimir Effect ◽  
Numerical Results ◽  
Plane Geometry ◽  
Finite Conductivity ◽  
Rich Variety ◽  
Proximity Force Approximation ◽  
Multipolar Expansion

We present calculations of the Casimir interaction between a sphere and a plane, using a multipolar expansion of the scattering formula. This configuration enables us to study the nontrivial dependence of the Casimir force on the geometry, and its correlations with the effects of imperfect reflection and temperature. The accuracy of the Proximity Force Approximation (PFA) is assessed, and is shown to be affected by imperfect reflexion. Our analytical and numerical results at ambient temperature show a rich variety of interplays between the effects of curvature, temperature, finite conductivity, and dissipation.

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 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.

DEMONSTRATING THE STRONG GEOMETRY DEPENDENCE OF THE CASIMIR FORCE ON A SURFACE WITH DEEP, NANOSCALE CORRUGATIONS

2010 ◽  
Vol 25 (11) ◽  
pp. 2212-2222 ◽  
Author(s):  
H. B. CHAN ◽  
Y. BAO ◽  
J. ZOU ◽  
R. A. CIRELLI ◽  
F. KLEMENS ◽  
...  
Keyword(s):  
Casimir Force ◽  
Flat Surface ◽  
Torsional Oscillator ◽  
Silicon Surfaces ◽  
Finite Conductivity ◽  
Additive Approximation ◽  
Corrugated Surfaces ◽  
Geometry Dependence ◽  
Proximity Force Approximation ◽  
Gold Sphere

We measure the Casimir force gradient between silicon surfaces with nanoscale, rectangular corrugations and a gold sphere attached to a micromechanical torsional oscillator. By comparing the force gradients on the corrugated surfaces to that on a smooth, flat surface of the same material, we demonstrate that the Casimir force deviates from the value expected from the pairwise additive approximation and the proximity force approximation. The observed deviation qualitatively agrees with calculations that take into account the interplay between finite conductivity and geometry effects. However, the agreement is not exact, possibly due to uncertainties in the optical properties of the silicon substrate.

scholarly journals NEW CONSTRAINTS ON YUKAWA-TYPE INTERACTIONS FROM THE CASIMIR EFFECT

2012 ◽  
Vol 14 ◽  
pp. 200-214
Author(s):  
V. M. MOSTEPANENKO ◽  
V. B. BEZERRA ◽  
G. L. KLIMCHITSKAYA ◽  
C. ROMERO
Keyword(s):  
Standard Model ◽  
Casimir Force ◽  
Casimir Effect ◽  
Beyond The Standard Model ◽  
Exact Theory ◽  
The Standard Model

Measurements of the Casimir force are used to obtain stronger constraints on the parameters of hypothetical interactions predicted in different unification schemes beyond the Standard Model. We review new strong constraints on the Yukawa-type interactions derived during the last two years from recent experiments on measuring the lateral Casimir force, Casimir force in configurations with corrugated boundaries and the Casimir-Polder force. Specifically, from measurements of the lateral Casimir force compared with the exact theory the strengthening of constraints up to a factor of 24 millions was achieved. We also discuss further possibilities to strengthen constraints on the Yukawa interactions from the Casimir effect.

CASIMIR FORCE BETWEEN A GRAVITATIONAL FIELD AND A FINITE OBJECT

2002 ◽  
Vol 11 (10) ◽  
pp. 1567-1572 ◽  
Author(s):  
FABRIZIO PINTO
Keyword(s):  
Gravitational Field ◽  
Casimir Force ◽  
Casimir Effect ◽  
Finite Size ◽  
Zero Point ◽  
Point Energy ◽  
Energy Field ◽  
Static Gravitational Field ◽  
Vacuum Gap ◽  
Infinite Media

In the typical Casimir effect, the boundaries of two semi-infinite media exert a force upon one another across a vacuum gap separating them. In this paper, I argue that a static gravitational field can be regarded as a "soft" boundary which interacts with a test object of finite size through the electromagnetic zero-point-energy field. Therefore, a pressure exists upon a single slab placed in a gravitational field and surrounded by a vacuum. Interestingly, this extremely small Casimir pressure of the gravitational field may cause relative displacements in ground-based sensing microstructures larger than those from astrophysical gravitational waves in macroscopic antennas.

scholarly journals THE SCATTERING APPROACH TO THE CASIMIR FORCE

2010 ◽  
Vol 25 (11) ◽  
pp. 2201-2211 ◽  
Author(s):  
S. REYNAUD ◽  
A. CANAGUIER-DURAND ◽  
R. MESSINA ◽  
A. LAMBRECHT ◽  
P. A. MAIA NETO
Keyword(s):  
Casimir Force ◽  
Nanostructured Surfaces ◽  
3D Space ◽  
Geometry Dependence ◽  
Specific Calculations ◽  
Proximity Force Approximation

We present the scattering approach which is nowadays the best tool for describing the Casimir force in realistic experimental configurations. After reminders on the simple geometries of 1d space and specular scatterers in 3d space, we discuss the case of stationary arbitrarily shaped mirrors in electromagnetic vacuum. We then review specific calculations based on the scattering approach, dealing for example with the forces or torques between nanostructured surfaces and with the force between a plane and a sphere. In these various cases, we account for the material dependence of the forces, and show that the geometry dependence goes beyond the trivial Proximity Force Approximation often used for discussing experiments.

scholarly journals Reply to “Comment on ‘Anomalies in electrostatic calibrations for the measurement of the Casimir force in a sphere-plane geometry’”

2009 ◽  
Vol 79 (2) ◽  
Author(s):  
W. J. Kim ◽  
M. Brown-Hayes ◽  
D. A. R. Dalvit ◽  
J. H. Brownell ◽  
R. Onofrio
Keyword(s):  
Casimir Force ◽  
Plane Geometry
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