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.

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.

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 CORRELATION BETWEEN PLASMA AND TEMPERATURE CORRECTIONS TO THE CASIMIR FORCE

2002 ◽  
Vol 17 (06n07) ◽  
pp. 761-766 ◽  
Author(s):  
CYRIAQUE GENET ◽  
ASTRID LAMBRECHT ◽  
SERGE REYNAUD
Keyword(s):  
Finite Temperature ◽  
Casimir Force ◽  
Optical Response ◽  
Correlation Factor ◽  
Experimental Results ◽  
Finite Conductivity ◽  
Plasma Model ◽  
Theoretical Predictions

When comparing experimental results with theoretical predictions of the Casimir force, the accuracy of the theory is as important as the precision of experiments. Here we evaluate the Casimir force when finite conductivity of the reflectors and finite temperature are simultaneously taken into account. We show that these two corrections are correlated, i.e. that they can not, in principle, be evaluated separately and simply multiplied. We estimate the correlation factor which measures the deviation from this common approximation. We focus our attention on the case of smooth and plane plates with a metallic optical response modeled by a plasma model.

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.

Analytical Solutions for the Static Instability of Nano-Switches Under the Effect of Casimir Force and Electrostatic Actuation

2009 ◽  
Author(s):  
Mahdi Mojahedi ◽  
Hamid Moeenfard ◽  
Mohammad Taghi Ahmadian
Keyword(s):  
Casimir Force ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Perturbation Expansion ◽  
Electrostatic Actuation ◽  
Design Tool ◽  
Accurate Design ◽  
Nonlinear Boundary Value ◽  
Static Instability ◽  
Fringing Field Effect

This paper deals with the problem of static instability of nano switches under the effect of Casimir force and electrostatic actuation. The nonlinear fringing field effect has been accounted for in the model. Using a Galerkin decomposition method and considering only one mode, the nonlinear boundary value problem describing the static behavior of nano-switch, is reduced to a nonlinear boundary value ordinary differential equation which is solved using the homotopy perturbation method (HPM). In order to ensure the precision of the results, the number of included terms in the perturbation expansion has been investigated. Results have been compared with numerical results and also with previously published analytical results. It was observed that HPM modifies the overestimation of N/MEMS instability limits reported in the literature and can be used as an effective and accurate design tool in the analysis of N/MEMS.

On-the-fly Symmetrical Quasi-classical Dynamics with Meyer-Miller Mapping Hamiltonian for the Treatment of Nonadiabatic Dynamics at Conical Intersections

2020 ◽  
Author(s):  
Deping Hu ◽  
Yu Xie ◽  
Jiawei Peng ◽  
Zhenggang Lan
Keyword(s):  
Ground State ◽  
Zero Point ◽  
Classical Dynamics ◽  
Nonadiabatic Dynamics ◽  
Conical Intersections ◽  
Point Energy ◽  
Simulation Protocol ◽  
Polyatomic Systems ◽  
Dynamics Method ◽  
Better Than

The ‘on-the-fly’ version of the symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian (SQC/MM) is implemented to study the nonadiabatic dynamics at conical intersections of polyatomic systems. The current ‘on-the-fly’ implementation of the SQC/MM method is based on the adiabatic representation and the dressed momentum. To include the zero-point energy (ZPE) correction of the electronic mapping variables, we employed both the γ-adjusted and γ-fixed approaches. Nonadiabatic dynamics of the methaniminium cation (CH2NH2+) and azomethane are simulated using the on-the-fly SQC/MM method. For CH2NH2+, both two ZPE correction approaches give reasonable and consistent results. However, for azomethane, the γ-adjusted version of the SQC/MM dynamics behaves much better than the γ-fixed version. The further analysis indicates that it is always recommended to use the γ-adjusted SQC/MM dynamics in the on-the-fly simulation of photoinduced dynamics of polyatomic systems, particularly when the excited-state is well separated from the ground state in the Frank-Condon region. This work indicates that the on-the-fly SQC/MM method is a powerful simulation protocol to deal with the nonadiabatic dynamics of realistic polyatomic systems.

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.

scholarly journals Using the Radial Velocity Spectrometer at the Dominion Astrophysical Observatory

1999 ◽  
Vol 170 ◽  
pp. 98-101
Author(s):  
J. Skuljan ◽  
J. B. Hearnshaw ◽  
P. L. Cottrell
Keyword(s):  
Radial Velocity ◽  
Cross Correlation ◽  
Zero Point ◽  
Flux Monitor ◽  
Gaussian Functions ◽  
Standard Values ◽  
Better Than

AbstractTwo observing runs have been undertaken at the Dominion Astrophysical Observatory (DAO) using the radial velocity spectrometer (RVS). About 800 observations have been performed with both the K and F masks. All cross-correlation profiles have been divided by the corresponding flux monitor records and full gaussian functions have been fitted in order to determine the profile centers. A number of IAU standard radial velocity stars have been observed, with a typical internal precision for a given star of about 100 m s−1, which is a factor of two or three better than the usually adopted value for the RVS. Zero-point offsets between these observations and the standard values were also investigated.

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