The physical origin of the Casimir force is connected with existence zero-point and thermal fluctuations. effect very general finds applications in various fields physics. This review limited to rapid progress at intersection experiment theory that has been achieved last few years. It includes a critical assessment proposed approaches resolution puzzles arising Lifshitz van der Waals forces real materials. All primary experiments on measurement between macroscopic bodies Casimir-Polder an...

2.1.Граничные условия -идеализированный вариант внешнего поля.2.2.Кван товая механика струны.2.3.Полные наборы решений уравнения Клейна -Фока.2.4.Бесконечная энергия нулевых колебаний зависит от граничных условий.2.5.Наблюдаемая величина -регуляризованная разность энергий колебаний.2.6.Граничные моделируют топологию.2.7.Эффект Казимира как поляризация вакуума.2.8.Более реалистическая модельполупроницаемые стенки.2.9.Массивное поле.2.10.О физическом смысле казимировской энергии вакуума.3

A micromechanical torsion oscillator has been used to strengthen the limits on new Yukawa forces by determining Casimir pressure between two gold-coated plates. By significantly reducing random errors and obtaining electronic parameters of gold coatings, we were able conclusively exclude predictions large thermal effects below $1\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ constraints corrections Newtonian gravity in interaction range from 29.5 nm 86 nm.

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

We report new constraints on extra-dimensional models and other physics beyond the standard model based measurements of Casimir force between two dissimilar metals for separations in range $0.2--1.2\ensuremath{\mu}\mathrm{m}.$ The a Au-coated sphere Cu-coated plate microelectromechanical torsional oscillator was measured statically with an absolute error 0.3 pN. In addition, pressure parallel plates determined dynamically $\ensuremath{\approx}0.6\mathrm{mPa}.$ Within limits experimental...

The Casimir and van der Waals forces acting between two metallic plates or a sphere (lens) above plate are calculated, accounting for the finite conductivity of metals. A simple formalism surface modes is briefly presented which makes it possible to obtain generalization Lifshitz results case semispaces covered by thin layers. Additional clarification regularization procedure provides means reliable not only force but also energy density. This, in turn, leads value configuration plate, both...

The experimental demonstration of the modification Casimir force [Proc. K. Ned. Akad. Wet. 51, 793 (1948)] between a gold coated sphere and single-crystal Si membrane by light pulses is performed. specially designed fabricated was irradiated with $514\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ laser $5\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$ width in high vacuum, leading to change charge-carrier density. difference presence absence radiation measured means an atomic microscope as function...

We give a rigorous analytical derivation of low-temperature behavior the Casimir entropy in framework Lifshitz formula combined with Drude dielectric function. An earlier result that at zero temperature is not equal to and depends on parameters system confirmed, i.e., third law thermodynamics (the Nernst heat theorem) violated. illustrate resolution this thermodynamical puzzle context surface impedance approach by several calculations thermal force for both real metals dielectrics. Different...

We present measurement results for the gradient of Casimir force between an Au-coated sphere and plate obtained by means atomic microscope operated in a frequency-shift technique. This experiment was performed at pressure $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ Torr with hollow glass 41.3 $\ensuremath{\mu}$m radius. Special attention is paid to electrostatic calibrations, including problem patches. All calibration parameters are shown be separation independent after...

The lateral Casimir force, which arises between aligned sinusoidally corrugated surfaces of a sphere and plate, was measured for the case small corrugation period beyond applicability region proximity force approximation (PFA). increased amplitudes corrugations on both plate allowed observation an asymmetry i.e., deviation its profile from perfect sine function. dependences phase shift test bodies were at different separations in two sets measurements with sphere. maximum magnitude as...

We demonstrate the Casimir interaction between two ferromagnetic boundary surfaces using dynamic atomic force microscope. The experimental data are found to be in excellent agreement with predictions of Lifshitz theory for magnetic combined plasma model approach. It is shown that materials role hypothetical patch potentials opposite required reconciliation Drude model.

We present the complete results for dynamic experiment on measuring gradient of Casimir force between magnetic (Ni-coated) surfaces a plate and sphere. Special attention is paid to description some details setup, its calibration, error analysis, background effects. Computations are performed in framework Lifshitz theory at nonzero temperature with an account analytic corrections proximity approximation surface roughness using both Drude plasma model approaches. The interaction sphere due...

The gradient of the Casimir force between a Si-SiO${}_2$-graphene substrate and an Au-coated sphere is measured by means dynamic atomic microscope operated in frequency shift technique. It shown that presence graphene leads to up 9% increase at shortest separation considered. This qualitative agreement with predictions additive theory using Dirac model graphene.

We find the combined effect of nonzero temperature and finite conductivity onto Casimir force between real metals. Configurations two parallel plates a sphere (lens) above plate are considered. Perturbation theory in parameters (the relative penetration depth zero-point oscillations into metal) is developed. Perturbative results compared with computations. Recent improper computations based on Lifshitz formula for discussed.

We consider detailed roughness and conductivity corrections to the Casimir force in recent measurement employing an atomic microscope. The of test bodies---a metal plate a sphere---was investigated with microscope scanning electron microscope, respectively. It consists separate crystals different heights stochastic background. amplitude relative zero level was determined were calculated up fourth order small parameter (which is this divided by distance between two bodies). Also due finite...

The lateral Casimir force acting between a sinusoidally corrugated gold plate and sphere was calculated measured. experimental setup based on the atomic microscope specially adapted for measurement of force. measured oscillates as function phase difference two corrugations. Both systematic random errors are analyzed amplitude $3.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\mathrm{N}$ at separation distance 221 nm with resulting relative error 24% 95% confidence probability....

Many extensions to the standard model lead possibility of new forces which would produce Yukawa corrections Newtonian gravity. Models in gravitational and gauge interactions are unified at $\ensuremath{\sim}1\mathrm{TeV}$ using large extra dimensions could Yukawa-type law submillimeter distances. In some models with $n=3$ dimensions, deviations from gravity occur separations $\ensuremath{\sim}5\mathrm{nm},$ a distance scale accessible an atomic force microscope (AFM). Here we present...

We compare theory and experiment in the Casimir force measurement between gold surfaces performed with atomic microscope. Both random systematic experimental errors are found leading to a total absolute error equal 8.5 pN at 95% confidence. In terms of relative errors, precision 1.75% is obtained shortest separation 62 nm confidence level (at 60% 1% confirmed separation). An independent determination accuracies theoretical calculations its application configuration carefully made. Special...

A measurement of the Casimir force between a gold coated sphere and two Si plates different carrier densities is performed using high vacuum based atomic microscope. The results are compared with Lifshitz theory good agreement found. Our experiment demonstrates that by changing density semiconductor plate several orders magnitude it possible to modify interaction. This result may find applications in nanotechnology.