Critical Casimir force in 4He films: confirmation of finite-size scaling

We present new capacitance measurements of critical Casimir force-induced thinning of 4He films near the superfluid transition, focused on the region below Tlambda where the effect is the greatest. 4He films of 238, 285, and 340 A thickness are adsorbed on atomically smooth, N-doped silicon substrates. The Casimir force scaling function theta, deduced from the thinning of these three films, collapses onto a single universal curve, attaining a minimum theta=-1.30+/-0.03 at x=td1/nu=-9.7+/-0.8 A1/nu. The collapse confirms the finite-size scaling origin of the dip in the film thickness. Separately, we also confirm the presence down to 2.13 K of the Goldstone or surface fluctuation force, which makes the superfluid film approximately 2 A thinner than the normal film.     

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.     

Thermodynamic Casimir effect in 4He films near Tlambda: Monte Carlo results

The universal finite-size scaling function of the critical Casimir force for the three dimensional XY universality class with Dirichlet boundary conditions is determined using Monte Carlo simulations. The results are in excellent agreement with recent experiments on 4He Films at the superfluid transition and with available theoretical predictions.     

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.     

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.     

The Casimir Effect for Parallel Plates in the Spacetime with a Fractal Extra Compactified Dimension

The Casimir effect for massless scalar fields satisfying Dirichlet boundary conditions on the parallel plates in the presence of one fractal extra compactified dimension is analyzed. We obtain the Casimir energy density by means of the regularization of multiple zeta function with one arbitrary exponent. We find a limit on the scale dimension like $\delta>\frac{1}{2}$ to keep the negative sign of the renormalized Casimir energy which is the difference between the regularized energy for two parallel plates and the one with no plates. We derive and calculate the Casimir force relating to the influence from the fractal additional compactified dimension between the parallel plates. The larger scale dimension leads to the greater revision on the original Casimir force. The two kinds of curves of Casimir force in the case of integer-numbered extra compactified dimension or fractal one are not superposition, which means that the Casimir force show whether the dimensionality of additional compactified space is integer or fraction.     

Repulsive and attractive Casimir forces between magnetodielectric slabs

The Casimir force between two parallel magnetodielectric slabs is investigated by means of Casimir–Lifshitz Theory. For two magnetodielectric slabs, one is permittivity-negative, while the other is permeability-negative in the real frequency space. Numerical results show that when the separation between these two slabs is small (or large), the Casimir force is repulsive, while for the intermediate separation, the Casimir force is attractive. As a consequence, there are two equilibria with zero Casimir force, and a repulsive–attractive–repulsive transition takes place with increasing the separation. Therefore, if the separation between two interacting slabs is manipulated in the small (or large) separation region, it is possible to overcome the stiction in micromechanical and nanomechanical systems.     

The role of the “Casimir force analogue” at the microscopic processes of crystallization and melting

Melting (crystallization), a phase transition from a crystalline solid to a liquid state, is a common phenomenon in nature. We suggest a new factor, “the Casimir force analogue”, to describe mechanisms of melting and crystallization. The Casimir force analogue is a force occurring between the surfaces of solid and liquid phases of metals caused by different energy density of phonons of these phases. It explains abrupt changes in geometry and thermodynamic parameters at a melting point. “The Casimir force analogue” helps to estimate latent melting heat and to gain an insight into a solid–liquid transition problem.     

A new approach to the evaluation of Casimir and van der Waals forces in the transition region

This paper studies the incorporation of Casimir and van der Waals forces applied to a nanostructure with parallel configuration. The focus of this study is in a transition region in which Casimir force gradually transforms into van der Waals force. It is proposed that in the transition region, a proportion of both Casimir and van der Waals forces, as the interacting nanoscale forces, can be considered based on the separation distance between upper structure and substrate during deflection. Moreover, as the separation distance descends during deflection, the nanoscale forces could transform from Casimir to a proportion of both Casimir and van der Waals forces and so as to van der Waals. This is also extended to the entire surface of the nanostructure in such a way that any point of the structure may be subjected to Casimir, van der Waals or a proportion of both of them about its separation distance from the substrate. Therefore, a mathematical model is presented which calculate the incorporation of Casimir and van der Waals forces considering transition region and their own domination area. The mechanical behavior of a circular nano-plate has been investigated as a case study to illustrate how different approaches to nanoscale forces lead to different results. For this purpose, the pull-in phenomena and frequency response in terms of magnitude have been studied based on Eringen nonlocal elasticity theory. The results are presented using different values of the nonlocal parameter and indicated in comparison with those of the classical theory. These results also amplify the idea of studying the mechanical behavior of nanostructures using the nonlocal elasticity theory.     

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.     

Casimir force measurement using dynamic holography

The first holographic measurements are reported of the force between macroscopic objects mediated by zero-point electromagnetic fluctuations (Casimir force). A holographic interferometer is used to measure mirror oscillations with an amplitude of 1 pm. The objects under study are two thin metal films deposited on dielectric substrates. When one film is periodically oscillated, the first and second harmonics of the Casimir force acting on the other are detected. For the first time, an order-of-magnitude estimate is obtained for the Casimir force by using radiation pressure as a natural reference scale. The discrepancy between calculated and measured values of the Casimir force may be attributed to the small thickness and low conductivity of the metal films.     

Influence of surface electronic structure on the Casimir force

Recent nonlocal microscopic theory of Casimir force which expresses the interaction energy between two metallic slabs in terms of surface polariton propagators calculated from diamagnetic and paramagnetic current-current response functions, sensitive to details of the surface electron density profiles and single-particle excitations on the surfaces, is used here to calculate various contributions to the Casimir energies for a silver film described by two different models. Current-current response functions are constructed from energy levels and wave functions obtained in two different models: jellium and Chulkov one-dimensional model potential, and the results are compared with the local plasmon model results. The results show how the details of such surface electronic structure modify Casimir force.     

Casimir effect confronts cosmological constant

It has been speculated that the zero-point energy of the vacuum, regularized due to the existence of a suitable ultraviolet cut-off scale, could be the source of the non-vanishing cosmological constant that is driving the present acceleration of the universe. We show that the presence of such a cut-off can significantly alter the results for the Casimir force between parallel conducting plates and even lead to repulsive Casimir force when the plate separation is smaller than the cut-off scale length. Using the current experimental data we rule out the possibility that the observed cosmological constant arises from the zero-point energy which is made finite by a suitable cut-off. Any such cut-off which is consistent with the observed Casimir effect will lead to an energy density which is at least about 10¹² times larger than the observed one, if gravity couples to these modes. The implications are discussed.     

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.     

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.     

Casimir force in dense confined electrolytes

ABSTRACT

Understanding the force between charged surfaces immersed in an electrolyte solution is a classic problem in soft matter and liquid-state theory. Recent experiments showed that the force decays exponentially but the characteristic decay length in a concentrated electrolyte is significantly larger than what liquid-state theories predict based on analysing correlation functions in the bulk electrolyte. Inspired by the classical Casimir effect, we consider an additional mechanism for force generation, namely the confinement of density fluctuations in the electrolyte by the walls. We show analytically within the random phase approximation, which assumes the ions to be point charges, that this fluctuation-induced force is attractive and also decays exponentially, albeit with a decay length that is half of the bulk correlation length. These predictions change dramatically when excluded volume effects are accounted for within the mean spherical approximation. At high ion concentrations the Casimir force is found to be exponentially damped oscillatory as a function of the distance between the confining surfaces. Our analysis does not resolve the riddle of the anomalously long screening length observed in experiments, but suggests that the Casimir force due to mode restriction in density fluctuations could be an hitherto under-appreciated source of surface–surface interaction.     

Casimir力、Hamaker力及黏附“突跳”研究

针对微观黏附中出现的"突跳"问题,建立了正弦分布粗糙面黏附模型;基于Casimir效应推导出Casimir力表达式;基于Wigner-Seitz微观理论,推导出包含斥力项的Hamaker力表达式;经过对黏附过程数值仿真,发现存在两个"突跳"过程,曲线存在两个拐点,而非目前研究所得的单个"突跳"过程;仿真结果同相关实验对比,结果符合较好.从而为微纳器件检测和原子分子操纵等提供理论基础.     

Vacuum Boundary Effects

The Casimir effect is highly dependent on the shape and structure of space boundaries. This dependence is encoded in the variation of vacuum energy with the different types of boundary conditions. We analyze from a global perspective the properties of the Casimir energy as a function on the largest space of the consistent boundary conditions M_F\mathcal{M}_{F} for a massless scalar field confined between to homogeneous parallel plates. In particular, we analyze the analytic properties of this function and point out the existence of a third order phase transition at periodic boundary conditions. We also characterize the boundary conditions which give rise to attractive or repulsive Casimir forces. In the interface between both regimes we find a very interesting family of boundary conditions without Casimir effect, and fully characterize the boundary conditions which do not induce any type of Casimir force.     

Towards measuring variations of Casimir energy by a superconducting cavity

We consider a Casimir cavity, one plate of which is a thin superconducting film. We show that when the cavity is cooled below the critical temperature for the onset of superconductivity, the sharp variation (in the far infrared) of the reflection coefficient of the film engenders a variation in the value of the Casimir energy. Even though the relative variation in the Casimir energy is very small, its magnitude can be comparable to the condensation energy of the superconducting film, and this gives rise to a number of testable effects, including a significant increase in the value of the critical magnetic field, required to destroy the superconductivity of the film. The theoretical ground is therefore prepared for the first experiment ever aimed at measuring variations of the Casimir energy itself.     

Three-dimensional Casimir piston for massive scalar fields

We consider Casimir force acting on a three-dimensional rectangular piston due to a massive scalar field subject to periodic, Dirichlet and Neumann boundary conditions. Exponential cut-off method is used to derive the Casimir energy. It is shown that the divergent terms do not contribute to the Casimir force acting on the piston, thus render a finite well-defined Casimir force acting on the piston. Explicit expressions for the total Casimir force acting on the piston is derived, which show that the Casimir force is always attractive for all the different boundary conditions considered. As a function of a - the distance from the piston to the opposite wall, it is found that the magnitude of the Casimir force behaves like 1/a⁴ when a→0⁺ and decays exponentially when a→∞. Moreover, the magnitude of the Casimir force is always a decreasing function of a. On the other hand, passing from massless to massive, we find that the effect of the mass is insignificant when a is small, but the magnitude of the force is decreased for large a in the massive case.