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V. M. Mostepanenko

Publications and source records attributed to V. M. Mostepanenko.

At least 145 records · Page 8Linked to original sources
arXiv2011

Constraints on non-Newtonian gravity from measuring the Casimir force in a configuration with nanoscale rectangular corrugations

We report constraints on the parameters of Yukawa-type corrections to Newtonian gravity from measurements of the gradient of the Casimir force in the configuration of an Au-coated sphere above a Si plate covered with corrugations of trapezoidal shape. For this purpose, the exact expression for the gradient of Yukawa force in the experimental configuration is derived and compared with that obtained using the proximity force approximation. The reported constraints are of almost the same strength as those found previously from several different experiments on the Casimir force and extend over a wide interaction range from 30 to 1260\,nm. It is discussed how to make them stronger by replacing the material of the plate.

hep-ph↗
arXiv2011

Impact of surface imperfections on the Casimir force for lenses of centimeter-size curvature radii

The impact of imperfections, which are always present on surfaces of lenses with centimeter-size curvature radii, on the Casimir force in the lens-plate geometry is investigated. It is shown that the commonly used formulation of the proximity force approximation is inapplicable for spherical lenses with surface imperfections, such as bubbles and pits. More general expressions for the Casimir force are derived that take surface imperfections into account. Using these expressions we show that surface imperfections can both increase and decrease the magnitude of the Casimir force up to a few tens of percent when compared with the case of a perfectly spherical lens. We demonstrate that the Casimir force between a perfectly spherical lens and a plate described by the Drude model can be made approximately equal to the force between a sphere with some surface imperfection and a plate described by the plasma model, and vice versa. In the case of a metallic sphere and semiconductor plate, approximately the same Casimir forces are obtained for four different descriptions of charge carriers in the semiconductor if appropriate surface imperfections on the lens surface are present. The conclusion is made that there is a fundamental problem in the interpretation of measurement data for the Casimir force, obtained by using spherical lenses of centimeter-size radii, and their comparison with theory.

cond-mat.other↗
arXiv2010

Possibility of measuring the thermal Casimir interaction between a plate and a cylinder attached to a micromachined oscillator

We investigate the possibility of measuring the thermal Casimir force and its gradient in the configuration of a plate and a microfabricated cylinder attached to a micromachined oscillator. The Lifshitz-type formulas in this configuration are derived using the proximity force approximation. The accuracy for the obtained expressions is determined from a comparison with exact results available in ideal metal case. Computations of the thermal correction to both the Casimir force and its gradient are performed in the framework of different theoretical approaches proposed in the literature. The correction to the Casimir force and its gradient due to lack of parallelism of the plate and cylinder is determined using the nonmultiplicative approach. The error introduced in the theory due to the finite length of the cylinder is estimated. We propose that both static and dynamic experiments measuring the thermal Casimir interaction between a cylinder and a plate using a micromachined oscillator can shed additional light on the thermal Casimir force problem. Specifically, it is shown that the static experiment is better adapted for the measurement of thermal effects.

quant-ph↗
arXiv2010

Comment on "Temperature dependence of the Casimir force for lossy bulk media"

Recently Yampol'skii et al. [Phys. Rev. A v.82, 032511 (2010)] advocated that Lifshitz theory is not applicable when the characteristic wavelength of the fluctuating electromagnetic field, responsible for the thermal correction to the Casimir force, is larger than the size of the metal test bodies. It was claimed that this is the case in experiments which exclude Lifshitz theory combined with the Drude model. We calculate the wavelengths of the evanescent waves giving the dominant contribution to the thermal correction and we find that they are much smaller than the sizes of the test bodies. The opposite conclusion obtained by the authors arose from a confusion between propagating and evanescent waves.

quant-ph↗
arXiv2010

Possibility to measure thermal effects in the Casimir force

We analyze the possibility to measure small thermal effects in the Casimir force between metal test bodies in configurations of a sphere above a plate and two parallel plates. For sphere-plate geometry used in many experiments we investigate the applicability of the proximity force approximation (PFA) to calculate thermal effects in the Casimir force and its gradient. It is shown that for real metals the two formulations of the PFA used in the literature lead to relative differences in the obtained results being less than a small parameter equal to the ratio of separation distance to sphere radius. For ideal metals the PFA results for the thermal correction are obtained and compared with available exact results. It is emphasized that in the experimental region in the zeroth order of the small parameter mentioned above the thermal Casimir force and its gradient calculated using the PFA (and thermal corrections in their own right) coincide with respective exact results. For real metals available exact results are outside the application region of the PFA. However, the exact results are shown to converge to the PFA results when the small parameter goes down to the experimental values. We arrive at the conclusion that large thermal effects predicted by the Drude model approach, if existing at all, could be measured in both static and dynamic experiments in sphere-plate and plate-plate configurations. As to the small thermal effects predicted by the plasma model approach, the static experiment in the configuration of two parallel plates is found to be the best for its observation.

cond-mat.mtrl-sci↗
arXiv2010

Comparison of the experimental data for the Casimir pressure with the Lifshitz theory at zero temperature

We perform detailed comparison of the experimental data of the experiment on the determination of the Casimir pressure between two parallel Au plates with the theoretical values computed using the Lifshitz formula at zero temperature. Computations are done using the optical data for the complex index of refraction of Au extrapolated to low frequencies by means of the Drude model with both most often used and other suggested Drude parameters. It is shown that the experimental data exclude the Lifshitz formula at zero temperature at a 70% confidence level if the Drude model with most often used values of the parameters is employed. If other values of the Drude parameters are used, the Lifshitz formula at zero frequency is experimentally excluded at a 95% confidence level. The Lifshitz formula at zero temperature combined with the generalized plasma-like model with most often used value of the plasma frequency is shown to be experimentally consistent. We propose a decisive experiment which will shed additional light on the role of relaxation properties of conduction electrons in the Casimir effect.

quant-ph↗
arXiv2010

On the validity of constraints on light elementary particles and extra-dimensional physics from the Casimir effect

We discuss the constraints on the parameters of a Yukawa interaction obtained from the indirect measurements of the Casimir pressure between parallel plates using the sphere-plate configuration. Recently, it was claimed in the literature that the application of the proximity force approximation (PFA) to the calculation of a Yukawa interaction in the sphere-plate configuration could lead to a large error of order 100\% in the constraints obtained. Here we re-calculate the constraints both exactly and using the PFA, and arrive at identical results. We elucidate the reasons why an incorrect conclusion was obtained suggesting that the PFA is inapplicable to calculate the Yukawa force.

quant-ph↗
arXiv2010

Lateral Casimir force between sinusoidally corrugated surfaces: Asymmetric profiles, deviations from the proximity force approximation and comparison with exact theory

The lateral Casimir force, which arises between aligned sinusoidally corrugated surfaces of a sphere and a plate, was measured for the case of a small corrugation period beyond the applicability region of the proximity force approximation. The increased amplitudes of the corrugations on both the sphere and the plate allowed observation of an asymmetry of the lateral Casimir force, i.e., deviation of its profile from a perfect sine function. The dependences of the lateral force on the phase shift between the corrugations on both test bodies were measured at different separations in two sets of measurements with different amplitudes of corrugations on the sphere. The maximum magnitude of the lateral force as a function of separation was also measured in two successive experiments. All measurement data were compared with the theoretical approach using the proximity force approximation and with the exact theory based on Rayleigh expansions with no fitting parameters. In both cases real material properties of the test bodies and nonzero temperature were taken into account. The data were found to be in a good agreement with the exact theory but deviate significantly from the predictions of the proximity force approximation approach. This provides the quantitative confirmation for the observation of diffraction-type effects that are disregarded within the PFA approach. Possible applications of the phenomenon of the lateral Casimir force in nanotechnology for the operation of micromachines are discussed.

quant-ph↗
arXiv2010

Magnetic materials and the problem of thermal Casimir force

We investigate the thermal Casimir interaction between two magnetodielectric plates made of real materials. On the basis of the Lifshitz theory, it is shown that for diamagnets and for paramagnets in the broad sense (with exception of ferromagnets) the magnetic properties do not influence the magnitude of the Casimir force. For ferromagnets, taking into account the realistic dependence of magnetic permeability on frequency, we conclude that the impact of magnetic properties on the Casimir interaction arises entirely from the contribution of the zero-frequency term in the Lifshitz formula. The computations of the Casimir free energy and pressure are performed for the configurations of two plates made of ferromagnetic metals (Co and Fe), for one plate made of ferromagnetic metal and the other of nonmagnetic metal (Au), for two ferromagnetic dielectric plates (on the basis of polystyrene), and for a ferromagnetic dielectric plate near a nonmagnetic metal plate. The dielectric permittivity of metals is described using both the Drude and the plasma model approaches. It is shown that the Casimir repulsion through the vacuum gap can be realized in the configuration of a ferromagnetic dielectric plate near a nonmagnetic metal plate described by the plasma model. In all cases considered, the respective analytical results in the asymptotic limit of large separations between the plates are obtained. The impact of the magnetic phase transition through the Curie temperature on the Casimir interaction is considered. In conclusion, we propose several experiments allowing to determine whether the magnetic properties really influence the Casimir interaction and to independently verify the Drude and plasma model approaches to the thermal Casimir force.

cond-mat.other↗
arXiv2010

Advance and prospects in constraining the Yukawa-type corrections to Newtonian gravity from the Casimir effect

We report stronger constraints on the parameters of Yukawa-type corrections to Newtonian gravity from measurements of the lateral Casimir force between sinusoidally corrugated surfaces of a sphere and a plate. In the interaction range from 1.6 to 14 nm the strengthening of previously known high confidence constraints up to a factor of $2.4\times 10^7$ is achieved using these measurements. It is shown that the replacement of a plane plate with a corrugated one in the measurements of the normal Casimir force by means of an atomic force microscope would result in the strengthening of respective high confidence constraints on the Yukawa-type interaction by a factor of $1.1\times 10^{12}$. The use of a corrugated plate instead of a plane plate in the experiment by means of a micromachined oscillator also leads to strengthening of the obtained constraints. We further obtain constraints on the parameters of Yukawa-type interaction from the data of experiments measuring the gradient of the Casimir pressure between two parallel plates and the gradient of the Casimir-Polder force between an atom and a plate. The obtained results are compared with the previously known constraints. The possibilities of how to further strengthen the constraints on non-Newtonian gravity are discussed.

hep-th↗
arXiv2009

The Casimir Effect and the Foundations of Statistical Physics

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.

quant-ph↗
arXiv2009

Thermal Casimir Force between Magnetic Materials

We investigate the Casimir pressure between two parallel plates made of magnetic materials at nonzero temperature. It is shown that for real magnetodielectric materials only the magnetic properties of ferromagnets can influence the Casimir pressure. This influence is accomplished through the contribution of the zero-frequency term of the Lifshitz formula. The possibility of the Casimir repulsion through the vacuum gap is analyzed depending on the model used for the description of the dielectric properties of the metal plates.

quant-ph↗
arXiv2009

On the definition of dielectric permittivity for media with temporal dispersion in the presence of free charge carriers

We show that in the presence of free charge carriers the definition of the frequency-dependent dielectric permittivity requires additional regularization. As an example, the dielectric permittivity of the Drude model is considered and its time-dependent counterpart is derived and analyzed. The respective electric displacement cannot be represented in terms of the standard Fourier integral. The regularization procedure allowing to circumvent these difficulties is suggested. For purpose of comparison it is shown that the frequency-dependent dielectric permittivity of insulators satisfies all rigorous mathematical criteria. This permits us to conclude that in the presence of free charge carriers the concept of dielectric permittivity is not as well defined as for insulators and we make a link to widely discussed puzzles in the theory of thermal Casimir force which might be caused by the use of such kind permittivities.

quant-ph↗
arXiv2009

Demonstration of the asymmetric lateral Casimir force between corrugated surfaces in the nonadditive regime

The measurement of the lateral Casimir force between two aligned sinusoidally corrugated Au-coated surfaces has been performed in the nonadditive regime. The use of deeper corrugations also allowed to demonstrate an asymmetry in the phase dependences of the lateral Casimir force, as predicted earlier. The measurement data are found to be in excellent agreement with the exact theoretical results computed at T=300 K including effect of real material properties. The deviations between the exact theory and the proximity force approximation are quantified. The obtained results are topical for applications in nanomachines.

quant-ph↗
arXiv2009

Why Screening Effects Do Not Influence the Casimir Force

The Lifshitz theory of dispersion forces leads to thermodynamic and experimental inconsistencies when the role of drifting charge carriers is included in the model of the dielectric response. Recently modified reflection coefficients were suggested that take into account screening effects and diffusion currents. We demonstrate that this theoretical approach leads to a violation of the third law of thermodynamics (Nernst's heat theorem) for a wide class of materials and is excluded by the data from two recent experiments. The physical reason for its failure is explained by the violation of thermal equilibrium, which is the fundamental applicability condition of the Lifshitz theory, in the presence of drift and diffusion currents.

quant-ph↗
arXiv2009

Problems in the Lifshitz Theory of Atom-Wall Interaction

Problems in the Lifshitz theory of atom-wall interaction arise when the dc conductivity of dielectric wall is included into the model of the dielectric response. We review the low-temperature behavior of the free energy and entropy of dispersion interaction for both dielectric and metallic walls. Consistency of the obtained results with thermodynamics and experimental data is analyzed. Recent attempts to include the screening effects and diffusion currents into the Lifshitz theory are considered. It is shown that this leads to the violation of the Nernst heat theorem for wide classes of wall materials. The physical reasons for the emergence of thermodynamic and experimental inconsistencies are elucidated.

quant-ph↗
arXiv2009

The impact of magnetic properties on atom-wall interaction

The Lifshitz-type formulas for the free energy and Casimir-Polder force acting between an atom possessing a permanent magnetic moment and a wall made of different materials are derived. Simple model allowing analytic results is considered where the atomic magnetic susceptibility is frequency-independent and wall is made of ideal metal. Numerical computations of the Casimir-Polder force are performed for H atom interacting with walls made of ideal metal, nonmagnetic (Au) and ferromagnetic (Fe) metals and of ferromagnetic dielectric. It is shown that for the first three wall materials the inclusion of the magnetic moment of an atom decreases and for the fourth material increases the magnitude of the Casimir-Polder force.

quant-ph↗