Casimir force with the inclusion of a finite thickness of interacting plates

The Casimir force between two thin metal films is calculated with allowance made for a finite thickness of the films and a finite plasma frequency. The conditions are determined under which the Casimir force in the films can be weakened considerably (by at least one order of magnitude) as compared to massive metal plates. A comparison with the available experimental data is performed and the conclusion is drawn that the observed values of the Casimir force for the films can be explained in terms of the existing theory under the assumption that the wavelength of plasma oscillations in real films is larger than 1000 nm.     

Optical detection of the Casimir force between macroscopic objects

We report the optical detection of mechanical deformation of a macroscopic object induced by the Casimir force. An adaptive holographic interferometer based on a photorefractive BaTiO3:Co crystal was used to measure periodical nonlinear deformations of a thin pellicle caused by an oscillating Casimir force. A reasonable agreement between the experimental and calculated values of the first and second harmonics of the Casimir force oscillations has been obtained.     

Casimir force between thin films of real metals

The Casimir force between two finite-thickness metal films has been calculated for realistic plasma frequencies of metals. The result obtained indicates the possibility of weakening of the Casimir force for real films by approximately an order of magnitude at the appropriate choice of the parameters in qualitative agreement with the existing experimental data.     

Anomalous temperature dependence of the Casimir force for thin metal films

Within the framework of the Drude dispersive model, we predict an unusual nonmonotonic temperature dependence of the Casimir force for thin metal films. For certain conditions, this force decreases with temperature due to the decrease of the metallic conductivity, whereas the force increases at high temperatures due to the increase of the thermal radiation pressure. We consider the attraction of a film to: either (i) a bulk ideal metal with a planar boundary, or (ii) a bulk metal sphere (lens). The experimental observation of the predicted decreasing temperature dependence of the Casimir force can put an end to the long-standing discussion on the role of the electron relaxation in the Casimir effect.     

Technique for investigating the spatial structure of thin films at a nanolevel

A holographic microscope is intended for investigation and visual observation of nanoobjects that are thin metal films or macromolecules. A module providing for the experimental research of such objects has been designed and built. The optimal thickness of the metal films has been estimated. Software for processing the interference patterns with the aim of obtaining a holographic image of nanoobjects has been developed.     

Long-range magnetic interaction due to the Casimir effect

The zero-point quantum fluctuations of the electromagnetic field in vacuum are known to give rise to a long-range attractive force between metal plates (Casimir effect). For ferromagnetic layers separated by vacuum, it is shown that the interplay of the Casimir effect and of the magneto-optical Kerr effect gives rise to a long-range magnetic interaction. The Casimir magnetic force is found to decay as D-1 in the limit of short distances, and as D-5 in the limit of long distances. Explicit expressions for realistic systems are given in the large- and small-distance limits. An experimental test of the Casimir magnetic interaction is proposed.     

Thermal Casimir effect in ideal metal rectangular boxes

The thermal Casimir effect in ideal metal rectangular boxes is considered using the method of zeta functional regularization. A renormalization procedure is suggested which provides the finite expression for the Casimir free energy in any restricted quantization volume. This expression satisfies the classical limit at high temperature and leads to zero thermal Casimir force for systems with infinite characteristic dimensions. In the case of two parallel ideal metal planes the results, as derived previously using thermal quantum field theory in Matsubara formulation and other methods, are reproduced starting from the expression obtained. It is shown that for rectangular boxes the temperature-dependent contribution to the electromagnetic Casimir force can be both positive and negative depending on side lengths. Numerical computations of the scalar and electromagnetic Casimir free energy and force are performed for cubes.     

Frequency map analysis of the 3D vibrational dynamics of the LiCN/LiNC molecular system

The Casimir effect is a force arising in the macroscopic world as a result of radiation pressure of vacuum fluctuations. It thus plays a key role in the emerging domain of nano-electro-mechanical systems (NEMS). This role is reviewed in the present paper, with discussions of the influence of the material properties of the mirrors, as well as the geometry dependence of the Casimir effect between corrugated mirrors. In particular, the lateral component of the Casimir force and restoring torque between metal plates with misaligned corrugations are evaluated.     

Nonequilibrium electromagnetic fluctuations: heat transfer and interactions

The Casimir force between arbitrary objects in equilibrium is related to scattering from individual bodies. We extend this approach to heat transfer and Casimir forces in nonequilibrium cases where each body, and the environment, is at a different temperature. The formalism tracks the radiation from each body and its scatterings by the other objects. We discuss the radiation from a cylinder, emphasizing its polarized nature, and obtain the heat transfer between a sphere and a plate, demonstrating the validity of proximity transfer approximation at close separations and arbitrary temperatures.     

含色散特异材料三明治结构的量子悬浮效应

在金属板与电介质材料板基底间插入色散特异材料板形成三明治结构,并对其Casimir作用力进行了研究.基于Casimir-Lifshitz理论,通过麦克斯韦应力张量计算了真空涨落的辐射压,并对三明治结构利用电磁模式传输矩阵方法进行了数值计算分析.计算结果表明,原本两板结构中存在的Casimir吸引力,在插入特异材料板后的三明治结构中将转变为斥力,从而使轻薄的金属板产生量子悬浮效应。讨论了特异材料板的色散电磁响应特性以及电介质板基底的影响,结果表明特异材料磁等离子频率越大、磁共振频率越小以及电介质板基底的介电常数越小时,三明治结构中获得的斥力越大.此外,板间距增加到一定范围时,三明治结构中将出现Casimir平衡回复力.特异材料填充因子越小、三明治结构中层距和层厚越大时,三明治结构间的回复力会出现在较长距的位置.三明治结构中的量子悬浮效应与平衡回复力可保证微纳米机械系统稳定性,展现出基于真空辐射压的应用前景.     

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 to 0.3 microm 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.     

Analytic approach to the thermal Casimir force between metal and dielectric

The analytic asymptotic expressions for the Casimir free energy, pressure and entropy at low temperature in the configuration of one metal and one dielectric plate are obtained. For this purpose we develop the perturbation theory in a small parameter proportional to the product of the separation between the plates and the temperature. This is done using both the simplified model of an ideal metal and of a dielectric with constant dielectric permittivity and for the realistic case of the metal and dielectric with frequency-dependent dielectric permittivities. The analytic expressions for all related physical quantities at high temperature are also provided. The obtained analytic results are compared with numerical computations and good agreement is found. We demonstrate for the first time that the Lifshitz theory, when applied to the configuration of metal-dielectric, satisfies the requirements of thermodynamics if the static dielectric permittivity of a dielectric plate is finite. If it is infinitely large, the Lifshitz formula is shown to violate the Nernst heat theorem. The implications of these results for the thermal quantum field theory in Matsubara formulation and for the recent measurements of the Casimir force between metal and semiconductor surfaces are discussed.     

A microscopic approach to Casimir and Casimir–Polder forces between metallic bodies

We consider the Casimir–Polder interaction energy between a metallic nanoparticle and a metallic plate, as well as the Casimir interaction energy between two macroscopic metal plates, in terms of the many-body dispersion interactions between their constituents. Expressions for two- and three-body dispersion interactions between the microscopic parts of a real metal are first obtained, both in the retarded and non-retarded limits. These expressions are then used to evaluate the overall two- and three-body contributions to the macroscopic Casimir–Polder and Casimir force, and to compare them with each other, for the two following geometries: metal nanoparticle/half-space and half-space/half-space, where all the materials are assumed perfect conductors. The above evaluation is obtained by summing up the contributions from the microscopic constituents of the bodies (metal nanoparticles). In the case of nanoparticle/half-space, our results fully agree with those that can be extracted from the corresponding macroscopic results, and explicitly show the non-applicability of the pairwise approximation for the geometry considered. In both cases, we find that, while the overall two-body contribution yields an attractive force, the overall three-body contribution is repulsive. Also, they turn out to be of the same order, consistently with the known non applicability of the pairwise approximation. The issue of the rapidity of convergence of the many-body expansion is also briefly discussed.     

Casimir force at both nonzero temperature and finite conductivity

We find the combined effect of nonzero 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 improper computations based on the Lifshitz formula for the temperature Casimir force are discussed.     

Finite-temperature Casimir effect in piston geometry and its classical limit

We consider the Casimir force acting on a d-dimensional rectangular piston due to a massless scalar field with periodic, Dirichlet and Neumann boundary conditions and an electromagnetic field with perfect electric-conductor and perfect magnetic-conductor boundary conditions. The Casimir energy in a rectangular cavity is derived using the cut-off method. It is shown that the divergent part of the Casimir energy does not contribute to the Casimir force acting on the piston, thus renders an unambiguously defined Casimir force acting on the piston. At any temperature, it is found that the Casimir force acting on the piston increases from −∞ to 0 when the separation a between the piston and the opposite wall increases from 0 to ∞. This implies that the Casimir force is always an attractive force pulling the piston towards the closer wall, and the magnitude of the force gets larger as the separation a gets smaller. Explicit exact expressions for the Casimir force for small and large plate separations and for low and high temperatures are computed. The limits of the Casimir force acting on the piston when some pairs of transversal plates are large are also derived. An interesting result regarding the influence of temperature is that in contrast to the conventional result that the leading term of the Casimir force acting on a wall of a rectangular cavity at high temperature is the Stefan–Boltzmann (or black-body radiation) term which is of order T ^d+1, it is found that the contributions of this term from the two regions separating the piston cancel with each other in the case of piston. The high-temperature leading-order term of the Casimir force acting on the piston is of order T, which shows that the Casimir force has a nontrivial classical ℏ→0 limit. Explicit formulas for the classical limit are computed.     

Vortex fluctuations in the critical Casimir effect of superfluid and superconducting films

Vortex-loop renormalization techniques are used to calculate the magnitude of the critical Casimir forces in superfluid films. The force is found to become appreciable when the size of the thermal vortex loops is comparable to the film thickness, and the results for TT(c). When applied to a high-T(c) superconducting film connected to a bulk sample, the Casimir force causes a voltage difference to appear between the film and the bulk, and estimates show that this may be readily measurable.     

Generalized mathematical novel model of thermoelastic diffusion with four phase lags and higher-order time derivative

The European Physical Journal Plus - We calculate the Casimir force between two parallel ideal metal plates when there is an intervening chiral medium present. Making use of methods of quantum...     

Critical Casimir effect in three-dimensional Ising systems: measurements on binary wetting films

The critical Casimir force (CF) is observed in thin wetting films of a binary liquid mixture close to the liquid/vapor coexistence. X-ray reflectivity shows thickness (L) enhancement near the bulk consolute point. The extracted Casimir amplitude Delta(+-)=3+/-1 agrees with the theoretical universal value for the antisymmetric 3D Ising films. The onset of CF in the one-phase region occurs at L/xi approximately 5 regardless of whether the bulk correlation length xi is varied with temperature or composition. The shape of the Casimir scaling function depends monotonically on the dimensionality.     

Modulation of the Casimir force by laser pulses: Influence of oxide films on the silicon surface

The possibility of modulating the Casimir force that acts in an air medium between a gold sphere and a silicon plate irradiated by laser pulses has been studied. It has been demonstrated that the oxide film that is formed on the silicon surface in air hardly affects the possibility of modulating the Casimir force when the distances between interacting bodies are of the order of 100 nm. With an increase in the distance, the modulation depth decreases; however, this region is of less practical interest, because the Casimir forces become too weak.     

Effect of the electric current on the Casimir force between graphene sheets

The dependence of the thermal component of the Casimir force and Casimir friction between graphene sheets on the drift velocity of charge carriers in one of the sheets has been analyzed. It has been shown that the drift motion results in the measurable change in the thermal Casimir force owing to the Doppler effect. The thermal Casimir force, as well as Casimir friction, increases strongly in the case of resonant photon tunneling, when the energy of an emitted photon coincides with the excitation energy of an electron-hole pair. In the case of resonant photon tunneling, the dominant contribution to the Casimir friction even at temperatures above room temperature comes from quantum friction caused by quantum fluctuations. Quantum friction can be detected in an experiment on the friction drag between graphene sheets in a high electric field.