Casimir Force Between a Flat Plate and a Spherical Lens: Application to the Results of a New Experiment

1997 ◽  
Vol 12 (34) ◽  
pp. 2613-2622 ◽  
Author(s):  
V. B. Bezerra ◽  
G. L. Klimchitskaya ◽  
C. Romero
Keyword(s):  
Flat Plate ◽  
Experimental Error ◽  
Recent Experiment ◽  
Casimir Force ◽  
Finite Size ◽  
Finite Conductivity ◽  
Geometrical Shape ◽  
Spherical Lens ◽  
Arbitrary Size ◽  
Interacting Surfaces

The Casimir force is calculated in a configuration consisting of a lens placed above a flat plate of arbitrary size used in recent experiment. The corrections due to the finite size of the plate are shown to be negligible. On the other hand, corrections due to the small distortions of interacting surfaces, their deviation from the perfect geometrical shape and due to the finite metal conductivity were found to be several times larger than the relative experimental error. It is shown that the corrections due to distortions and finite conductivity have opposite signs and may compensate each other.

scholarly journals CASIMIR FORCE UNDER THE INFLUENCE OF REAL CONDITIONS

2001 ◽  
Vol 16 (19) ◽  
pp. 3291-3308 ◽  
Author(s):  
B. GEYER ◽  
G. L. KLIMCHITSKAYA ◽  
V. M. MOSTEPANENKO
Keyword(s):  
Casimir Force ◽  
Zero Point ◽  
Temperature Correction ◽  
Finite Conductivity ◽  
Parallel Plates ◽  
Plasma Model ◽  
Spherical Lens ◽  
Relevant Factors ◽  
Good Agreement ◽  
Zero Frequency

The Casimir force is calculated analytically for configurations of two parallel plates and a spherical lens (sphere) above a plate with an account of nonzero temperature, finite conductivity of the boundary metal and surface roughness. The permittivity of the metal is described by the plasma model. It is proved that in case of the plasma model the scattering formalism of quantum field theory in Matsubara formulation underlying Lifshitz formula is well defined and no modifications are needed concerning the zero-frequency contribution. The temperature correction to the Casimir force is found completely with respect to temperature and perturbatively (up to the second order in the relative penetration depth of electromagnetic zero-point oscillations into the metal) with respect to finite conductivity. The asymptotics of low and high temperatures are presented and contributions of longitudinal and perpendicular modes are determined separately. Serving as an example, aluminium test bodies are considered, showing good agreement between the obtained analytical results and previously performed numerical computations. The roughness correction is formally included and formulas are given permitting us to calculate the Casimir force under the influence of all relevant factors.

PERTURBATION EXPANSION OF THE CONDUCTIVITY CORRECTION TO THE CASIMIR FORCE

2001 ◽  
Vol 16 (18) ◽  
pp. 3103-3115 ◽  
Author(s):  
V. B. BEZERRA ◽  
G. L. KLIMCHITSKAYA ◽  
C. ROMERO
Keyword(s):  
Correction Factor ◽  
Casimir Force ◽  
Complex Refractive Index ◽  
Perturbation Expansion ◽  
Zero Point ◽  
Finite Conductivity ◽  
Plasma Model ◽  
Spherical Lens ◽  
Effective Plasma Frequency ◽  
Better Than

The perturbation expansion of the finite conductivity correction to the Casimir force is obtained up to the sixth order in the small parameter which represents the relative penetration depth of electromagnetic zero-point oscillations into the metal. Configurations consisting of two plates and a spherical lens placed above a plate are considered. The perturbation results are shown to coincide with the results of numerical computations in the framework of plasma model to better than 1%. The influence of the errors in the value of effective plasma frequency onto the correction factor is estimated. The plasma model correction factor to the Casimir force is compared with the ones computed in the context of Drude model and on the base of optical tabulated data for the complex refractive index. The exactness of each model is determined.

CASIMIR FORCE EXPERIMENTS IN AIR: TWO BIRDS WITH ONE STONE

2010 ◽  
Vol 25 (11) ◽  
pp. 2231-2239 ◽  
Author(s):  
S. DE MAN ◽  
K. HEECK ◽  
K. SMITH ◽  
R. J. WIJNGAARDEN ◽  
D. IANNUZZI
Keyword(s):  
Atomic Force Microscope ◽  
High Precision ◽  
Electrostatic Potential ◽  
Casimir Force ◽  
Hydrodynamic Force ◽  
Force Sensor ◽  
Force Measurements ◽  
Atomic Force ◽  
Potential Measure ◽  
Interacting Surfaces

We present a short overview of the recent efforts of our group in the design of high precision Casimir force setups. We first describe our Atomic Force Microscope based technique that allows one to simultaneously and continuously calibrate the instrument, compensate for a residual electrostatic potential, measure the Casimir force, and, in the presence of a fluid in the gap between the interacting surfaces, measure the hydrodynamic force. Then we briefly discuss a new force sensor that adapts well to Casimir force measurements in critical environments.

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 RESTRICTIONS ON THE HYPOTHETICAL LONG RANGE INTERACTIONS FROM THE CASIMIR-TYPE NULL EXPERIMENT WITH THREE TEST BODIES

1994 ◽  
Vol 09 (29) ◽  
pp. 2671-2680 ◽  
Author(s):  
M. BORDAG ◽  
V. M. MOSTEPANENKO ◽  
I. YU. SOKOLOV
Keyword(s):  
Long Range ◽  
Power Law ◽  
Casimir Force ◽  
Power Laws ◽  
Gravitational Attraction ◽  
Spherical Lens ◽  
Plane Plate ◽  
Wide Range ◽  
Long Range Interactions

A realistic null experiment is suggested in which the Casimir force between a plane plate and a spherical lens is compensated by the force of gravitational attraction. This configuration is shown to be very sensitive to the existence of additional hypothetical forces of Yukawa-type or power laws. From the suggested null experiment the restrictions on the Yukawa constant α can be strengthened by a factor up to 1000 in a wide range 10−8 m < λ < 10−4 m and by a factor of 10 for λ from several centimeters to several meters. For power law interactions the strengthening of restrictions by a factor of 20 is possible for the force decreasing as r−5.

scholarly journals Critical Casimir Force inHe4Films: Confirmation of Finite-Size Scaling

2006 ◽  
Vol 97 (7) ◽  
Author(s):  
A. Ganshin ◽  
S. Scheidemantel ◽  
R. Garcia ◽  
M. H. W. Chan
Keyword(s):  
Casimir Force ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Size Scaling

scholarly journals Modeling of Small DC Magnetic Field Response in Trilayer Magnetoelectric Laminate Composites

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
B. Zadov ◽  
A. Elmalem ◽  
E. Paperno ◽  
I. Gluzman ◽  
A. Nudelman ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Piezoelectric Layer ◽  
Permanent Magnets ◽  
Finite Size ◽  
Finite Conductivity ◽  
Electric Field Effect ◽  
Induced Voltage ◽  
The Finite Element Method ◽  
Laminate Composites ◽  
Analytical Result

We consider a magnetoelectric laminate which comprises two magnetostrictive (Ni) layers and an in-between piezoelectric layer (PZT). Using the finite-element method-based software COMSOL, we numerically calculate the induced voltage between the two faces of the PZT piezoelectric layer, by an external homogeneous small-signal magnetic field threading the three-layer Ni/PZT/Ni laminate structure. A bias magnetic field is simulated as being produced by two permanent magnets, as it is done in real experimental setups. For approaching the real materials’ properties, a measured magnetization curve of the Ni plate is used in the computations. The reported results take into account the finite-size effects of the structure, such as the fringing electric field effect and the demagnetization, as well as the effect of the finite conductivity of the Ni layers on the output voltage. The results of the simulations are compared with the experimental data and with a widely known analytical result for the induced magnetoelectric voltage.

scholarly journals Casimir Force between Two Vortices in a Turbulent Bose–Einstein Condensate

Atoms ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 77
Author(s):  
José Tito Mendonça ◽  
Hugo Terças ◽  
João D. Rodrigues ◽  
Arnaldo Gammal
Keyword(s):  
Casimir Force ◽  
Occupation Number ◽  
Finite Size ◽  
Condensed Medium ◽  
Einstein Condensate ◽  
Density Fluctuations ◽  
Pitaevskii Equation ◽  
Phonon Modes ◽  
Bose Einstein Condensate ◽  
Bose Einstein

We consider the Casimir force between two vortices due to the presence of density fluctuations induced by turbulent modes in a Bose–Einstein condensate. We discuss the cases of unbounded and finite condensates. Turbulence is described as a superposition of elementary excitations (phonons or BdG modes) in the medium. Expressions for the Casimir force between two identical vortex lines are derived, assuming that the vortices behave as point particles. Our analytical model of the Casimir force is confirmed by numerical simulations of the Gross–Pitaevskii equation, where the finite size of the vortices is retained. Our results are valid in the mean-field description of the turbulent medium. However, the Casimir force due to quantum fluctuations can also be estimated, assuming the particular case where the occupation number of the phonon modes in the condensed medium is reduced to zero and only zero-point fluctuations remain.

Separation Gap Estimation in Dynamic Systems Actuated by Casimir Force

2011 ◽  
Vol 254 ◽  
pp. 21-24
Author(s):  
Song Cui ◽  
Yeng Chai Soh
Keyword(s):  
Surface Roughness ◽  
Simulation Study ◽  
Dynamic Systems ◽  
Casimir Force ◽  
Estimation Method ◽  
Finite Conductivity ◽  
Unknown Parameters ◽  
Experimental Conditions

In this paper, a new estimation method is proposed to estimate the separation gap and other unknown parameters in Casimir force actuated systems. Real experimental conditions like the finite conductivity and surface roughness are considered as well. Simulation study shows that the method is accurate even when the system has severe nonlinearity.

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