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.     

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.     

Quantum effects in the Gowdy T3 cosmology

The Gowdy T³ Cosmology is an exact solution to the vacuum Einstein equations interpreted to be a single polarization of gravitational waves propagating in an anisotropic, spatially inhomogeneous background. The classical behavior is reviewed and related to standard cosmological parameters. Canonical quantization of the dynamical degrees of freedom is reviewed. An adiabatic vacuum state is constructed. Adiabatic regularization is used to obtain non-divergent stress-energy tensor vacuum expectation values. Casimir energy terms due to T³ imposed discrete modes are evaluated. The vacuum expectation values are analyzed in early and late time limits and evaluated numerically. The regularized expectation value is used as a source for the classical background spacetime in the spirit of semi-classical gravity. An entirely vacuum expectation value source term produces essentially the time reverse of the classical evolution. Classical stress-energy added to the source restores the classical behavior at late times only. The combined system collapses from infinite to small but non-zero volume and reexpands. The classical singularity is replaced by a symmetric bounce.     

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.     

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.     

Casimir Effect at Finite Temperature in the Presence of One Fractal Extra Compactified Dimension

We discuss the Casimir effect for massless scalar fields subject to the Dirichlet boundary conditions on the parallel plates at finite temperature in the presence of one fractal extra compactified dimension. We obtain the Casimir energy density with the help of the regularization of multiple zeta function with one arbitrary exponent and further the renormalized Casimir energy density involving the thermal corrections. It is found that when the temperature is sufficiently high, the sign of the Casimir energy remains negative no matter how great the scale dimension δ is within its allowed region. We derive and calculate the Casimir force between the parallel plates affected by the fractal additional compactified dimension and surrounding temperature. The stronger thermal influence leads the force to be stronger. The nature of the Casimir force keeps attractive.     

Casimir Forces for Robin Scalar Field on Cylindrical Shell in de Sitter Space

The Casimir stress on a cylindrical shell in background of conformally flat spacetime for massless scalar field is investigated. In the general case of Robin (mixed) boundary condition, formulae are derived for the vacuum expectation values of the energy–momentum tensor and vacuum forces acting on boundaries. The special case of the dS bulk is considered then different cosmological constants are assumed for the space inside and outside of the shell to have general results applicable to the case of cylindrical domain wall formations in the early universe.     

Casimir Effect Under Two Dimensional Black Hole Spacetime Background with Global Monopole

A thin layer of the event horizon vicinity to the two-dimension black hole with a global monopole is considered as a system of the Casimir type. The energy-momentum tensor is derived in Boulware vacuum, Hartle-Hawking vacuum and Unruh vacuum respectively. The values are derived in the massless scalar field which satisfies the Dirichlet boundary conditions. Using the Wald's axioms, the result is got which is the same with the one derived by the usual regularized methods. Meanwhile, the energy, energy density, and pressure acting on the boundaries at the asymptotically flat background also are calculated too, and from the energy, Casimir force is derived. The Casimir energy and Casimir force are compared respectively in the background before and after radiation. PACS: 42.50.Lc.     

Bose-einstein condensation of exciton polaritons in high-Q planar microcavities with GaAs quantum wells

The walls of the box which contains matter represent a membrane that allows the relativistic quantum vacuum to pass but not matter. That is why the pressure of matter in the box may be considered as the analog of the osmotic pressure. However, we demonstrate that the osmotic pressure of matter is modified due to interaction of matter with vacuum. This interaction induces the nonzero negative vacuum pressure inside the box, as a result the measured osmotic pressure becomes smaller than the matter pressure. As distinct from the Casimir effect, this induced vacuum pressure is the bulk effect and does not depend on the size of the box. This effect dominates in the thermodynamic limit of the infinite volume of the box. Analog of this effect has been observed in the dilute solution of ³He in liquid ⁴He, where the superfluid ⁴He plays the role of the non-relativistic quantum vacuum, and 3He atoms play the role of matter.     

Quantum Vacuum Fluctuations in a Chromomagnetic-Like Background

In this paper, we study the effects associated to quantum vacuum fluctuations of vectorial perturbations of the Abelian SU(2) Yang-Mills field in a static and homogeneous chromomagnetic-like background field, at zero temperature. We use periodic and antiperiodic boundary conditions in order to calculate the Casimir energy by means of the frequency sum technique and of the regularization method based on zeta functions, analyzing its behavior in the weak and strong coupling regimes. We compare the obtained results with the similar ones found for scalar and spinor fields placed in an ordinary magnetic field background. We show that only in the weak coupling regime the non-trivial topology of the system encoded in the antiperiodic boundary conditions changes the nature of the Casimir force with respect to the periodic ones. Considering the weak coupling scenario, we show that the introduction of a third polarization state in the perturbations makes manifest the effects on the Casimir energy due to the coupling with the chromomagnetic-like background field, for both the boundary conditions. Finally, in the strong coupling regime, in which the quantum vacuum is not stable due to the Nielsen-Olesen instabilities, we evaluate the effects of a compact extra dimension on its stabilization.     

Mesoscopic Casimir forces in quantum vacuum

Traditionally, it is assumed that the Casimir vacuum pressure does not depend on the ultraviolet cutoff. There are, however, some arguments that the effect actually depends on the regularization procedure and thus on trans-Planckian physics. We provide the condensed matter example where the Casimir forces do explicitly depend on microscopic (correspondingly trans-Planckian) physics due to the mesoscopic finite-N effects, where N is the number of bare particles in condensed matter (or correspondingly the number of elements comprising the quantum vacuum). The finite-N effects lead to mesoscopic fluctuations of the vacuum pressure. The amplitude of the mesoscopic fluctuations of the Casimir force in a system with linear dimension L is a factor of N ^1/3～L/a _p larger than the traditional value of the Casimir force given by effective theory, where a _p =?/p _p is the interatomic distance which plays the role of the Planck length.     

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.     

Cutoff dependence of the Casimir effect

The problem of calculating the Casimir force on two conducting planes by means of the stress tensor is examined. The evaluation of this quantity is carried out using an explicit regularization procedure which has its origin in the underlying (2+1) dimensional Poincaré invariance of the system. The force between the planes is found to depend on the ratio of two independent cutoff parameters, thereby rendering any prediction for the Casimir effect an explicit function of the particular calculational scheme employed. Similar results are shown to obtain in the case of the conducting sphere. Received: 15 October 2000 / Revised version: 10 January 2001 / Published online: 6 April 2001     

Topological phases of quantum theories. Chern-Simons theory

We analyze the vacuum structure (degeneracy, nodes and symmetries) of some quantum theories with special emphasis on the study of its dependence on the geometry and topology of the classical configuration space. The study of the topological limit shows that many low energy properties of those quantum theories can be inferred from the structure of their topological phases. After reviewing some simple pure quantum mechanical models (planar rotor, magnetic monopole and quantum Hall effect) we focus on the study of the rich relationship existing between topologically massive gauge theories and their topological phases, Chern-Simons theories. In particular we show that, although in a finite volume the degeneracy of the quantum vacuum of gauge theories depends on the topology of the underlying Riemann surface, in an infinite volume the vacuum is unique. Finally, the topological structure of Chern-Simons theory is analyzed in a covariant formalism within a geometric regularization scheme. We discuss in some detail the structure of the different metric dependent contributions to the Chern-Simons partition function and the associated topological invariants.     

Finite temperature Casimir effect in Kaluza–Klein spacetime

In this article, we consider the finite temperature Casimir effect in Kaluza–Klein spacetime due the vacuum fluctuation of massless scalar field with Dirichlet boundary conditions. We consider the general case where the extra dimensions (internal space) can be any compact connected manifold or orbifold without boundaries. Using piston analysis, we show that the Casimir force is always attractive at any temperature, regardless of the geometry of the internal space. Moreover, the magnitude of the Casimir force increases as the size of the internal space increases and it reduces to the Casimir force in (3+1)$(3+1)$-dimensional Minkowski spacetime when the size of the internal space shrinks to zero. In the other extreme where the internal space is large, the Casimir force can increase beyond all bound. Asymptotic behaviors of the Casimir force in the low and high temperature regimes are derived and it is observed that the magnitude of the Casimir force grows linearly with temperature in the high temperature regime.     

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.     

Vacuum Effects on Massive Spinor Fields: S 1× R 3 Topology

The aim of this work was to investigate the role played by an external field on the Casimir energy density for massive fermions under S ¹× R ³ topology. Both twisted- and untwisted-spin connections are considered and the calculation in a closed form is performed using an alternative approach based on the combination of the analytic regularization method and the Euler–Maclaurin summation formula. It is shown that no mass scale appears in the final result and, therefore, Casimir effect arises only from the boundary conditions and vacuum fluctuations induced by the coupling with the external field. PACS numbers: 11.10.Wx     

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.     

A new boundary method for electromagnetic scattering from inhomogeneous bodies

A new numerical method for scattering from inhomogeneous bodies is presented. In particular, the 2D case of a TM-polarizated incident wave scattered by an infinite cylinder is considered. The scattered field is sought in two different domains. The first one is a bounded region inside the scattering body with an inhomogeneous permittivity ε(x,y). The second one is an unbounded homogeneous region outside the scatterer. An approximate solution for the scattered field inside the scatterer is sought by applying the QTSM technique. The method of discrete sources is used to approximate the scattered field in the unbounded region outside the scattering body. A comparison of the numerical solution with an analytic solution is performed.