Temperature Dependence Ofthe Casimir Force Formetals (original) (raw)
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Calculation of the Casimir force between similar and dissimilar metal plates at finite temperature
Journal of Physics A: Mathematical and General, 2005
The Casimir pressure is calculated between parallel metal plates, containing the materials Au, Cu, or Al. Our motivation for making this calculation is the need of comparing theoretical predictions, based on the Lifshitz formula, with experiments that are becoming gradually more accurate. In particular, the finite temperature correction is considered, in view of the recent discussion in the literature on this point. A special attention is given to the case where the difference between the Casimir pressures at two different temperatures, T = 300 K and T = 350 K, is involved. This seems to be a case that will be experimentally attainable in the near future, and it will be a critical test of the temperature correction.
On the Temperature Dependence of the Casimir Effect
2005
The temperature dependence of the Casimir force between a real metallic plate and a metallic sphere is analyzed on the basis of optical data concerning the dispersion relation of metals such as gold and copper. Realistic permittivities imply, together with basic thermodynamic considerations, that the transverse electric zero mode does not contribute. This results in observable differences with the conventional prediction, which does not take this physical requirement into account. The results are shown to be consistent with the third law of thermodynamics, as well as being consistent with current experiments. However, the predicted temperature dependence should be detectable in future experiments. The inadequacies of approaches based on ad hoc assumptions, such as the plasma dispersion relation and the use of surface impedance without transverse momentum dependence, are discussed.
A recent experiment [J. L. Garrett, D. A. T. Somers, and J. N. Munday, Phys. Rev. Lett 120, 040401 (2018)] measured for the first time the gradient of the Casimir force between two gold spheres in vacuum at room temperature, and placed a bound on the magnitude of the deviation of the measured force from the proximity force approximation (PFA). The present work extends a previous theoretical analysis of this experiment [G. Bimonte, Phys. Rev. D 97, 085011 (2018)], by analyzing in detail how the magnitude of the deviation from PFA is affected by the inclusion or neglect of ohmic dissipation at zero frequency, a much debated issue in the current Casimir literature, which goes by the name of the Drude vs plasma controversy. We analyze as well the effect of connecting the plates to charge reservoirs, which is the standard configuration used in Casimir experiments. We describe a simple and effective decimation procedure, allowing for a faster computation of the Casimir force for large aspect ratios of the system.
Present status of controversies regarding the thermal Casimir force
Journal of Physics A: Mathematical and General, 2006
It is well known that, beginning in 2000, the behavior of the thermal correction to the Casimir force between real metals has been hotly debated. As was shown by several research groups, the Lifshitz theory, which provides the theoretical foundation for the calculation of both the van der Waals and Casimir forces, leads to different results depending on the model of metal conductivity used. To resolve these controversies, the theoretical considerations based on the principles of thermodynamics and new experimental tests were invoked. We analyze the present status of the problem (in particular, the advantages and disadvantages of the approaches based on the surface impedance and on the Drude model dielectric function) using rigorous analytical calculations of the entropy of a fluctuating field. We also discuss the results of a new precise experiment on the determination of the Casimir pressure between two parallel plates by means of a micromechanical torsional oscillator.
Temperature dependence of the Casimir force
European Journal of Physics, 2014
The Casimir force-at first a rather unexpected consequence of quantum electrodynamics-was discovered by Hendrik Casimir in Eindhoven in 1948. It predicts that two uncharged metal plates experience an attractive force because of the zero-point fluctuations of the electromagnetic field. The idea was tested experimentally in the 1950's and 1960's, but the results were not so accurate that one could make a definite conclusion regarding the existence of the effect. Evgeny Lifshitz expanded the theory in 1955 so as to deal with general dielectric media. Much experimental work has later been done to test the theory's predictions, especially with regards to the temperature dependence of the effect. The existence of the effect itself was verified beyond doubt by Sabisky and Anderson in 1973. Another quarter century had to pass before Lamoreaux and collaborators were able to confirm-or at least make plausible-the temperature dependence predicted by Lifshitz formula in combination with reasonable input data for the material's dispersive properties. The situation is not yet clear-cut, however; there are recent experiments indicating results in disagreement with those of Lamoreaux. In the present paper a brief review is given of the status of this research field.
The Casimir force between real materials: Experiment and theory
Reviews of Modern Physics, 2009
The physical origin of the Casimir force is connected with the existence of zero-point and thermal fluctuations. The Casimir effect is very general and finds applications in various fields of physics. This review is limited to the rapid progress at the intersection of experiment and theory that has been achieved in the last few years. It includes a critical assessment of the proposed approaches to the resolution of the puzzles arising in the applications of the Lifshitz theory of the van der Waals and Casimir forces to real materials. All the primary experiments on the measurement of the Casimir force between macroscopic bodies and the Casimir-Polder force between an atom and a wall that have been performed in the last decade are reviewed, including the theory needed for their interpretation. The methodology for the comparison between experiment and theory in the force-distance measurements is presented. The experimental and theoretical results described here provide a deeper understanding of the phenomenon of dispersion forces in real materials and offer guidance for the application of Lifshitz theory for the interpretation of the measurement results.
A recent experiment [J. L. Garrett, D. A. T. Somers, and J. N. Munday, Phys. Rev. Lett 120, 040401 (2018)] measured for the first time the gradient of the Casimir force between two gold spheres in vacuum at room temperature, and placed a bound on the magnitude of the deviation of the measured force from the proximity force approximation (PFA). The present work extends a previous theoretical analysis of this experiment [G. Bimonte, Phys. Rev. D 97, 085011 (2018)], by analyzing in detail how the magnitude of the deviation from PFA is affected by the inclusion or neglect of ohmic dissipation at zero frequency, a much debated issue in the current Casimir literature, which goes by the name of the Drude vs plasma controversy. We analyze as well the effect of connecting the conductors to charge reservoirs, which is the standard configuration used in Casimir experiments. We describe a simple and effective decimation procedure, allowing for a faster computation of the Casimir force for large aspect ratios of the system.
New Features of the Thermal Casimir Force at Small Separations
Physical Review Letters, 2003
The difference of the thermal Casimir forces at different temperatures between real metals is shown to increase with a decrease of the separation distance. This opens new opportunities for the demonstration of the thermal dependence of the Casimir force. Both configurations of two parallel plates and a sphere above a plate are considered. Different approaches to the theoretical description of the thermal Casimir force are shown to lead to different measurable predictions.
Temperature dependence of the Casimir effect
Physical Review E, 2005
In view of the increasing accuracy of Casimir experiments, there is a need for performing accurate theoretical calculations. Using accurate experimental data for the permittivities we present, via the Lifshitz formula applied to the standard Casimir setup with two parallel plates, accurate theoretical results in case of the metals Au, Cu and Al. Both similar and dissimilar cases are considered. Concentrating in particular on the finite temperature effect, we show how the Casimir pressure varies with separation for three different temperatures, T = {1, 300, 350}K. The metal surfaces are taken to be perfectly plane. The experimental data for the permittivities are generally yielding results that are in good agreement with those calculated from the Drude relation with finite relaxation frequency.
Comparison Between Experiment and Theory for the Thermal Casimir Force
International Journal of Modern Physics A, 2012
We analyze recent experiments on measuring the thermal Casimir force with account of possible background effects. Special attention is paid to the validity of the proximity force approximation (PFA) used in the comparison between the experimental data and computational results in experiments employing a sphere-plate geometry. The PFA results are compared with the exact results where they are available. The possibility to use fitting procedures in theory-experiment comparison is discussed. On this basis we reconsider experiments exploiting spherical lenses of centimeter-size radii.