Narrow Results

The Lifshitz theory provides a semiclassical description of the Casimir–Polder atom-plate interaction, where the electromagnetic field is quantized, whereas the material of the plate is considered as a continuous medium. This places certain restrictions on its application regarding the allowable atom-plate separation distances and the dielectric properties of the plate material. Below, we demonstrate that in some recent literature the application conditions of the Lifshitz theory established by its founders are violated by applying it at too short separations and using the dielectric permittivities possessing the negative imaginary parts in violation of the second law of thermodynamics.

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.

We review recent results obtained in the physics of the thermal Casimir force acting between two dielectrics, dielectric and metal, and between metal and semiconductor. The detailed derivation for the low-temperature behavior of the Casimir free energy, pressure and entropy in the configuration of two real dielectric plates is presented. For dielectrics with finite static dielectric permittivity it is shown that the Nernst heat theorem is satisfied. Hence, the Lifshitz theory of the van der Waals and Casimir forces is demonstrated to be consistent with thermodynamics. The nonzero dc conductivity of dielectric plates is proved to lead to a violation of the Nernst heat theorem and, thus, is not related to the phenomenon of dispersion forces. The low-temperature asymptotics of the Casimir free energy, pressure and entropy are derived also in the configuration of one metal and one dielectric plate. The results are shown to be consistent with thermodynamics if the dielectric plate possesses a finite static dielectric permittivity. If the dc conductivity of a dielectric plate is taken into account this results in the violation of the Nernst heat theorem. We discuss both the experimental and theoretical results related to the Casimir interaction between metal and semiconductor with different charge carrier density. Discussions in the literature on the possible influence of spatial dispersion on the thermal Casimir force are analyzed. In conclusion, the conventional Lifshitz theory taking into account only the frequency dispersion remains the reliable foundation for the interpretation of all present experiments.

The Lifshitz theory and its modifications are discussed with respect to the Nernst heat theorem and the experimental data of several recent experiments. An analysis of all available information leads to the conclusion that some concepts of statistical physics might need reconsideration.

The problem of thermal Casimir force, which consists in disagreement of theoretical predictions of the fundamental Lifshitz theory with the measurement data of high precision experiments and some peculiar properties of the Casimir entropy, is reviewed. We discuss different approaches to the resolution of this problem proposed in the literature during the last 20 years. Particular attention is given to the role of the effects of spatial dispersion. The recently suggested nonlocal Drude-like permittivities which take proper account of the dissipation of conduction electrons and bring the predictions of the Lifshitz theory in agreement with experiment and requirements of thermodynamics are considered. The prospects of this approach in the ultimate resolution of the problem of thermal Casimir force are evaluated.

The Casimir effect in graphene systems is reviewed with a emphasis made on the large thermal correction to the Casimir force predicted at short separations between the test bodies. The computational results for the Casimir pressure and for the thermal correction are presented for both pristine graphene and real graphene sheets, which possess nonzero energy gap and chemical potential, obtained by means of exact polarization tensor. Two experiments on measuring the gradient of the Casimir force between an Au-coated sphere and graphene-coated substrates performed by using a modified atomic force microscope cantilever-based technique are described. It is shown that the measurement data of both experiments are in agreement with theoretical predictions of the Lifshitz theory using the polarization tensor. Additionally, several important improvements made in the second experiment, allowed to demonstrate the predicted large thermal effect in the Casimir interaction at short separations. Possible implications of this result to the resolution of long-term problems of Casimir physics are discussed.

Surfactant micelles (cetyltrimethylammonium chloride) adsorbed on Au(111) exhibit orientational order dictated by the gold crystal axes. To explain this phenomenon, we take into account the ionic contribution to the dielectric response of the metal. Since the motion of an ion inside the metallic lattice is restricted by its neighbors in an anisotropic way, the total dielectric response of the metal acquires directional dependence. A crystalline substrate is thus able to generate both torque and attraction on geometrically asymmetric objects. Numerical calculations show that the resulting anisotropic van der Waals force is indeed capable of orienting rod-like dielectric micelles on a Au(111) surface.

The problem of thermal Casimir force, which consists in disagreement of theoretical predictions of the fundamental Lifshitz theory with the measurement data of high precision experiments and some peculiar properties of the Casimir entropy, is reviewed. We discuss different approaches to the resolution of this problem proposed in the literature during the last 20 years. Particular attention is given to the role of the effects of spatial dispersion. The recently suggested nonlocal Drude-like permittivities which take proper account of the dissipation of conduction electrons and bring the predictions of the Lifshitz theory in agreement with experiment and requirements of thermodynamics are considered. The prospects of this approach in the ultimate resolution of the problem of thermal Casimir force are evaluated.

The Casimir effect in graphene systems is reviewed with a emphasis made on the large thermal correction to the Casimir force predicted at short separations between the test bodies. The computational results for the Casimir pressure and for the thermal correction are presented for both pristine graphene and real graphene sheets, which possess nonzero energy gap and chemical potential, obtained by means of exact polarization tensor. Two experiments on measuring the gradient of the Casimir force between an Au-coated sphere and graphene-coated substrates performed by using a modified atomic force microscope cantilever-based technique are described. It is shown that the measurement data of both experiments are in agreement with theoretical predictions of the Lifshitz theory using the polarization tensor. Additionally, several important improvements made in the second experiment, allowed to demonstrate the predicted large thermal effect in the Casimir interaction at short separations. Possible implications of this result to the resolution of long-term problems of Casimir physics are discussed.

The Lifshitz theory and its modifications are discussed with respect to the Nernst heat theorem and the experimental data of several recent experiments. An analysis of all available information leads to the conclusion that some concepts of statistical physics might need reconsideration.