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.     

Oscillating Casimir Effect of a Trapped Fermi Gas

We study the Casimir effect for two parallel slabs immersed in a harmonically trapped Fermi gas. The Casimir force and its distribution on the slabs are calculated. It is found that the Casimir force oscillates with the separation L _z of the slabs and can be either attractive or repulsive, depending sensitively on the size of L _z . It is also found that the size and sign of the Casimir pressure (i.e., the Casimir force on the unit area) oscillates with the variation of the distance r away from the center of the harmonic potential and its amplitude decreases with the increase of r.     

Oscillating Casimir force between two slabs in a Fermi sea

The Casimir effect for two parallel slabs immersed in an ideal Fermi sea is investigated at both zero and nonzero temperatures. It is found that the Casimir effect in a Fermi gas is distinctly different from that in an electromagnetic field or a massive Bose gas. In contrast to the familiar result that the Casimir force decreases monotonically with the increase of the separation L between two slabs in an electromagnetic field and a massive Bose gas, the Casimir force in a Fermi gas oscillates as a function of L. The Casimir force can be either attractive or repulsive, depending sensitively on the magnitude of L. In addition, it is found that the amplitude of the Casimir force in a Fermi gas decreases with the increase of the temperature, which also is contrary to the case in a Bose gas, since the bosonic Casimir force increases linearly with the increase of the temperature in the region T < T_c, where T_c is the critical temperature of the Bose-Einstein condensation.     

Attractive and repulsive Casimir vacuum energy with general boundary conditions

The infrared behaviour 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 attractive or repulsive Casimir forces between the plates. In the interface between both regimes we find a very interesting family of boundary conditions which do not induce any type of Casimir force. We also show that the attractive regime holds far beyond identical boundary conditions for the two plates required by the Kenneth–Klich theorem and that the strongest attractive Casimir force appears for periodic boundary conditions whereas the strongest repulsive Casimir force corresponds to anti-periodic boundary conditions. Most of the analysed boundary conditions are new and some of them can be physically implemented with metamaterials.     

负折射率材料对产生Casimir排斥力的影响

研究了负折射率材料对产生Casimir排斥效应的影响. 两材料板间的Casimir排斥力的发生取决于两板以及其间媒质的电磁特性,通过理论与数值结果的分析研究给出电磁特性所影响排斥力的产生趋势. 对于由Drude-Lorentz型色散关系描述等效介电常数和磁导率的负折射率材料,调节各特征频率参数可实现Casimir排斥效应. 关键词： Casimir排斥力 负折射率材料 Drude-Lorentz型色散关系     

Casimir Force of Piston Systems with Arbitrary Cross Sections under Different Boundary Conditions

We study the Casimir force between two pistons under different boundary conditions inside an infinite cylinder with arbitrary cross section. It is found that the attractive or repulsive character of the Casimir force for a scalar field is determined only by the boundary condition along the longitudinal direction and is independent of the cross section, transverse boundary conditions and the mass of the field. Under symmetric Dirichlet-Dirichlet, Neumann-Neumann and periodic longitudinal boundary conditions the Casimir force is always attractive, but is repulsive under non-symmetric Dirichlet-Neumann and anti-periodic longitudinal boundary conditions. The Casimir force of the electromagnetic field in an ideal conductive piston is also investigated. This force is always attractive regardless of the shape of the cross section and the transverse boundary conditions.     

Chiral Anomaly-Enhanced Casimir Interaction between Weyl Semimetals

We theoretically study the Casimir interaction between Weyl semimetals.When the distance a between semiinfinite Weyl semimetals is in the micrometer regime,the Casimir attraction can be enhanced by the chiral anomaly.The Casimir attraction depends sensitively on the relative orientations between the separations(b_1,b_2)of Weyl nodes in the Brillouin zone and show anisotropic behavior for the relative orientation of these separations(b_1,b_2) when they orient parallel to the interface.This anisotropy is quite larger than that in conventional birefringent materials.The Casimir force can be repulsive in the micrometer regime if the Weyl semimetal slabs are sufficiently thin and the direction of Weyl nodes separations(b_1,b_2) is perpendicular to the interface.The Casimir attraction between Weyl semimetal slabs decays slower than 1/a4 when the Weyl nodes separations b_1 and b_2 are both parallel to the interface.     

Pressure of the fluctuating vacuum: Interpretation of the attractive and repulsive Casimir force

We calculate the Casimir force between two magnetodielectric slabs. The force expression is expressed in terms of parameters with which the repulsive effect is more transparent and convenient for numerical analysis. Finally, we propose a physical interpretation of the effect which clarifies the sign of force properly.     

Bose-Einstein condensation and Casimir effect of trapped ideal Bose gas in between two slabs

We study the Bose-Einstein condensation for a 3-d system of ideal Bose gas which is harmonically trapped along two perpendicular directions and is confined in between two slabs along the other perpendicular direction. We calculate the Casimir force between the two slabs for this system of trapped Bose gas. At finite temperatures this force for thermalized photons in between two plates has a classical expression which is independent of ħ. At finite temperatures the Casimir force for our system depends on ħ. For the calculation of Casimir force we consider only the Dirichlet boundary condition. We show that below condensation temperature (T_c) the Casimir force for this non-interacting system decreases with temperature (T) and at , it is independent of temperature. We also discuss the Casimir effect on 3-d highly anisotropic harmonically trapped ideal Bose gas.     

Infinite slabs and other weird plane symmetric space–times with constant positive density

We present the exact solution of Einstein’s equation corresponding to a static and plane symmetric distribution of matter with constant positive density located below z = 0. This solution depends essentially on two constants: the density ρ and a parameter κ. We show that these space–times finish down below at an inner singularity at finite depth. We show that for κ ≥ 0.3513 . . . the dominant energy condition is satisfied all over the space–time. We match this solution to the vacuum one and compute the external gravitational field in terms of slab’s parameters. Depending on the value of κ, these slabs can be attractive, repulsive or neutral. In the first case, the space–time also finishes up above at an empty repelling singular boundary. In the other cases, they turn out to be semi-infinite and asymptotically flat when z → ∞. We also find solutions consisting of joining an attractive slab and a repulsive one, and two neutral ones. We also discuss how to assemble a “gravitational capacitor” by inserting a slice of vacuum between two such slabs.     

Tunable Casimir repulsion with three-dimensional topological insulators

In this Letter, we show that switching between repulsive and attractive Casimir forces by means of external tunable parameters could be realized with two topological insulator plates. We find two regimes where a repulsive (attractive) force is found at small (large) distances between the plates, canceling out at a critical distance. For a frequency range where the effective electromagnetic action is valid, this distance appears at length scales corresponding to 1 - ?(ω) ～ (2/π)αθ.     

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.     

Opposites attract: a theorem about the Casimir Force

We consider the Casimir interaction between (nonmagnetic) dielectric bodies or conductors. Our main result is a proof that the Casimir force between two bodies related by reflection is always attractive, independent of the exact form of the bodies or dielectric properties. Apart from being a fundamental property of fields, the theorem and its corollaries also rule out a class of suggestions to obtain repulsive forces, such as the two hemisphere repulsion suggestion and its relatives.     

The grounds for time dependent market potentials from dealers’ dynamics

We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers’ feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market’s potential force. When markets are dominated by dealers with positive feedback the resulting potential force is repulsive, while the effect of negative feedback enhances the attractive potential force.     

Repulsive and attractive critical Casimir forces

When confining vacuum fluctuations between two identical walls, the Casimir force manifests itself as a mutual attraction of the walls. When confining concentration fluctuations of a binary liquid mixture, an analogous force should exist near the critical temperature T_C; it is called the critical Casimir force. Here we show experimentally that this purely entropic force can be either attractive or repulsive, depending on the boundary conditions for the fluctuations. For symmetrical boundary conditions an attractive force is found while asymmetrical ones lead to a repulsive force. This is observed directly by confining the fluctuations in a thin wetting film. Depending on the boundary conditions either a thinning or a thickening of the film is observed when T→T_C.     

Attractive Casimir forces in a closed geometry

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.     

The asymptotic behavior of Casimir force in the presence of compactified universal extra dimensions

The Casimir effect for parallel plates in the presence of compactified universal extra dimensions within the frame of Kaluza–Klein theory is analyzed. Having regularized and discussed the expressions of Casimir force in the limit, we show that the nature of Casimir force is repulsive if the distance between the plates is large enough and the higher-dimensional spacetime is, the greater the value of repulsive Casimir force between plates is. The repulsive nature of the force is not consistent with the experimental phenomena.     

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.     

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.     

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.