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.     

Variations of Casimir energy from a superconducting transition

We consider a five-layer Casimir cavity, including 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 microwave region) of the reflection coefficient of the film produces 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 thus causes a significant increase in the value of the critical magnetic field, required to destroy the superconductivity of the film. The proposed scheme might also help clarifying the current controversy about the magnitude of the contribution to Casimir free energy from the TE zero mode, as we find that alternative treatments of this mode strongly affect the shift of critical field.     

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.     

Detection of casimir photons with electrons

We propose a method for the detection of a dynamical Casimir effect. Assuming that the Casimir photons are being generated in an electromagnetic cavity with a vibrating wall (dynamical Casimir effect), we consider electrons passing through the cavity to be interacting with the intracavity field. We show that the dynamical Casimir effect can be observed via the measurement of the change in the average or in the variance of the electron’s kinetic energy. We point out that the enhancement of the effect due to finite temperatures makes it easier to detect the Casimir photons.     

有限温度下的Casimir效应

利用路径积分量子化方法,计算出两个平行的、理想的金属板之间,在有限温度下自由的量子电磁场和内部费米子单圈图对Casimir力的贡献.     

Casimir Force for a Maxwell-Chern-Simons System via Model Transformation

We show that the Hamiltonian for a Maxwell-Chern-Simons (MCS) model can be expressed in a diagonalized equivalent form involving only a massive scalar field variable in a three-dimensional space-time. We use this mapping between the two models, the MCS and a single massive scalar field, to understand the agreement of the Casimir force between parallel lines derived in both models. Since the Casimir force is heavily dependent on the boundary conditions (BC), we show that only certain types of BC can be considered for the two models, within the method of calculation outlined here. We also discuss the behavior of the BC with respect to the gauge symmetry present in the initial model.     

Casimir interaction among objects immersed in a fermionic environment

Using ensembles of two, three, and four spheres immersed in a fermionic background we evaluate the (integrated) density of states and the Casimir energy. We thus infer that for sufficiently smooth objects, whose various geometric characteristic lengths are larger then the Fermi wave length one can use the simplest semiclassical approximation (the contribution due shortest periodic orbits only) to evaluate the Casimir energy. We also show that the Casimir energy for several objects can be represented fairly accurately as a sum of pairwise Casimir interactions between pairs of objects.     

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.     

规范协变理论中的Casimir效应

在U(1)规范场理论中,用Feynman路径积分方法,简明地显示了:(1)鬼粒子对真空能量(Casimir能量)的贡献;(2)不同的协变规范对真空能量的影响。 关键词：     

The Casimir interaction of a massive vector field between concentric spherical bodies

The Casimir interaction energy due to the vacuum fluctuations of a massive vector field between two perfectly conducting concentric spherical bodies is computed. The TE contribution to the Casimir interaction energy is a direct generalization of the massless case but the TM contribution is much more complicated. Each TM mode is a linear combination of a transverse mode which is the generalization of a TM mode in the massless case and a longitudinal mode that does not appear in the massless case. In contrast to the case of two parallel perfectly conducting plates, there are no TM discrete modes that vanish identically in the perfectly conducting spherical bodies. Numerical simulations show that the Casimir interaction force between the two bodies is always attractive.     

Casimir effect and geometric optics

We propose a new approach to the Casimir effect based on classical ray optics. We define and compute the contribution of classical optical paths to the Casimir force between rigid bodies. We reproduce the standard result for parallel plates and agree over a wide range of parameters with a recent numerical treatment of the sphere and plate with Dirichlet boundary conditions. Our approach improves upon the proximity force approximation. It can be generalized easily to other geometries, other boundary conditions, to the computation of Casimir energy densities, and to many other situations.     

Casimir friction force between a SiO<Subscript>2</Subscript> probe and a graphene-coated SiO<Subscript>2</Subscript> substrate

The possibility of mechanical detection of Casimir friction with the use of a noncontact atomic force microscope is discussed. A SiO₂ probe tip located above a graphene-coated SiO₂ substrate is subjected to the frictional force caused by a fluctuating electromagnetic field produced by a current in graphene. This frictional force will create the bend of a cantilever, which can be measured by a modern noncontact atomic force microscope. Both the quantum and thermal contributions to the Casimir frictional force can be measured using this experimental setup. This result can also be used to mechanically detect Casimir friction in micro- and nanoelectromechanical systems.     

Radiative Correction to Casimir Effect

Radiative correction to Casimir effect is calculated in the U(1).gauge field theory by using Feyman path integral method. The expressions for the radiative correction to the Casimir energy and the Casimir force are given.     

Zero-Point Energy of Quantum Fields in a Schwarzschild Geometry

The effective Lagrangian and the zero-point (or Casimir) energy is calculated from the zeta-function which is obtained by the heat kernel method using the expansion of (Bormann and Antonsen, 1995). Calculated this way this unavoidable energy contribution is automatically regularised and ready for further investigation. Interesting observations include a large energy contribution (from scalar field and fermionic zero-point fluctuations) that is non-zero as the mass goes to zero, perhaps indicating a topological origin. Also, plots of the contribution of gauge boson fields to the zero-point energy, as a function of radial distance (gravitational field strength) and the size of the gauge boson coupling (gauge field strength) shows great variation, notably the occurrence of resonances.     

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.     

二维情况下内部有质量费米子单圈图对Casimir力的贡献

采用Feynman的路径积分量子化方法,计算出两个平行的、理想的金属线之间,在绝对零度下量子电磁场在有质量费米子单圈图近似下的Casimir效应.     

Casimir stress in an inhomogeneous medium

The Casimir effect in an inhomogeneous dielectric is investigated using Lifshitz’s theory of electromagnetic vacuum energy. A permittivity function that depends continuously on one Cartesian coordinate is chosen, bounded on each side by homogeneous dielectrics. The result for the Casimir stress is infinite everywhere inside the inhomogeneous region, a divergence that does not occur for piece-wise homogeneous dielectrics with planar boundaries. A Casimir force per unit volume can be extracted from the infinite stress but it diverges on the boundaries between the inhomogeneous medium and the homogeneous dielectrics. An alternative regularization of the vacuum stress is considered that removes the contribution of the inhomogeneity over small distances, where macroscopic electromagnetism is invalid. The alternative regularization yields a finite Casimir stress inside the inhomogeneous region, but the stress and force per unit volume diverge on the boundaries with the homogeneous dielectrics. The case of inhomogeneous dielectrics with planar boundaries thus falls outside the current understanding of the Casimir effect.     

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.     

Casimir Effect for Dielectric Plates

We generalize Kupisewska method to the three-dimensional system and another derivation of the Casimir effect between two dielectric plates is presented based on the explicit quantization of the electromagnetic field in the presence of dielectrics, where the physical meaning of “evanescent mode” is discussed. The Lifshitz's formula is rederived using all the vacuum mode functions, which include the contribution of the ‘evanescent modes’. Only in the case of the perfect metallic plates will the evanescent modes become unimportant.