arXiv subjects

V. M. Mostepanenko

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

At least 217 records · Page 12Linked to original sources

arXiv2003

Constraints on Non-Newtonian Gravity from Recent Casimir Force Measurements

Corrections to Newton's gravitational law inspired by extra dimensional physics and by the exchange of light and massless elementary particles between the atoms of two macrobodies are considered. These corrections can be described by the potentials of Yukawa-type and by the power-type potentials with different powers. The strongest up to date constraints on the corrections to Newton's gravitational law are reviewed following from the Eötvos- and Cavendish-type experiments and from the measurements of the Casimir and van der Waals force. We show that the recent measurements of the Casimir force gave the possibility to strengthen the previously known constraints on the constants of hypothetical interactions up to several thousand times in a wide interaction range. Further strengthening is expected in near future that makes Casimir force measurements a prospective test for the predictions of fundamental physical theories.

gr-qc↗

arXiv2003

Improved tests of extra-dimensional physics and thermal quantum field theory from new Casimir force measurements

We report new constraints on extra-dimensional models and other physics beyond the Standard Model based on measurements of the Casimir force between two dissimilar metals for separations in the range 0.2--1.2 $μ$m. The Casimir force between an Au-coated sphere and a Cu-coated plate of a microelectromechanical torsional oscillator was measured statically with an absolute error of 0.3 pN. In addition, the Casimir pressure between two parallel plates was determined dynamically with an absolute error of $\approx 0.6$ mPa. Within the limits of experimental and theoretical errors, the results are in agreement with a theory that takes into account the finite conductivity and roughness of the two metals. The level of agreement between experiment and theory was then used to set limits on the predictions of extra-dimensional physics and thermal quantum field theory. It is shown that two theoretical approaches to the thermal Casimir force which predict effects linear in temperture are ruled out by these experiments. Finally, constraints on Yukawa corrections to Newton's law of gravity are strengthened by more than an order of magnitude in the range 56 nm to 330 nm.

hep-ph↗

arXiv2003

Comment on "Does the transverse electric zero mode contribute to the Casimir effect for a metal?"

Recently J.S. Hoye, I.Brevik, J.B. Aarseth, and K.A. Milton [Phys. Rev. E v.67, 056116 (2003); quant-ph/0212125] proposed that if the Lifshitz formula is combined with the Drude model, the transverse electric zero mode does not contribute to the result for real metals and there arises a linear temperature correction to the Casimir force at small temperatures. The authors claim that in spite of the fact that the Casimir entropy in their approach is negative, the Nernst heat theorem is satisfied. In the present Comment we show that the authors' conclusion regarding the Nernst heat theorem is in error. We demonstrate also the resolution of this thermodynamic puzzle based on the use of the surface impedance instead of the Drude dielectric function. The results of numerical computations obtained by the authors are compared with those from use of the surface impedance approach which are thermodynamically consistent.

quant-ph↗

arXiv2003

Surface-impedance approach solves problems with the thermal Casimir force between real metals

The surface impedance approach to the description of the thermal Casimir effect in the case of real metals is elaborated starting from the free energy of oscillators. The Lifshitz formula expressed in terms of the dielectric permittivity depending only on frequency is shown to be inapplicable in the frequency region where a real current may arise leading to Joule heating of the metal. The standard concept of a fluctuating electromagnetic field on such frequencies meets difficulties when used as a model for the zero-point oscillations or thermal photons in the thermal equilibrium inside metals. Instead, the surface impedance permits not to consider the electromagnetic oscillations inside the metal but taking the realistic material properties into account by means of the effective boundary condition. An independent derivation of the Lifshitz-type formulas for the Casimir free energy and force between two metal plates is presented within the impedance approach. It is shown that they are free of the contradictions with thermodynamics which are specific to the usual Lifshitz formula for dielectrics in combination with the Drude model. We demonstrate that in the impedance approach the zero-frequency contribution is uniquely fixed by the form of impedance function and does not need any of the ad hoc prescriptions intensively discussed in the recent literature. As an example, the computations of the Casimir free energy between two gold plates are performed at different separations and temperatures. It is argued that the surface impedance approach lays a reliable framework for the future measurements of the thermal Casimir force.

quant-ph↗

arXiv2003

New features of the thermal Casimir force at small separations

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.

quant-ph↗

arXiv2003

Perturbation approach to the Casimir force between two bodies made of different real metals

The Casimir force acting between two test bodies made of different metals is considered. The finiteness of the conductivity of the metals is taken into account perturbatively up to the fourth order of the relative penetration depths of electromagnetic zero-point oscillations into the metals. The influence of nonzero temperature is computed explicitly for separate orders of perturbation and found to be important in the zeroth and first orders only. The configurations of two parallel plates and a sphere (spherical lens) above a plate are considered made of $Au$ and $Cr$. The obtained results can be used to take into account also the surface roughness. Thus, the total amount of the Casimir force between different metals with all correction factors is determined. This may be useful in various applications.

quant-ph↗

arXiv2002

Correlation of energy and free energy for the thermal Casimir force between real metals

The energy of fluctuating electromagnetic field is investigated for the thermal Casimir force acting between parallel plates made of real metal. It is proved that for nondissipative media with temperature independent dielectric permittivity the energy at nonzero temperature comprises of the (renormalized) energies of the zero-point and thermal photons. In this manner photons can be considered as collective elementary excitations of the matter of plates and electromagnetic field. If the dielectric permittivity depends on temperature the energy contains additional terms proportional to the derivatives of dielectric permittivity with respect to temperature, and the quasiparticle interpretation of the fluctuating field is not possible. The correlation between energy and free energy is considered. Previous calculations of the Casimir energy in the framework of the Lifshitz formula at zero temperature and optical tabulated data supplemented by the Drude model at room temperature are analysed. It is demonstrated that this quantity is not a good approximation either for the free energy or the energy. A physical interpretation of this hybrid quantity is suggested. The contradictory results in the recent literature on whether the zero-frequency term of the Lifshitz formula for the perpendicular polarized modes has any effective contribution to the physical quantities are discussed. Four main approaches to the resolution of this problem are specified. The precise expressions for entropy of the fluctuating field between plates made of real metal are obtained, which helps to decide between the different approaches. The conclusion is that the Lifshitz formula supplemented by the plasma model and the surface impedance approach are best suited to describe the thermal Casimir force between real metals.

quant-ph↗

arXiv2002

Experimental and Theoretical Investigation of the Lateral Casimir Force Between Corrugated Surfaces

The lateral Casimir force acting between a sinusoidally corrugated gold plate and sphere was calculated and measured. The experimental setup was based on the atomic force microscope specially adapted for the measurement of the lateral Casimir force. The measured force oscillates sinusoidally as a function of the phase difference between the two corrugations. Both systematic and random errors are analysed and a lateral force amplitude of $3.2\times 10^{-13} $N was measured at a separation distance of 221 nm with a resulting relative error 24% at a 95% confidence probability. The dependence of the measured lateral force amplitude on separation was investigated and shown to be consistent with the inverse fourth power distance dependence. The complete theory of the lateral Casimir force is presented including finite conductivity and roughness corrections. The obtained theoretical dependence was analysed as a function of surface separation, corrugation amplitudes, phase difference, and plasma wavelength of a metal. The theory was compared with the experimental data and shown to be in good agreement. The constraints on hypothetical Yukawa-type interactions following from the measurements of the lateral Casimir force are calculated. The possible applications of the lateral vacuum forces to nanotechnology are discussed.

quant-ph↗

arXiv2002

Thermodynamical aspects of the Casimir force between real metals at nonzero temperature

We investigate the thermodynamical aspects of the Casimir effect in the case of plane parallel plates made of real metals. The thermal corrections to the Casimir force between real metals were recently computed by several authors using different approaches based on the Lifshitz formula with diverse results. Both the Drude and plasma models were used to describe a real metal. We calculate the entropy density of photons between metallic plates as a function of the surface separation and temperature. Some of these approaches are demonstrated to lead to negative values of entropy and to nonzero entropy at zero temperature depending on the parameters of the system. The conclusion is that these approaches are in contradiction with the third law of thermodynamics and must be rejected. It is shown that the plasma dielectric function in combination with the unmodified Lifshitz formula is in perfect agreement with the general principles of thermodynamics. As to the Drude dielectric function, the modification of the zero-frequency term of the Lifshitz formula is outlined that not to violate the laws of thermodynamics.

quant-ph↗

arXiv2002

Demonstration of the Lateral Casimir Force

The lateral Casimir force between a sinusoidally corrugated gold coated plate and large sphere was measured for surface separations between 0.2 $μ$m to 0.3 $μ$m using an atomic force microscope. The measured force shows the required periodicity corresponding to the corrugations. It also exhibits the necessary inverse fourth power distance dependence. The obtained results are shown to be in good agreement with a complete theory taking into account the imperfectness of the boundary metal. This demonstration opens new opportunities for the use of the Casimir effect for lateral translation in microelectromechanical systems.

quant-ph↗

arXiv2001

Casimir force under the influence of real conditions

The Casimir force is calculated analytically for configurations of two parallel plates and a spherical lens (sphere) above a plate with account of nonzero temperature, finite conductivity of the boundary metal and surface roughness. The permittivity of the metal is described by the plasma model. It is proved that in case of the plasma model the scattering formalism of quantum field theory in Matsubara formulation underlying Lifshitz formula is well defined and no modifications are needed concerning the zero-frequency contribution. The temperature correction to the Casimir force is found completely with respect to temperature and perturbatively (up to the second order in the relative penetration depth of electromagnetic zero-point oscillations into the metal) with respect to finite conductivity. The asymptotics of low and high temperatures are presented and contributions of longitudinal and perpendicular modes are determined separately. Serving as an example, aluminium test bodies are considered showing good agreement between the obtained analytical results and previously performed numerical computations. The roughness correction is formally included and formulas are given permitting to calculate the Casimir force under the influence of all relevant factors.

quant-ph↗

arXiv2001

New constraints on ultrashort-ranged Yukawa interactions from atomic force microscopy

Models in which the gravitational and gauge interactions are unified at ~1 TeV lead to the possibility that large extra dimensions would produce Yukawa-type corrections to the Newtonian gravitational law at small distances. In some models with n = 3 extra dimensions, deviations from Newtonian gravity would occur at separations ~5 nm, a distance scale accessible to an atomic force microscope (AFM). Here we present constraints on the Yukawa corrections derived from the latest AFM Casimir force measurement by Mohideen, et al. which are up to 19 times stronger than those obtained from their previous experiment. We then discuss new designs for AFM experiments which have the potential to significantly improve upon these constraints.

hep-ph↗

arXiv2001

New Developments in the Casimir Effect

We provide a review of both new experimental and theoretical developments in the Casimir effect. The Casimir effect results from the alteration by the boundaries of the zero-point electromagnetic energy. Unique to the Casimir force is its strong dependence on shape, switching from attractive to repulsive as function of the size, geometry and topology of the boundary. Thus the Casimir force is a direct manifestation of the boundary dependence of quantum vacuum. We discuss in depth the general structure of the infinities in the field theory which are removed by a combination of zeta-functional regularization and heat kernel expansion. Different representations for the regularized vacuum energy are given. The Casimir energies and forces in a number of configurations of interest to applications are calculated. We stress the development of the Casimir force for real media including effects of nonzero temperature, finite conductivity of the boundary metal and surface roughness. Also the combined effect of these important factors is investigated in detail on the basis of condensed matter physics and quantum field theory at nonzero temperature. The experiments on measuring the Casimir force are also reviewed, starting first with the older measurements and finishing with a detailed presentation of modern precision experiments. The latter are accurately compared with the theoretical results for real media. At the end of the review we provide the most recent constraints on the corrections to Newtonian gravitational law and other hypothetical long-range interactions at submillimeter range obtained from the Casimir force measurements.

quant-ph↗

arXiv2001

Temperature dependence of the Casimir force between real metals: problems and approach to their resolution

We investigate the Casimir force acting between real metals at nonzero temperature. It is shown that the zero-frequency term of Lifshitz formula has interpretation problem in the case of real metal described by Drude model. It happens because the scattering theory underlying Lifshitz formula is not well formulated when the dielectric permittivity takes account of dissipation. To give the zeroth term of Lifshitz formula the definite meaning different prescriptions were used recently by different authors with diversed results. These results are shown to be improper and in disagreement with experiment and the general physical requirements. We propose the new prescription which is a generalization of Schwinger, DeRaad and Milton recipe formulated earlier for ideal metals. On this base the detailed numerical and analytical computations of the temperature Casimir force are performed in configuration of two plane plates and a spherical lens (sphere) above a plate. The corrections due to nonzero temperature and finite conductivity found in the paper are in agreement with the limiting case of perfect metal and fit all experimental and theoretical requirements. Among other facts, the previous results obtained in frames of plasma model are confirmed. It appears they are the limiting case of Drude model computations when the relaxation parameter goes to zero. The comparison with the Casimir force acting between dielectric test bodies is made.

quant-ph↗

arXiv2001

Constraints on non-Newtonian gravity from the Casimir force measurements between two crossed cylinders

Constraints on the Yukawa-type corrections to Newtonian gravitational law are obtained resulting from the measurement of the Casimir force between two crossed cylinders. The new constraints are stronger than those previously derived in the interaction range between 1.5 nm and 11 nm. The maximal strengthening in 300 times is achieved at 4.26 nm. Possible applications of the obtained results to the elementary particle physics are discussed.

hep-ph↗

arXiv2000

Possible violation of Newtonian gravitational law at small distances and constraints on it from the Casimir effect

The recent ideas that the gravitational and gauge interactions become united at the weak scale lead to Yukawa-type corrections to the Newtonian gravitational law at small distances. We briefly summarize the best constraints on these corrections obtained recently from the experiments on the measurement of the Casimir force. The new constraints on the Yukawa-type interaction are derived from the latest Casimir force measurement between a large gold coated sphere and flat disk using an atomic force microscope. The obtained constraints are stronger up to 19 times comparing the previous experiment with aluminum surfaces and up to 4500 times comparing the Casimir force measurements between dielectrics. The application range of constraints obtained by means of an atomic force microscope is extended.

hep-ph↗

arXiv2000

Casimir and van der Waals force between two plates or a sphere (lens) above a plate made of real metals

The Casimir and van der Waals forces acting between two metallic plates or a sphere (lens) above a plate are calculated accounting for the finite conductivity of the metals. The simple formalism of surface modes is briefly presented which allows the possibility to obtain the generalization of Lifshitz results for the case of two semi-spaces covered by the thin layers. Additional clarifications of the regularization procedure provides the means to obtain reliable results not only for the force but also for the energy density. This, in turn, leads to the value of the force for the configuration of a sphere (lens) above a plate both of which are covered by additional layers. The Casimir interaction between Al and Au test bodies is recalculated using the optical tabulated data for the complex refractive index of these metals. The computations turn out to be in agreement with the perturbation theory up to the fourth order in relative penetration depth of electromagnetic zero point oscillations into the metal. The disagreements between the results recently presented in the literature are resolved. The Casimir force between Al bodies covered by the thin Au layers is computed and the possibility to neglect spatial dispersion effects is discussed as a function the layer thickness. The van der Waals force is calculated including the transition region to the Casimir force. The pure non-retarded van der Waals force law between Al and Au bodies is shown to be restricted to a very narrow distance interval from 0.5 nm to (2--4) nm. New, more exact, values of the Hamaker constant for Al and Au are determined.

quant-ph↗

arXiv2000

Casimir force at both non-zero temperature and finite conductivity

We find the joint effect of non-zero temperature and finite conductivity onto the Casimir force between real metals. Configurations of two parallel plates and a sphere (lens) above a plate are considered. Perturbation theory in two parameters (the relative temperature and the relative penetration depth of zero point oscillations into the metal) is developed. Perturbative results are compared with computations. Recent evidence concerning possible existence of large temperature corrections at small separations between the real metals is not supported.

quant-ph↗