An improved proximity force approximation for electrostatics

A quite straightforward approximation for the electrostatic interaction between two perfectly conducting surfaces suggests itself when the distance between them is much smaller than the characteristic lengths associated with their shapes. Indeed, in the so called “proximity force approximation” the electrostatic force is evaluated by first dividing each surface into a set of small flat patches, and then adding up the forces due two opposite pairs, the contributions of which are approximated as due to pairs of parallel planes. This approximation has been widely and successfully applied in different contexts, ranging from nuclear physics to Casimir effect calculations. We present here an improvement on this approximation, based on a derivative expansion for the electrostatic energy contained between the surfaces. The results obtained could be useful for discussing the geometric dependence of the electrostatic force, and also as a convenient benchmark for numerical analyses of the tip–sample electrostatic interaction in atomic force microscopes.     

Surface roughness influence on the pull-in voltage of microswitches in presence of thermal and quantum vacuum fluctuations

In this work we investigate the influence of the combined effect from random self-affine roughness, finite conductivity, and finite temperature on the pull-in voltage in microswitches influenced by thermal and quantum vacuum fluctuations through the Casimir force and electrostatic forces. It is shown that for separations within the micron or sub-micron range the roughness influence plays a dominant role, while temperature starts to show its influence well above micron separations. Indeed, increasing the temperature leads to higher pull-in voltages since it leads to an increased Casimir force. The temperature influence is more significant for relatively large roughness exponent H ∼ 1, while its influence is significantly lower with increasing lateral roughness correlation length ξ or due to long wavelength surface smoothness.     

Casimir and Surface Tension Forces on a Single Interacting Bose–Einstein Condensate in Canonical Ensemble

The forces on a single Bose–Einstein condensate confined between two parallel plates consist of two components, namely, surface tension force and Casimir force. In canonical ensemble, these forces are quite different from the one in grand canonical ensemble. In small region with distance $$\ell $$ between two parallel plates, using double parabola approximation, we find that surface tension force decreases as $${{\ell }^{{ - 3}}}$$, whereas the Casimir force, in one-loop approximation of the quantum field, is proportional to $${{\ell }^{{ - 13/2}}}$$. The total force is also considered and its veer is found.     

An improved model for the cantilever NEMS actuator including the surface energy,fringing field and Casimir effects

The influence of the surface energy on the instability of nano-structures under the electrostatic force has been investigated in recent years by different researchers. It appears that in all prior research, the response of all structures becomes softer due to the surface effects. In the present study, the pull-in instability of a NEMS device incorporating the electrostatic force and Casimir intermolecular attraction for different values of the surface parameter is investigated by the Duan–Rach method of determined coefficients (MDC) in order to identify the remarkable effect of the surface energy. Although the obtained results verify the behavior of such structures in presence of the fringing field and the Casimir attraction same as the previous investigations, however the incremental effects of the surface energy cause the aforementioned structures to behave more stiffly in contrast.     

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.     

Repulsive Casimir forces

We discuss repulsive Casimir forces between dielectric materials with nontrivial magnetic susceptibility. It is shown that considerations based on the naive pairwise summation of van der Waals and Casimir-Polder forces may not only give an incorrect estimate of the magnitude of the total Casimir force but even the wrong sign of the force when materials with high dielectric and magnetic responses are involved. Indeed repulsive Casimir forces may be found in a large range of parameters, and we suggest that the effect may be realized in known materials. The phenomenon of repulsive Casimir forces may be of importance both for experimental study and for nanomachinery applications.     

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.     

New experimental limits on non-Newtonian forces in the micrometer range

We report measurements of the short-range forces between two macroscopic gold-coated plates using a torsion pendulum. The force is measured for separations between 0.7 and 7 μm and is well described by a combination of the Casimir force, including the finite-temperature correction, and an electrostatic force due to patch potentials on the plate surfaces. We use our data to place constraints on the Yukawa-type "new" forces predicted by theories with extra dimensions. We establish a new best bound for force ranges 0.4-4 μm and, for forces mediated by gauge bosons propagating in (4+n) dimensions and coupling to the baryon number, extract a (4+n)-dimensional Planck scale lower limit of M(*)>70 TeV.     

Casimir-Lifshitz theory and metamaterials

Based on a generalization of the Lifshiftz theory, we calculate Casimir forces involving magnetodielectric and possibly anisotropic metamaterials, focusing on the possibility of repulsive forces. It is found that Casimir repulsion decreases with magnetic dissipation, and even a small Drude background in metallic-based metamaterials acts to make attractive a Casimir force that would otherwise be predicted to be repulsive. The sign of the force also depends sensitively on the degree of optical anisotropy of the metamaterial and on the form of the frequency dependency of the magnetic response.     

Casimir Force at a Finite Cut-Off

We calculate the Casimir force at a finite cut-off Λ by summing the forces induced by the all fluctuation modes. We show that the Casimir force is independent of the cut-off function in the limit LΛ → ∞. There is a correction in the order of (LΛ)^-2, when LΛ is finite and large. This correction becomes remarkable when L is comparable with the microscopic length scale Λ^-1. It has been demonstrated that the Casimir force at a finite cut-off should be defined by summing forces of all fluctuation modes, instead of the derivative of Casimir energy with respect to L where an additional derivative of the cut-off function has been introduced.     

Surface plasmon modes and the Casimir energy

We show the influence of surface plasmons on the Casimir effect between two plane parallel metallic mirrors at arbitrary distances. Using the plasma model to describe the optical response of the metal, we express the Casimir energy as a sum of contributions associated with evanescent surface plasmon modes and propagative cavity modes. In contrast to naive expectations, the plasmonic mode contribution is essential at all distances in order to ensure the correct result for the Casimir energy. One of the two plasmonic modes gives rise to a repulsive contribution, balancing out the attractive contributions from propagating cavity modes, while both contributions taken separately are much larger than the actual value of the Casimir energy. This also suggests possibilities to tailor the sign of the Casimir force via surface plasmons.     

卡西米尔力

量子电动力学中的卡西米尔力是真空零点能的体现.广义的卡西米尔力则依赖于涨落介质的类型广泛地出现于物理中,包括量子,临界,戈德斯通模,以及非平衡卡西米尔力.长程关联的涨落介质和约束是产生卡西米尔力的两个条件.本文通过回顾卡西米尔物理的发展,讨论了不同类型的卡西米尔力,几种正规化方法,并对卡西米尔物理的进一步发展做了展望.     

Casimir forces, surface fluctuations, and thinning of superfluid film

Recent experiments on the wetting of 4He have shown that the film becomes thinner at the lambda transition and in the superfluid phase. The difference in thickness above and below the transition has been attributed to a Casimir interaction which is a consequence of a broken continuous symmetry in the bulk superfluid. However, the observed thinning of the film is larger than can be accounted by this Casimir force. We show that surface fluctuations give rise to an additional force, similar in form but larger in magnitude, which may explain the observations.     

On the importance of sp-electrons in the surface relaxation of d-band metals

We present arguments to the effect that the self-consistent smoothing of the mobile sp-electron distribution gives rise to electrostatic forces which are a major contribution to the initial relaxing forces on the outermost ions at a d-band metal surface. Numerical estimates for the (001) face of α-Fe are given, showing that for the surface ions the surface Madelung force from the sp-electrons is inward and about $\text{3}\text{1}\text{2}$ times stronger than an outward short-range force simulating the effect of d-electrons.     

External forces outside of a layered electron gas

We calculate the external forces outside of the surface of a layered electron gas (LEG). The LEG is a model of a metal where the electrical current is carried in parallel layers, and there is no current between layers. It describes the high-temperature cuprate superconductors and many other layered solids. We calculate the image potential from an external charge, the van der Waals potential from a neutral atom and the Casimir force between the parallel surfaces of two LEGs. Our theory does not use dielectric functions. We write down the quantum mechanical Hamiltonian, calculate the exact ground state energy and deduce the forces from the energy. We also show that the LEG has no surface plasmon.     

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.     

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.     

On the Relation Between Casimir Forces and Bulk Correlations

Within a microscopic approach we show that in the case of an ideal quantum gas enclosed in a slit the Casimir force can be simply expressed in terms of the bulk one-particle density matrix. The corresponding formula, which holds both for bosons and fermions, allows to relate the range of the Casimir force to the bulk correlation length. The low-temperature behavior of the Casimir forces is derived.     

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.     

Edge effects in electrostatic calibrations for the measurement of the Casimir force

We have performed numerical simulations to evaluate the effect on the capacitance of finite size boundaries realistically present in the parallel plane, sphere-plane, and cylinder-plane geometries. The potential impact of edge effects in assessing the accuracy of the parameters obtained in the electrostatic calibrations of Casimir force experiments is then discussed.