arXiv subjects

V. M. Mostepanenko

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

At least 55 records · Page 3Linked to original sources

arXiv2020

Quantum field theoretical description of the Casimir effect between two real graphene sheets and thermodynamics

The analytic asymptotic expressions for the Casimir free energy and entropy for two parallel graphene sheets possessing nonzero energy gap $Δ$ and chemical potential $μ$ are derived at arbitrarily low temperature. Graphene is described in the framework of thermal quantum field theory in the Matsubara formulation by means of the polarization tensor in (2+1)-dimensional space-time. Different asymptotic expressions are found under the conditions $Δ>2μ$, $Δ=2μ$, and $Δ<2μ$ taking into account both the implicit temperature dependence due to a summation over the Matsubara frequencies and the explicit one caused by a dependence of the polarization tensor on temperature as a parameter. It is shown that for both $Δ>2μ$ and $Δ<2μ$ the Casimir entropy satisfies the third law of thermodynamics (the Nernst heat theorem), whereas for $Δ=2μ$ this fundamental requirement is violated. The physical meaning of the discovered anomaly is considered in the context of thermodynamic properties of the Casimir effect between metallic and dielectric bodies.

cond-mat.other↗

arXiv2020

The Nernst heat theorem for an atom interacting with graphene: Dirac model with nonzero energy gap and chemical potential

We derive the low-temperature behavior of the Casimir-Polder free energy for a polarizable atom interacting with graphene sheet which possesses the nonzero energy gap $Δ$ and chemical potential $μ$. The response of graphene to the electromagnetic field is described by means of the polarization tensor in the framework of Dirac model on the basis of first principles of thermal quantum field theory in the Matsubara formulation. It is shown that the thermal correction to the Casimir-Polder energy consists of three contributions. The first of them is determined by the Matsubara summation using the polarization tensor defined at zero temperature, whereas the second and third contributions are caused by an explicit temperature dependence of the polarization tensor and originate from the zero-frequency Matsubara term and the sum of all Matsubara terms with nonzero frequencies, respectively. The asymptotic behavior for each of the three contributions at low temperature is found analytically for any value of the energy gap and chemical potential. According to our results, the Nernst heat theorem for the Casimir-Polder free energy and entropy is satisfied for both $Δ> 2μ$ and $Δ< 2μ$. We also reveal an entropic anomaly arising in the case $Δ= 2μ$. The obtained results are discussed in connection with the long-standing fundamental problem in Casimir physics regarding the proper description of the dielectric response of matter to the electromagnetic field.

cond-mat.mes-hall↗

arXiv2020

Nernst heat theorem for the Casimir-Polder interaction between a magnetizable atom and ferromagnetic dielectric plate

We find the low-temperature behavior of the Casimir-Polder free energy for a polarizable and magnetizable atom interacting with a plate made of ferromagnetic dielectric material. It is shown that the corresponding Casimir-Polder entropy goes to zero with vanishing temperature, i.e., the Nernst heat theorem is satisfied, if the dc conductivity of the plate material is disregarded in calculations. If the dc conductivity is taken into account, the Nernst theorem is violated. These results are discussed in light of recent experiments.

quant-ph↗

arXiv2020

Constraints on non-Newtonian gravity and axionlike particles from measuring the Casimir force in nanometer separation range

We obtain constraints on the Yukawa-type corrections to Newton's gravitational law and on the coupling constant of axionlike particles to nucleons following from the experiment on measuring the Casimir force between an Au-coated microsphere and a silicon carbide plate. For this purpose, both the Yukawa-type force and the force due to two-axion exchange between nucleons are calculated in the experimental configuration. In the interaction range of Yukawa force exceeding 1 nm and for axion masses above 17.8 eV, the obtained constraints are much stronger than those found previously from measuring the lateral Casimir force between sinusoidally corrugated surfaces. These results are compared with the results of other laboratory experiments on constraining non-Newtonian gravity and axionlike particles in the relevant interaction ranges.

hep-ph↗

arXiv2020

Nonequilibrium effects in the Casimir force between two similar metallic plates kept at different temperatures

We study the Casimir pressure between two similar plates of finite thickness kept at different temperatures in the case when the dielectric permittivity of the plates depends on temperature. It is suggested to consider the dielectric permittivity at two different temperatures as the permittivities of two dissimilar bodies, thus allowing to apply the theory of Casimir forces out of thermal equilibrium developed earlier in the literature. Following this approach, we show that, in addition to the equilibrium contribution to the nonequilibrium Casimir pressure, a proper nonequilibrium contribution arises for temperature-dependent dielectric permittivities. Furthermore, the equilibrium contribution in this case does not equal the mean of the equilibrium Casimir pressures at the temperatures of the plates. As an application, the total nonequilibrium Casimir pressure between two gold plates and between two titanium plates is calculated as a function of the plate thickness and their separation, using the Drude and the plasma model. For plate separations ranging from 0.5 to 2 micrometers, the relative difference between the theoretical predictions for these two models reaches 39%. The proper nonequilibrium term may be as large as 4% of the magnitude of the total nonequilibrium pressure.

quant-ph↗

arXiv2020

The Casimir force, causality and the Gurzhi model

An extended Drude model, termed as the Gurzhi model, which takes into account the electron-phonon and electron-electron interactions, is applied to calculate the Casimir force between two metallic plates. It is shown that although the dielectric permittivity of the Gurzhi model has a first order pole in the upper half-plane of complex frequencies and, thus, violates the causality principle, it can be used in a restricted frequency interval in combination with the experimental permittivity determined by the optical data for the complex index of refraction. The imaginary part of the Gurzhi dielectric permittivity of Au at low frequencies demonstrates better agreement with the permittivity given by the optical data than the simple Drude model. The Casimir pressure between two Au plates is computed using the Gurzhi, Drude and plasma model approaches, taking into account the optical data, as well as with the simple Drude and plasma models. The contribution of the electron-electron scattering to the Casimir pressure is estimated. Although a comparison with the measurement data of two precise experiments show that the Gurzhi model does not resolve the Casimir puzzle, the obtained results suggest further clarification of this fundamental problem.

cond-mat.mes-hall↗

arXiv2019

Precision measurements of the gradient of the Casimir force between ultra clean metallic surfaces at larger separations

We report precision measurements of the Casimir interaction at larger separation distances between the Au-coated surfaces of a sphere and a plate in ultrahigh vacuum using a much softer cantilever of the dynamic atomic force microscope-based setup and two-step cleaning procedure of the vacuum chamber and test body surfaces by means of UV light and Ar-ion bombardment. Compared to the previously performed experiment, two more measurement sets for the gradient of the Casimir force are provided which confirmed and slightly improved the results. Next, additional measurements have been performed with a factor of two larger oscillation amplitude of the cantilever. This allowed obtaining meaningful results at much larger separation distances. The comparison of the measurement data with theoretical predictions of the Lifshitz theory using the dissipative Drude model to describe the response of Au to the low-frequency electromagnetic field fluctuations shows that this theoretical approach is experimentally excluded over the distances from 250 to 1100nm (i.e., a major step forward has been made as compared to the previous work where it was excluded up to only 820nm). The theoretical approach using the dissipationless plasma model at low frequencies is shown to be consistent with the data over the entire measurement range from 250 to 1300nm. The possibilities to explain these puzzling results are discussed.

quant-ph↗

arXiv2019

Some remarks on axion dark matter, dark energy and energy of the quantum vacuum

In connection with the problem of dark matter, we discuss recent results on constraining the parameters of axion-to-nucleon interaction following from the experiment on measuring the difference of Casimir forces. It is shown that this experiment not only leads to competitive constraints, but provides stronger support to other constraints obtained in Casimir physics so far. The description of dark energy by means of cosmological constant originated from the quantum vacuum is considered in terms of the renormalization procedures in quantum field theory. It is argued that only the renormalized value of cosmological constant directly connected with the observed density of dark energy is of physical significance, so that some statements in the literature concerning the vacuum catastrophe may be considered as an exaggeration.

hep-ph↗

arXiv2019

Recent measurements of the Casimir force: Comparison between experiment and theory

We consider experiments on measuring the Casimir interaction which have been performed in the last four years. The emphasis is made on measuring differences in the Casimir pressures under a transition of the plate metal from normal to superconducting state and on the Casimir metrology platform using a commercial micromechanical sensor. In both cases several problems in the comparison between experiment and theory are discussed.

quant-ph↗

arXiv2019

Reflectance of graphene-coated dielectric plates in the framework of Dirac model: Joint action of energy gap and chemical potential

We investigate the reflectance of a dielectric plate coated with a graphene sheet which possesses the nonzero energy gap and chemical potential at any temperature. The general formalism for the reflectance using the polarization tensor is presented in the framework of Dirac model. It allows calculation of the reflectivity properties for any material plate coated with real graphene sheet on the basis offirst principles of quantum electrodynamics. Numerical computations of the reflectance are performed for the graphene-coated SiO$_2$ plate at room, liquid-nitrogen, and liquid-helium temperatures. We demonstrate that there is a nontrivial interplay between the chemical potential, energy gap, frequency, and temperature in their joint action on the reflectance of a graphene-coated plate. Specifically, it is shown that at the fixed frequency of an incident light an increase of the chemical potential and the energy gap affect the reflectance in opposite directions by increasing and decreasing it, respectively. According to our results, the reflectance approaches unity at sufficiently low frequencies and drops to that of an uncoated plate at high frequencies for any values of the chemical potential and energy gap. The impact of temperature on the reflectance is found to be more pronounced for graphene coatings with smaller chemical potentials. The obtained results could be applied for optimization of optical detectors and other devices exploiting graphene coatings.

cond-mat.mes-hall↗

arXiv2019

The Casimir pressure between metallic plates out of thermal equilibrium: Proposed test for the relaxation properties of free electrons

We propose a test on the role of relaxation properties of conduction electrons in the Casimir pressure between two parallel metal-coated plates kept at different temperatures. It is shown that for sufficiently thick metallic coatings the Casimir pressure and pressure gradient are determined by the mean of the equilibrium contributions calculated at temperatures of the two plates and by the term independent on separation. Numerical computations of the nonequilibrium pressures are performed for two parallel Au plates of finite thickness as a function of separation and temperature of one of the plates using the plasma and Drude models for extrapolation of the optical data of Au to low frequencies. The obtained results essentially depend on the extrapolation used. Modifications of the CANNEX setup, originally developed to measure the Casimir pressure and pressure gradient in thermal equilibrium, are suggested, which allow different temperatures of one of the plates. Computations of the nonequilibrium pressure and pressure gradient are performed for a realistic experimental configuration. According to our results, even with only a 10~K difference in temperature between the plates, the experiment could discriminate between different theoretical predictions for the total pressure and its gradient, as well as for the contributions to them due to nonequilibrium, at high confidence.

quant-ph↗

arXiv2019

Examining the Casimir puzzle with upgraded technique and advanced surface cleaning

We performed measurements of the gradient of the Casimir force between Au-coated surfaces of a sphere and a plate by means of significantly upgraded dynamic atomic force microscope (AFM) based technique. By introducing combined cleaning procedure of interior surfaces of the vacuum chamber and the test bodies by means of UV light and Ar ions, we reached higher vacuum and eliminated the role of electrostatic patches. Furthermore, the use of much softer cantilever allowed a sixfold decrease of the systematic error in measuring the force gradient. The experimental data are compared with theoretical predictions of the Lifshitz theory taking into account corrections due to the inaccuracy of the proximity force approximation and that due to surface roughness. It is shown that the theoretical approach accounting for the relaxation properties of free electrons is excluded by the data up to a larger than previous sphere-plate separation of 820~nm, whereas an alternative approach is found in a very good agreement with the data. Importance of these results in connection with the foundations of quantum statistical physics is discussed.

cond-mat.mes-hall↗

arXiv2019

The effect of agglomeration of magnetic nanoparticles on the Casimir pressure through a ferrofluid

The impact of agglomeration of magnetic nanoparticles on the Casimir pressure is investigated in the configuration of two material plates and a layer of ferrofluid confined between them. Both cases of similar and dissimilar plates are considered in the framework of the Lifshitz theory of dispersion forces. It is shown that for two dielectric (SiO_2) plates, as well as for one dielectric (SiO_2) and another one metallic (Au) plates, an agglomeration of magnetite nanoparticles results in only quantitative differences in the values of the Casimir pressure if the optical data for Au are extrapolated to low frequencies by means of the Drude model. If, however, an extrapolation by means of the plasma model is used in computations, which is confirmed in experiments on measuring the Casimir force, one finds that the pressure changes its sign when some share of magnetic nanoparticles of sufficiently large diameter is merged into clusters by two or three items. The revealed effect of sign change is investigated in detail at different separations between the plates, diameters of magnetic nanoparticles and shares of particles merged into clusters of different sizes. The obtained results may be useful when developing ferrofluid-based microdevices and for resolution of outstanding problems in the theory of Casimir forces.

physics.app-ph↗

arXiv2019

Whether an enormously large energy density of the quantum vacuum is catastrophic

The problem of an enormously large energy density of the quantum vacuum is discussed in connection with the concept of renormalization of physical parameters in quantum field theory. Using the method of dimensional regularization, it is recalled that the normal ordering procedure of creation and annihilation operators is equivalent to a renormalization of the cosmological constant leading to its zero and nonzero values in Minkowski space-time and in the standard cosmological model, respectively. It is argued that a frequently discussed gravitational effect, resulting from an enormously large energy density described by the nonrenormalized (bare) cosmological constant, might be nonobservable much like some other bare quantities introduced in the formalism of quantum field theory.

physics.gen-ph↗

arXiv2019

Fluctuation-induced free energy of thin peptide films

We apply the Lifshitz theory of dispersion forces to find a contribution to the free energy of peptide films which is caused by the zero-point and thermal fluctuations of the electromagnetic field. For this purpose, using available information about the imaginary parts of dielectric permittivity of peptides, the analytic representation for permittivity of typical peptide along the imaginary frequency axis is devised. Numerical computations of the fluctuation-induced free energy are performed at room temperature for the freestanding peptide films, containing different fractions of water, and for similar films deposited on dielectric (SiO$_2$) and metal (Au) substrates. It is shown that the free energy of a freestanding peptide film is negative and, thus, contributes to its stability. The magnitude of the free energy increases with increasing fraction of water and decreases with increasing thickness of a film. For peptide films deposited on a dielectric substrate the free energy is nonmonotonous. It is negative for thicker than 100 nm films, reaches the maximum value at some film thickness, but vanishes and changes its sign for thinner than 100 nm films. The fluctuation-induced free energy of peptide films deposited on metallic substrate is found to be positive which makes films less stable. In all three cases, simple analytic expressions for the free energy of sufficiently thick films are found. The obtained results may be useful to attain film stability in the next generation of organic microdevices with further shrinked dimensions.

physics.app-ph↗

arXiv2019

Impact of magnetic nanoparticles on the Casimir pressure in three-layer systems

The Casimir pressure is investigated in three-layer systems where the intervening stratum possesses magnetic properties. This subject is gaining in importance in connection with ferrofluids and their use in various microelectromechanical devices. We present general formalism of the Lifshitz theory adapted to the case of ferrofluid sandwiched between two dielectric walls. The Casimir pressure is computed for the cases of kerosene- and water-based ferrofluids containing a 5% fraction of magnetite nanoparticles with different diameters between silica glass walls. For this purpose, we have found the dielectric permittivities of magnetite and kerosene along the imaginary frequency axis employing the available optical data and used the familiar dielectric properties of silica glass and water, as well as the magnetic properties of magnetite. We have also computed the relative difference in the magnitudes of the Casimir pressure which arises on addition of magnetite nanoparticles to pure carrier liquids. It is shown that for nanoparticles of 20 nm diameter at 2 micrometer separation between the walls this relative difference exceeds 140% and 25% for kerosene- and water-based ferrofluids, respectively. An interesting effect is found that at a fixed separation between the walls an addition of magnetite nanoparticles with some definite diameter makes no impact on the Casimir pressure. The physical explanation for this effect is provided. Possible applications of the obtained results are discussed.

cond-mat.mes-hall↗

arXiv2018

Low-temperature behavior of the Casimir-Polder free energy and entropy for an atom interacting with graphene

The analytic expressions for the free energy and entropy of the Casimir-Polder interaction between a polarizable and magnetizable atom and a graphene sheet are found in the limiting case of low temperature. In so doing, the response of graphene to electromagnetic fluctuations is described in the framework of the Dirac model by means of the polarization tensor in (2+1)-dimensional space-time. It is shown that the dominant contribution to the low-temperature behavior is given by an explicit dependence of the polarization tensor on temperature as a parameter. We demonstrate that the Lifshitz theory of atom-graphene interaction satisfies the Nernst heat theorem, i.e., is thermodynamically consistent. On this basis possible reasons of thermodynamic inconsistency arising for the Casimir-Polder and Casimir interactions in the case of Drude metals are discussed. The conclusion is made that although large thermal effect arising in the Casimir interaction between Drude metals at short separations should be considered as an artifact, the giant thermal effect predicted for graphene systems is an important physical phenomenon which awaits for its experimental observation.

quant-ph↗

arXiv2018

Impact of chemical potential on the reflectance of graphene in the infrared and microwave domains

The reflectance of graphene is investigated in the framework of the Dirac model with account of its realistic properties, such as nonzero chemical potential and band gap, at any temperature. For this purpose, the exact reflection coefficients of the electromagnetic waves on a graphene sheet expressed via the polarization tensor and ultimately via the electrical conductivity of graphene have been used. The reflectance of graphene is computed as a function of frequency and chemical potential at different temperatures and values of the band-gap parameter. The minimum values of the reflectance are found which are reached in the infrared domain at the points of vanishing imaginary part of the conductivity of graphene. For a gapped graphene, the maximum reflectance equal to unity is reached at the points where the imaginary part of conductivity diverges. The computational results demonstrate an interesting interplay between the band gap and chemical potential in their combined effect on the reflectance. Specifically, there are wide frequency intervals where the reflectance of graphene increases with increasing chemical potential and decreasing band gap. The numerical computations are found to be in good agreement with the analytic asymptotic expressions in the regions of their applicability. Several technological areas, where the obtained results could be used, are listed.

cond-mat.mes-hall↗