We study the Casimir force in piston-like geometries semiclassically. The force on the piston is finite and physical, but to leading semiclassical approximation depends strongly on the shape of the surrounding cavity. Whereas this force is attractive for pistons in a parallelepiped with flat cylinder head, for which the semiclassical approximation by periodic orbits is exact, this approximation to the force on the piston vanishes for a semi-cylindrical head and becomes repulsive for a cylinder of circular cross section with a hemispherical head. In leading semiclassical approximation the sign of the force is related to the generalized Maslov index of short periodic orbits between the piston and its casing.
This manuscript has been withdrawn, since the authors have detected numerical inaccuracies that invalidate their main results concerning the existence of repulsive Casimir forces within a rectangular piston. Formulas presented in the manuscript keep still valid. The authors deeply apologize for this mistake.
Recently, a method based on stochastic quantization has been proposed to compute the Casimir force and its fluctuations in arbitrary geometries. It relies on the spectral decomposition of the Laplacian operator in the given geometry. Both quantum and thermal fluctuations are considered. Here we use such method to compute the Casimir force on the plates of a finite piston of arbitrary cross section. Asymptotic expressions valid at low and high temperatures and short and long distances are obtained. The case of a piston with triangular cross section is analysed in detail. The regularization of t…
We consider a massless scalar field obeying Dirichlet boundary conditions on the walls of a two-dimensional L x b rectangular box, divided by a movable partition (piston) into two compartments of dimensions a x b and (L-a) x b. We compute the Casimir force on the piston in the limit L -> infinity. Regardless of the value of a/b, the piston is attracted to the nearest end of the box. Asymptotic expressions for the Casimir force on the piston are derived for a << b and a >> b.
We have computed numerically the Casimir force between two identical pistons inside a very long cylinder, considering different shapes for the pistons. The pistons can be considered as quantum billiards, whose spectrum determines the vacuum force. The smooth part of the spectrum fixes the force at short distances, and depends only on geometric quantities like the area or perimeter of the piston. However, correcting terms to the force, coming from the oscillating part of the spectrum which is related to the classical dynamics of the billiard, are qualitatively different for classically integrab…
Casimir pistons are models in which finite Casimir forces can be calculated without any suspect renormalizations. It has been suggested that such forces are always attractive. We present three scenarios in which that is not true. Two of these depend on mixing two types of boundary conditions. The other, however, is a simple type of quantum graph in which the sign of the force depends upon the number of edges.
We study the Casimir piston for massless scalar fields obeying Dirichlet boundary conditions in a three dimensional cavity with sides of arbitrary lengths $a,b$ and $c$ where $a$ is the plate separation. We obtain an exact expression for the Casimir force on the piston valid for any values of the three lengths. As in the electromagnetic case with perfect conductor conditions, we find that the Casimir force is negative (attractive) regardless of the values of $a$, $b$ and $c$. Though cases exist where the interior contributes a positive (repulsive) Casimir force, the total Casimir force on the …
The Casimir force due to a scalar field on a piston in a cylinder of radius $r$ with a spherical cap of radius $R>r$ is computed numerically in the world-line approach. A geometrical subtraction scheme gives the finite interaction energy that determines the Casimir force. The spectral function of convex domains is obtained from a probability measure on convex surfaces that is induced by the Wiener measure on Brownian bridges the convex surfaces are the hulls of. The vacuum force on the piston by a scalar field satisfying Dirichlet boundary conditions is attractive in these geometries, but the …
In this work we study the Casimir effect for massless scalar fields propagating in a piston geometry of the type $I\times N$ where $I$ is an interval of the real line and $N$ is a smooth compact Riemannian manifold. Our analysis represents a generalization of previous results obtained for pistons configurations as we consider all possible boundary conditions that are allowed to be imposed on the scalar fields. We employ the spectral zeta function formalism in the framework of scattering theory in order to obtain an expression for the Casimir energy and the corresponding Casimir force on the pi…
Using a multidimensional cut-off technique, we obtain expressions for the cut-off dependent part of the vacuum energy for parallelepiped geometries in any spatial dimension d. The cut-off part yields nonrenormalizable hypersurface divergences and we show explicitly that they cancel in the Casimir piston scenario in all dimensions. We obtain two different expressions for the d-dimensional Casimir force on the piston where one expression is more convenient to use when the plate separation a is large and the other when a is small (a useful $a \to 1/a$ duality). The Casimir force on the piston is …
In this paper we show how the stochastic quantization method developed by Parisi and Wu can be used to obtain Casimir forces. Both quantum and thermal fluctuations are taken into account by a Langevin equation for the field. The method allows the Casimir force to be obtained directly, derived from the stress tensor instead of the free energy. It only requires the spectral decomposition of the Laplacian operator in the given geometry. The formalism provides also an expression for the fluctuations of the force. As an application we compute the Casimir force on the plates of a finite piston of ar…
A piston is introduced into a spherical lune Casimir cavity turning it into two adjacent lunes separated by the (hemispherical) piston. On the basis of zeta function regularisation, the vacuum energy of the arrangement is finite for conformal propagation in space-time. For even spheres this energy is independent of the angle of the lune. For odd dimensions it is shown that for all Neumann, or all Dirichlet, boundary conditions the piston is attracted or repelled by the nearest wall if d=3,7,... or if d=1,5,..., respectively. For hybrid N-D conditions these requirements are switched. If a mass …
Perfect magnetic conductor (PMC) boundary conditions are dual to the more familiar perfect electric conductor (PEC) conditions and can be viewed as the electromagnetic analog of the boundary conditions in the bag model for hadrons in QCD. Recent advances and requirements in communication technologies have attracted great interest in PMC's and Casimir experiments involving structures that approximate PMC's may be carried out in the not too distant future. In this paper, we make a study of the zero-temperature PMC Casimir piston in $d+1$ dimensions. The PMC Casimir energy is explicitly evaluated…
We consider the ground state energy of the electromagnetic field in a piston geometry. In the idealised case, where the piston and the walls of the chamber are taken as perfect mirrors, the Casimir pressure on the piston is finite and independent of the small scale physics of the media that compose the mirrors; the Casimir-energy of the system can be regularised and is cutoff-independent. Yet we find that, when the body of the piston is filled with an inhomogeneous dielectric medium, the Casimir energy is cutoff-dependent, and the value of the pressure is thus inextricably dependent on the det…
We study Casimir forces on the partition in a closed box (piston) with perfect metallic boundary conditions. Related closed geometries have generated interest as candidates for a repulsive force. By using an optical path expansion we solve exactly the case of a piston with a rectangular cross section, and find that the force always attracts the partition to the nearest base. For arbitrary cross sections, we can use an expansion for the density of states to compute the force in the limit of small height to width ratios. The corrections to the force between parallel plates are found to have inte…
We evaluate the Casimir energy and force for a massive scalar field with general curvature coupling parameter, subject to Robin boundary conditions on two codimension-one parallel plates, located on a $(D+1)$-dimensional background spacetime with an arbitrary internal space. The most general case of different Robin coefficients on the two separate plates is considered. With independence of the geometry of the internal space, the Casimir forces are seen to be attractive for special cases of Dirichlet or Neumann boundary conditions on both plates and repulsive for Dirichlet boundary conditions o…
We consider the Casimir energy due to a massless scalar field in a geometry of an infinite wedge closed by a Dirichlet circular cylinder, where the wedge is formed by $δ$-function potentials, so-called semitransparent boundaries. A finite expression for the Casimir energy corresponding to the arc and the presence of both semitransparent potentials is obtained, from which the torque on the sidewalls can be derived. The most interesting part of the calculation is the nontrivial nature of the angular mode functions. Numerical results are obtained which are closely analogous to those recently foun…
Weyl semimetals are a class of topological materials that exhibit a bulk Hall effect due to time-reversal symmetry breaking. We show that for the idealized semi-infinite case, the Casimir force between two identical Weyl semimetals is repulsive at short range and attractive at long range. Considering plates of finite thickness, we can reduce the size of the long-range attraction even making it repulsive for all distances when thin enough. In the thin-film limit, we study the appearance of an attractive Casimir force at shorter distances due to the longitudinal conductivity. Magnetic field, thi…
We review various applications of the multiple scattering approach to the calculation of Casimir forces between separate bodies, including dispersion, wedge geometries, annular pistons, and temperature dependence. Exact results are obtained in many cases.
We theoretically predict that the Casimir force in vacuum between two Chern insulator plates can be repulsive (attractive) at long distances whenever the sign of the Chern numbers characterizing the two plates are opposite (equal). A unique feature of this system is that the sign of the force can be tuned simply by turning over one of the plates or alternatively by electrostatic doping. We calculate and take into account the full optical response of the plates and argue that such repulsion is a general phenomena for these systems as it relies on the quantized zero frequency Hall conductivity. …
The Casimir force due to a massless scalar field satisfying Dirichlet boundary conditions may attract or repel a piston in the neck of a flask-like container. Using the world-line formalism this behavior is related to the competing contribution to the interaction energy of two types of Brownian bridges. It qualitatively is also expected from attractive long-range two-body forces between constituents of the boundary. A geometric subtraction scheme is presented that avoids divergent contributions to the interaction energy and classifies the Brownian bridges that contribute to the force. These ar…
The Casimir force for charge-neutral, perfect conductors of non-planar geometric configurations have been investigated. The configurations are: (1) the plate-hemisphere, (2) the hemisphere-hemisphere and (3) the spherical shell. The resulting Casimir forces for these physical arrangements have been found to be attractive. The repulsive Casimir force found by Boyer for a spherical shell is a special case requiring stringent material property of the sphere, as well as the specific boundary conditions for the wave modes inside and outside of the sphere. The necessary criteria in detecting Boyer's…
We derive upper and lower bounds on the Casimir--Polder force between an anisotropic dipolar body and a macroscopic body separated by vacuum via algebraic properties of Maxwell's equations. These bounds require only a coarse characterization of the system---the material composition of the macroscopic object, the polarizability of the dipole, and any convenient partition between the two objects---to encompass all structuring possibilities. We find that the attractive Casimir--Polder force between a polarizable dipole and a uniform planar semi-infinite bulk medium always comes within 10% of the …
Recent experimental realizations of uniform confining potentials for ultracold atoms make it possible to create quantum acoustic resonators and explore nonequilibrium dynamics of quantum field theories. These systems offer a promising new platform for studying the dynamical Casimir effect, since they allow to achieve relativistic, i.e. near sonic, velocities of the boundaries. In comparison to previously studied optical and classical hydrodynamic systems ultracold atoms allow to realize a broader class of dynamical experiments combining both classical driving and vacuum squeezing. In this pape…
We investigate repulsive Casimir force between slabs containing left-handed materials with controllable electromagnetic properties. The sign of Casimir force is determined by the electric and magnetic properties of the materials, and it is shown that the formation of the repulsive force is related to the wave impedances of two slabs. The sign change of the Casimir force as a function of the distance is studied. Special emphasis is put on the restoring Casimir force which may be found to exist between perfectly conducting material and metamaterial slabs. This restoring force is a natural power …
A recent theoretical calculation shows that the Casimir force between two parallel plates can be repulsive for plates with nontrivial magnetic properties (O. Kenneth et al., Phys. Rev. Lett. 89, 033001 (2002)). According to the authors, the effect may be observed with known materials, such as ferrites and garnets, and it might be possible to engineer micro- or nanoelectromechanical systems (MEMS or NEMS) that could take advantage of a short range repulsive force. Here we show that on the contrary the Casimir force between two parallel plates in vacuum at micron and submicron distance is always…
We discuss the Casimir effect for boundary conditions involving perfect electromagnetic conductors (PEMCs). Based on the corresponding reciprocal Green's tensor we construct the Green's tensor for two perfectly reflecting plates with magnetoelectric coupling (non-reciprocal media) within the framework of macroscopic quantum electrodynamics. We calculate the Casimir force between two PEMC plates in terms of the PEMC parameter M and the duality transformation angle $θ$ resulting in a universal analytic expression that connects the attractive Casimir force with the repulsive Boyer force. We relat…
We study the Casimir force between a perfectly conducting and an infinitely permeable plate with the radiation pressure approach. This method illustrates how a repulsive force arises as a consequence of the redistribution of the vacuum-field modes corresponding to specific boundary conditions. We discuss also how the method of the zero-point radiation pressure follows from QED.
Like Casimir's original force between conducting plates in vacuum, Casimir forces are usually attractive. But repulsive Casimir forces can be achieved in special circumstances. These might prove useful in nanotechnology. We give examples of when repulsive quantum vacuum forces can arise with conducting materials.
In 1948 H.B.G.Casimir predicted that an attractive force between two perfectly conducting neutral plates exists due to changes in the electromagnetic vacuum energy caused by the influence of the plates. In 1956 E.M. Lifshitz derived an extension of Casimir's expression applicable to finite temperatures and arbitrary dielectric constants for the two half-spaces and the gap in between them. It is shown in this brief report that, while the Lifshitz formula predicts an attractive force for the case of identical dielectric constants for the two half-spaces, a repulsive force results in some circums…
Achieving strong repulsive Casimir forces through engineered coatings can pave the way for micro- and nano-electromechanical applications where adhesive forces currently cause reliability issues. Here, we exploit Lifshitz theory to identify the requirements for repulsive Casimir forces in gyrotropic media for two limiting cases (ultra-strong gyroelectric and non-gyroelectric). We show that the origin of repulsive force in media with strong gyrotropy such as Weyl semi-metals arises from the giant interconversion of polarization of vacuum fluctuations.
Using numerical analytic continuation, we compute the Zeta function for the Casimir Effect for circular geometries in 2+1 dimensions. After subtraction of the simple pole of the zeta function, essentially MS renormalization, we find the Casimir force is repulsive. Implications for the stability of 2+1 dimensional domain walls and Axion membranes in 3+1 dimensions are discussed, especially in the context of strongly coupled underlying physics.
We discuss repulsive Casimir forces between dielectric materials with non trivial magnetic susceptibility. It is shown that considerations based on naive pair-wise 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 response 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 ma…
Several problems at the interface between the field-theoretical description of the Casimir effect and experiments on measuring the Casimir force are discussed. One of these problems is connected with the definition of the Casimir free energy in ideal metal rectangular boxes satisfying the general physical requirements. It is shown that the consideration of rectangular boxes with a partition (piston) does not negate the previously known results obtained for boxes without a piston. Both sets of results are found to be in mutual agreement. Another problem is related to the use of the proximity fo…
We apply the generalized zeta function method to compute the Casimir energy and pressure between an unusual pair of parallel plates at finite temperature, namely: a perfectly conducting plate and an infinitely permeable one. The high and low temperature limits of these quantities are discussed; relationships between high and low temperature limits are estabkished by means of a modified version of the temperature inversion symmetry.
The physical origin of the negative thermal correction to the Casimir force between metals is clarified. For this purpose the asymptotic behavior of the thermal Casimir force is analyzed at large and small distances in the real frequency representation. Contributions from propagating and evanescent waves are considered separately. At large distances they cancel each other in substantial degree so that only the attractive Lifshitz limit survives. At smaller separations the repulsive evanescent contribution of s-polarization dominates in the case of two metals or a metal and a high-permittivity …
Our preceding paper introduced a method to compute Casimir forces in arbitrary geometries and for arbitrary materials that was based on a finite-difference time-domain (FDTD) scheme. In this manuscript, we focus on the efficient implementation of our method for geometries of practical interest and extend our previous proof-of-concept algorithm in one dimension to problems in two and three dimensions, introducing a number of new optimizations. We consider Casimir piston-like problems with nonmonotonic and monotonic force dependence on sidewall separation, both for previously solved geometries t…
Using an exact numerical method for finite nonplanar objects, we demonstrate a stable mechanical suspension of a silica cylinder within a metallic cylinder separated by ethanol, via a repulsive Casimir force between the silica and the metal. We investigate cylinders with both circular and square cross sections, and show that the latter exhibit a stable orientation as well as a stable position, via a method to compute Casimir torques for finite objects. Furthermore, the stable orientation of the square cylinder is shown to undergo an unusual 45 degrees transition as a function of the separation…
We consider the interaction pressure acting on the surface of a dielectric sphere enclosed within a magnetodielectric cavity. We determine the sign of this quantity regardless of the geometry of the cavity for systems at thermal equilibrium, extending the Dzyaloshinskii-Lifshitz-Pitaevskii result for homogeneous slabs. As in previous theorems regarding Casimir-Lifshitz forces, the result is based on the scattering formalism. In this case the proof follows from the variable phase approach of electromagnetic scattering. With this, we present configurations in which both the interaction and the s…
The experimentally demonstration of Casimir force transition from attraction to repulsion is still challenging. Herein, the Casimir forces for a sphere above a plate immersed in different liquids were precisely measured using Atomic force microscope, and the long-range repulsive Casimir force in the gold-cyclohexane-PTFE system is observed for the first time. The experimental data are consistent with the calculation by Lifshitz theory, which offers the direct evidence for the system of ε1<ε3<ε2. It further verifies the reasonability of van Zwol et al. dielectric model to describe the interveni…
In this paper the Casimir energy of two parallel plates made by materials of different penetration depth and no medium in between is derived. We study the Casimir force density and derive analytical constraints on the two penetration depths which are sufficient conditions to ensure repulsion. Compared to other methods our approach needs no specific model for dielectric or magnetic material properties and constitutes a complementary analysis.
The Casimir interactions in the solid-liquid-solid systems as a function of separation distance have been studied by the Lifshitz theory. The dielectric permittivity functions for a wide range of materials are described by Drude, Drude-Lorentz and oscillator models. We find that the Casimir forces between gold and silica or MgO materials are both the repulsive and attractive. We also find the stable forms for the systems. Our studies would provide a good guidance for the future experimental studies on the dispersion interactions.
We present two novel models for repulsive Casimir interaction between positive perturbations. One example relies on non locality of the dielectric response and one relies on interference between (attractive) modes. Such examples are impossible to achieve in 1d massless theories, as they are prohibited by a generalization of the result of Lambrecht, Jaekel and Reynaud [Phys.Lett. A 225 (1997)] to non local dielectrics and to negative perturbations
We perform a theoretical analysis of a setup intended to measure the repulsive (outward) Casimir forces predicted to exist inside of perfectly conducting rectangular cavities. We consider the roles of the conductivity of the real metals, of the temperature and surface roughness. The use of this repulsive force to reduce friction and wear in micro and nanoelectromechanical systems (MEMS and NEMS) is also considered.
The Casimir repulsion between a metal and a dielectric suspended in a liquid has been thoroughly studied in recent experiments. In the present paper we consider surface modes in three layered systems modeled by dielectric functions guaranteeing repulsion. It is shown that surface modes play a decisive role in this phenomenon at short separations. For a toy plasma model we find the contribution of the surface modes at all distances.
Casimir pistons are models in which finite Casimir forces can be calculated without any suspect renormalizations. It has been suggested that such forces are always attractive, but we present several counterexamples, notably a simple type of quantum graph in which the sign of the force depends upon the number of edges. We also show that Casimir forces in quantum graphs can be reliably computed by summing over the classical orbits, and study the rate of convergence of the periodic orbit expansion. In generic situations where no analytic expression is available, the sign and approximate magnitude…
We show how to compute Casimir forces at nonzero temperatures with time-domain electromagnetic simulations, for example using a finite-difference time-domain (FDTD) method. Compared to our previous zero-temperature time-domain method, only a small modification is required, but we explain that some care is required to properly capture the zero-frequency contribution. We validate the method against analytical and numerical frequency-domain calculations, and show a surprising high-temperature disappearance of a non-monotonic behavior previously demonstrated in a piston-like geometry.
We use the extended Lifshitz theory to study the behaviors of the Casimir forces between finite-thickness effective medium slabs. We first study the interaction between a semi-infinite Drude metal and a finite-thickness magnetic slab with or without substrate. For no substrate, the large distance $d$ dependence of the force is repulsive and goes as $1/d^5$; for the Drude metal substrate, a stable equilibrium point appears at an intermediate distance which can be tuned by the thickness of the slab. We then study the interaction between two identical chiral metamaterial slabs with and without su…
We study the influence of stationary axisymmetric spacetimes on Casimir energy. We consider a massive scalar field and analyze its dependence on the apparatus orientation with respect to the dragging direction associated with such spaces. We show that, for an apparatus orientation not considered before in the literature, the Casimir energy can change its sign, producing a repulsive force. As applications, we analyze two specific metrics: one associated with a linear motion of a cylinder and a circular equatorial motion around a gravitational source described by Kerr geometry.
Casimir and Casimir-Polder repulsion have been known for more than 50 years. The general "Lifshitz" configuration of parallel semi-infinite dielectric slabs permits repulsion if they are separated by a dielectric fluid that has a value of permittivity that is intermediate between those of the dielectric slabs. This was indirectly confirmed in the 1970s, and more directly by Capasso's group recently. It has also been known for many years that electrically and magnetically polarizable bodies can experience a repulsive quantum vacuum force. More amenable to practical application are situations wh…
We study the Casimir force acting on a conducting piston with arbitrary cross section. We find the exact solution for a rectangular cross section and the first three terms in the asymptotic expansion for small height to width ratio when the cross section is arbitrary. Though weakened by the presence of the walls, the Casimir force turns out to be always attractive. Claims of repulsive Casimir forces for related configurations, like the cube, are invalidated by cutoff dependence.
We study the Casimir-Polder potential of a multilevel alkali-metal atom near an optical nanofiber. We calculate the mean potential of the atom in a fine-structure level. We perform numerical calculations for the Casimir-Polder potentials of the ground state and a few low-lying excited states of a rubidium atom. We show that, unlike the potential of the ground state, which is negative and attractive, the potential of a low-lying excited state may take positive values, oscillate around the zero value with a decaying amplitude, and become repulsive in some regions of atom-to-surface distances. We…
The infrared behavior of quantum field theories confined in bounded domains is strongly dependent on the shape and structure of space boundaries. The most significant physical effect arises in the behaviour of the vacuum energy. The Casimir energy can be attractive or repulsive depending on the nature of the boundary. We calculate the vacuum energy for a massless scalar field confined between two homogeneous parallel plates with the most general type of boundary conditions depending on four parameters. The analysis provides a powerful method to identify which boundary conditions generate attra…
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.
We investigate the Casimir-Polder force acting on a polarizable microparticle in the geometry of a straight cosmic string. In order to develop this analysis we evaluate the electromagnetic field Green tensor on the imaginary frequency axis. The expression for the Casimir-Polder force is derived in the general case of anisotropic polarizability. In dependence of the eigenvalues for the polarizability tensor and of the orientation of its principal axes, the Casimir-Polder force can be either repulsive or attractive. Moreover, there are situations where the force changes the sign with separation.…
We critically review the possibilities of a repulsive Casimir interaction between materials which carry Chern-Simons surface actions for the electromagnetic field.
We study the Casimir effect in axion electrodynamics. A finite $θ$-term affects the energy dispersion relation of photon if $θ$ is time and/or space dependent. We focus on a special case with linearly inhomogeneous $θ$ along the $z$-axis. Then we demonstrate that the Casimir force between two parallel plates perpendicular to the $z$-axis can be either attractive or repulsive, dependent on the gradient of $θ$. We call this repulsive component in the Casimir force induced by inhomogeneous $θ$ the anomalous Casimir effect.
We consider the interaction between a ZnO nanorod and a SiO2 nanorod in bromobenzene. Using optical data for the interacting objects and ambient we calculate the force - from short-range attractive van der Waals force to intermediate range repulsive Casimir-Lifshitz force to long range entropically driven attraction. The nonretarded van der Waals interaction is attractive at all separations. We demonstrate a retardation driven repulsion at intermediate separations. At short separations (in the nonretarded limit) and at large separations (in the classical limit) the interaction is attractive. T…
