arXiv subjects

V. M. Mostepanenko

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

At least 19 recordsLinked to original sources

arXiv2026

The Casimir free energy of peptide films on a silicon substrate: Impact of dielectric-to-metal transition in silicon and nanoparticles in peptide

Using the Lifshitz theory of the van der Waals and Casimir forces, we calculate the Casimir free energy of thin peptide films deposited on silicon substrates. The Casimir free energy is found as a function of film thickness for different fractions of water in the film, in the presence of either nonmagnetic or magnetic nanoparticles, and under the impact of irradiation of a silicon substrate with laser pulses or dopants resulting in the dielectric-to-metal phase transition. It is shown that for a dielectric silicon there is the borderline value of the film thickness, such that the Casimir free energy is negative and contributes to the film stability for thicker films, but is positive and makes the film less stable for thinner ones. According to our results, the borderline value of peptide film thickness decreases with increasing volume fractions of water and in the film. This decrease is more pronounced for the magnetic nanoparticles and becomes stronger with increasing their radius. The borderline value of peptide film thickness is found as a function of the fraction of water in the film. If the silicon substrate is in metallic state, the Casimir free energy of peptide coating is always positive, which makes it less stable. Possible applications of the obtained results in organic electronics and biomedicine are discussed.

cond-mat.mes-hall↗

arXiv2026

Role of the Casimir force in the capacitive radio-frequency microelectromechanical switches

We determine the role of the fluctuation-induced Casimir force acting between a membrane of cylindrical shape and a bottom electrode in microelectromechanical capacitive switches. For this purpose, the Casimir force is computed taking into account the real properties of both a membrane and a bottom electrode materials with account of surface roughness. The obtained results are compared with those found for the smooth surfaces using the idealization of ideal metal. It is shown that an account of both the real material properties and surface roughness is crucial for obtaining the correct values of the Casimir force. According to our results, at the shortest separations, when the switch membrane is in contact with the transmission line, the magnitudes of the Casimir force may exceed the magnitudes of the electric one depending on the value of the operating voltage. The obtained values of the Casimir force can be used for determining the thickness of the switch membrane, which ensures the necessary magnitude of the restoring elastic force required for a stable cyclic functioning of the micromechanical switch with no pull-in.

cond-mat.mes-hall↗

arXiv2026

Why the Casimir Force for Magnetic Metals Computed by the Lifshitz Theory Using the Drude Model Disagrees with the Measurement Data

We consider the Casimir force in configurations with magnetic metal plates and analyze the reasons why the predictions of the Lifshitz theory using the dielectric permittivity of the Drude model are inconsistent with the measurement data. For this purpose, the contributions of the electromagnetic waves with the transverse magnetic and transverse electric polarizations to the Casimir force are computed using the Lifshitz theory expressed in terms of the pure imaginary Matsubara frequencies. Furthermore, the fractions of the evanescent and propagating waves in these contributions are found using an equivalent formulation of the Lifshitz theory along the real frequency axis. All computations are performed for Au-Ni and Ni-Ni plates using the Drude model and the experimentally consistent plasma model over the separation region from 0.5 to 6~mum, where the total force value is determined by conduction electrons. It is shown that the transverse magnetic contribution to the Casimir force does not depend on the used model of the dielectric permittivity, so that the total difference between the predictions of the Lifshitz theory using the Drude model and the measurement data is determined by the transverse electric contribution. In doing so, as opposed to the case of nonmagnetic metals, both fractions of the evanescent and propagating waves in this contribution depend on the model of the dielectric permittivity used in computations, whereas the magnetic properties of the plate metal influence the Casimir force solely through the fraction of propagating waves in the transverse electric contribution. The issue of a more adequate theoretical description of the electromagnetic response of magnetic metals is discussed.

quant-ph↗

arXiv2026

Quantum Theory and Unusual Dielectric Functions of Graphene

We address the spatially nonlocal dielectric functions of graphene at any frequency derived starting fromthe first principles of thermal quantum field theory using the formalism of the polarization tensor. After a brief review of this formalism, the longitudinal and transverse dielectric functions are considered at any relationship between the frequency and the wave vector. The analytic properties of their real and imaginary parts are investigated at low and high frequencies. Emphasis is given to the double pole at zero frequency which arises in the transverse dielectric function. The role of this unusual property for solving the problem of disagreement between experiment and theory in the Casimir effect is discussed. We guess that a more complete dielectric response of ordinary metals should also be spatially nonlocal and its transverse part may possess the double pole in the region of evanescent waves.

cond-mat.mes-hall↗

arXiv2025

Constraining Yukawa-type interaction and coupling constant of axionlike particles to nucleons from recent measurement of the Casimir-Polder interaction

We derive constraints on the parameters of the Yukawa-type interaction and on the coupling constant of axionlike particles to nucleons from the results of recent diffraction experiment on measuring the Casimir-Polder interaction between Ar atoms and a silicon nitride nanograting. It is shown that within the interaction range from 1 to 2 nm the obtained constraints are by up to a factor of 33.4 stronger than all the other ones found previously from measurement of the Casimir force. The derived constraints are weaker in strength than those deduced from the experiments on neutron scattering. The constraints on the coupling constants of axionlike particles to nucleons following from the diffraction experiment are up to a factor of 24.2 stronger withing the range of axion masses from 32.4 to 100 eV than the previously derived ones from experiments on measuring the Casimir force. They are weaker only in comparison to the constraints found from the experiment using the beams of molecular hydrogen. The potential of the Casimir effect for obtaining stronger constraints on the parameters of hypothetical interactions is discussed.

hep-ph↗

arXiv2025

Temperature Dependence of the Response Functions of Graphene: Impact on Casimir and Casimi-Polder Forces in and out of Thermal Equilibrium

We review and obtain some new results on the temperature dependence of spatially nonlocal response functions of graphene and their applications to calculation of both the equilibrium and nonequilibrium Casimir and Casimir-Polder forces. After a brief summary of the properties of the polarization tensor of graphene obtained within Dirac model in the framework of quantum field theory, we derive the expressions for the longitudinal and transverse dielectric functions. The behavior of these functions at different temperatures is investigated in the regions below and above the threshold. Special attention is paid to the double pole at zero frequency which is present in the transverse response function of graphene. An application of the response functions of graphene to calculation of the equilibrium Casimir force between two graphene sheets and Casimir-Polder forces between an atom (nanoparticle) and a graphene sheet is considered with due attention to the role of a nonzero energy gap, chemical potential and a material substrate underlying the graphene sheet. The same subject is discussed for out-of-thermal-equilibrium Casimir and Casimir-Polder forces. The role of the obtained and presented results for fundamental science and nanotechnology is outlined.

cond-mat.mes-hall↗

arXiv2025

Measurement of the Unusual Dielectric Response to Low-Frequency s-Polarized Evanescent Waves in Metals with {\break} Implications for the Casimir Effect

We report precision measurements of the lateral component of the oscillating magnetic field reflected from a copper plate, which is fully determined by s-polarized evanescent waves. The measurement data are compared with theoretical predictions of classical electrodynamics using the dielectric permittivity of copper as given by the Drude model. It is shown that these predictions are excluded by the measurement data which means that the currently used Drude model does not provide a complete description of the electromagnetic response of metals for s-polarized evanescent waves. The critical importance of this result for several fields of condensed matter physics and optics dealing with evanescent waves, including the Casimir effect, is discussed.

cond-mat.mtrl-sci↗

arXiv2025

Recent solution to the Casimir puzzle awaits its experimental confirmation

The plausible resolution of the Casimir puzzle implying that the dissipative Drude model is not applicable in the area of transverse electric evanescent waves is discussed. Calculations show that for the propagating waves, as well for the evanescent waves with transverse magnetic polarization, the Drude model can beused in calculations of the Casimir force by the Lifshitz theory with no contradictions with the measurement data. The lateral component of magnetic field of the magnetic dipole oscillating near a metallic surface is computed for the parameters of experiment in preparation which is aimed to directly check the validity of the Drude model in the area of transverse electric evanescent waves. By comparing with the case of graphene, whose dielectric response is spatially nonlocal and possesses the double pole at zero frequency, it is hypothesized that the success of the dissipationless plasma model in this area is also caused by the presence of a double pole.

quant-ph↗

arXiv2025

Comment on "Electric conductivity of graphene: Kubo model versus a nonlocal quantum field theory model (arXiv:2403.02279v3)"

Recently, Rodriguez-Lopez, Wang, and Antezza [Phys. Rev. B v.111, 115428 (2025)] compared the theoretical descriptions of electric conductivity of graphene given by the Kubo model and quantum field theory in terms of the polarization tensor. According to this article, in the spatially nonlocal case, the quantum field theoretical description contains ``hard inconsistencies". By modifying the equality, which relates the conductivity and polarization expressions, the predictions of quantum field theory were revised and brought in agreement with those following from the nonrelativistic Kubo model. Here, it is shown that this modification violates the requirement of gauge invariance and, thus, is unacceptable. By comparing both theoretical approaches, we demonstrate that all the results obtained within quantum field theory are physically well justified whereas an application of the modified expression for the conductivity of graphene leads to the consequences of nonphysical character.

cond-mat.mes-hall↗

arXiv2025

Impact of surface roughness on the stability of nanoelectromechanical pressure sensors in the Casimir regime

The stability of nanoelectromechanical pressure sensors working in the Casimir regime is considered with account of surface roughness on both the sensor membrane and the ground plate. The equilibrium positions of the sensor membrane are found from the balance between the external measured, elastic, electric pressures, and the Casimir pressure computed by means of the Lifshitz theory. It is shown that the stable equilibrium position of the sensor membrane is nearly independent of the surface roughness, whereas its unstable equilibrium position is shifted to larger membrane-plate separations. The use of these results for creatign pressure sensors with further shrinked dimensions is discussed.

quant-ph↗

arXiv2025

Nonequilibrium Casimir pressure for two graphene-coated plates: Quantum field theoretical approach

We consider the nonequilibrium Casimir pressure in the system of two parallel graphene-coated plates one of which is either warmer or cooler than the environment. The electromagnetic response of graphene coating characterized by the nonzero energy gap and chemical potential is described in the framework of the Dirac model by means of the polarization tensor. It is shown that the magnitude of the nonequilibrium Casimir pressure on a warmer plate than the environment is larger and on a cooler plate is smaller than the magnitude of the standard Casimir pressure in the state of thermal equilibrium. According to our results, the spatially local theory underestimates the role of the effects of nonequilibrium. This underestimation increases for asmaller chemical potential of the graphene coating and at lower temperatures of the cooled plate. Possible applications of the obtained results are discussed.

quant-ph↗

arXiv2025

A few remarks concerning application of the Lifshitz theory to calculation of the Casimir-Polder interaction

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.

quant-ph↗

arXiv2025

Polarization tensor in spacetime of three dimensions and quantum field theoretical description of the nonequilibrium Casimir force in graphene systems

The polarization tensor of graphene derived in the framework of the Dirac model using the methods of thermal quantum field theory in (2+1) dimensions is recast in a mathematically equivalent but more compact and convenient in computations form along the real frequency axis. The obtained unified expressions for the components of the polarization tensor are equally applicable in the regions of the on- and off-the-mass-shell electromagnetic waves. The advantages of the presented formalism are demonstrated on the example of nonequilibrium Casimir force in the configuration of two parallel graphene-coated dielectric plates one of which is either hotter or colder than the environment. This force is investigated as a function of temperature, the energy gap, and chemical potential of graphene coatings with account of the effects of spatial dispersion. Besides the thermodynamically nonequilibrium Casimir and Casimir-Polder forces, the obtained form of the polarization tensor can be useful for investigation of many diverse physical phenomena in graphene systems, such as surface plasmons, reflectances, electrical conductivity, radiation heat transfer, etc.

quant-ph↗

arXiv2024

Pull-in features of nanoswitches in the Casimir regime with account of contact repulsion

The cantilever tip of a nanoswitch in close proximity to the ground plate is considered with account of electrostatic, elastic, van der Waals (Casimir), and also contact repulsive forces. The van der Waals (Casimir) and contact repulsive forces are computed for a Si cantilever and either Au or Ni ground plates using the Lifshitz theory and the method of pairwise summation with account of surface roughness. It is shown that at short separations an impact of the van der Waals (Casimir) force leads to the pull-in and collapse of a cantilever onto the ground plate if the contact repulsion is disregarded. Taking into consideration contact repulsion, the nanoswitch is demonstrated to have the stable cyclic behavior with no pull-in when switching voltage on and off.

cond-mat.mes-hall↗

arXiv2024

Role of the Casimir force in micro- and nanoelectromechanical pressure sensors

The Casimir force caused by the electromagnetic fluctuations is computed in the configurations of micro- and nanoelectromechanical pressuresensors using Si membranes and either Si or Au-coated Si substrates. It is shown that if, under the influence of external pressure, the membrane-substrate separation drops to below 100 nm, the Casimir force makes a profound effect onthe sensor functioning. There exists the maximum value of external pressure depending on the sensor parameters such that it finds itself in a state of unstable equilibrium. For this and larger pressures, the Casimir force leads to a collapse of the sensor, which loses its functionality. For any smaller external pressures, there exist two equilibrium positions, one of which is unstable and another one is stable, at smaller and larger membrane-substrate separations, respectively. The latter can be safely used for the pressure measurements. Possible applications of the {obtained} results in the design of micro- and nanoelectromechanical pressure sensors of next generations with further decreased dimensions are discussed.

cond-mat.mes-hall↗

arXiv2024

On the convergence of the polarization tensor in space-time of three dimensions

In this paper, we consider the convergence properties of the polarization tensor of graphene obtained in the framework of thermal quantum field theory in three-dimensional space-time. During the last years, this problem attracted much attention in connection with calculation of the Casimir force in graphene systems and investigation of the electrical conductivity and reflectance of graphene sheets. There are contradictory statements in the literature, especially on whether this tensor has an ultraviolet divergence in three dimensions. Here, we analyze this problem using the well known method of dimensional regularization. It is shown that the thermal correction to the polarization tensor is finite at any $D$, whereas its zero-temperature part behaves differently for $D=3$ and 4. For $D=3$, it is obtained by the analytic continuation with no subtracting infinitely large terms. As to the space-time of $D=4$, the finite result for the polarization tensor at zero temperature is found after subtracting the pole term. Our results are in agreement with previous calculations of the polarization tensor at both zero and nonzero temperature. This opens possibility for a wider application of the quantum field theoretical approach in investigations of graphene and other two-dimensional novel materials.

hep-th↗

arXiv2024

Casimir-Polder attraction and repulsion between nanoparticles and graphene in out-of-thermal-equilibrium conditions

The nonequilibrium Casimir-Polder force between a nanoparticle and a graphene sheet kept at different temperatures is investigated in the framework of Dirac model using the formalism of the polarization tensor. It is shown that the force magnitude increases with increasing temperature of a graphene sheet. At larger separations an impact of nonequilibrium conditions on the force becomes smaller. According to our results, the attractive Casimir-Polder force vanishes at some definite nanoparticle-graphene separation and becomes repulsive at larger separations if the temperature of a graphene sheet is smaller than that of the environment. This effect may find applications both in fundamental investigations of graphene and for the control of forces in microdevices of bioelectronics.

quant-ph↗

arXiv2023

Quantum field theoretical framework for the electromagnetic response of graphene and dispersion relations with implications to the Casimir effect

The spatially nonlocal response functions of graphene obtained on the basis of first principles of quantum field theory using the polarization tensor are considered in the areas of both the on-the-mass-shell and off-the-mass-shell waves. It s shown that at zero frequency the longitudinal permittivity of graphene is the regular function, whereas the transverse one possesses a double pole for any nonzero wave vector. According to our results, both the longitudinal and transverse permittivities satisfy the dispersion (Kramers-Kronig) relations connecting their real and imaginary parts, as well as expressing each of these permittivities along the imaginary frequency axis via its imaginary part. For the transverse permittivity, the form of an additional term arising in the dispersion relations due to the presence of a double pole is found. The form of dispersion relations is unaffected by the branch points which arise on the real frequency axis in the presence of spatial nonlocality. The obtained results are discussed in connection with the well known problem of the Lifshitz theory which was found to be in conflict with the measurement data when using the much studied response function of metals. A possible way of attack on this problem based on the case of graphene is suggested.

quant-ph↗