Casimir Effect for Moving Branes in Static dS4+1 Bulk

In this paper we study the Casimir effect for conformally coupled massless scalar fields on background of Static dS₄₊₁ spacetime. We will consider the general plane–symmetric solutions of the gravitational field equations and boundary conditions of the Dirichlet type on the branes. Then we calculate the vacuum energy-momentum tensor in a configuration in which the boundary branes are moving by uniform proper acceleration in static de Sitter background. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally invariant field in static de Sitter space from the corresponding Rindler counterpart by the conformal transformation.     

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.     

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.     

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.     

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.     

Does the Unruh effect exist?

It is shown that quantization on the Fulling modes presupposes that the field vanishes on the spatial boundaries of the Rindler manifold. For this reason, Rindler space is physically unrelated with Minkowski space and the state of a Rindler observer cannot be described by the equilibrium density matrix with the Fulling-Unruh temperature. Therefore it is pointless to talk about an Unruh effect. The question of the behavior of an accelerated detector in the physical formulation of the problem remains open. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 12, 861–866 (25 June 1997)     

Thermofield dynamics and Casimir effect for fermions

A generalization of the Bogoliubov transformation is developed to describe a space compactified fermionic field. The method is the fermionic counterpart of the formalism introduced earlier for bosons [Phys. Rev. A 66 (2002) 052101], and is based on the thermofield dynamics approach. We analyze the energy-momentum tensor for the Casimir effect of a free massless fermion field in a d-dimensional box at finite temperature. As a particular case the Casimir energy and pressure for the field confined in a three-dimensional parallelepiped box are calculated. It is found that the attractive or repulsive nature of the Casimir pressure on opposite faces changes depending on the relative magnitude of the edges. We also determine the temperature at which the Casimir pressure in a cubic box changes sign and estimate its value when the edge of the cube is of the order of the confining lengths for baryons.     

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.     

Rindler solutions and their physical interpretation

We show that the singular behavior of Rindler solutions near horizon testifies to the currents of particles from a region arbitrarily close to the horizon. Besides, the Rindler solutions in right Rindler sector of Minkowski space can be represented as a superposition of only positive-or only negative-frequency plane waves; these states require infinite energy for their creation and possess infinite charge in a finite space interval, containing the horizon. The positive-or negative-frequency representations of Rindler solutions analytically continued to the whole Minkowski space make up a complete set of states in this space, which have, however, the aforementioned singularities. These positive (negative)-frequency states are characterized by positive (negative) total charge, the charge of the same sign in right (left) Rindler sector and by quantum number κ. But in other Lorentz invariant sectors they do not possess positive (negative)-definite charge density and have negative (positive) charge in left (right) Rindler sector. Therefore these states describe both the particle (antiparticle) and pairs, the mean number of which is given by Planck function of κ. These peculiarities make the Rindler set of solutions nonequivalent to the plane wave set and the inference on the existence of thermal currents for a Rindler observer moving in empty Minkowski space is unfounded. Zh. éksp. Teor. Fiz. 114, 777–785 (September 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Casimir Energy in Hartle--Hawking State

We calculate the Casimir effect at finite temperature in Minkowski spacetime by using statistical method, the approximate expressions of the Casimir effect in the low and high temperature limits are also discussed. Then employing some general properties of the renormalized stress tensor, we obtain the Casimir energy stress tensor in Hattie-Hawking state.     

Casimir effects: An optical approach II. Local observables and thermal corrections

We recently proposed a new approach to the Casimir effect based on classical ray optics (the “optical approximation”). In this paper we show how to use it to calculate the local observables of the field theory. In particular, we study the energy–momentum tensor and the Casimir pressure. We work three examples in detail: parallel plates, the Casimir pendulum and a sphere opposite a plate. We also show how to calculate thermal corrections, proving that the high temperature ‘classical limit’ is indeed valid for any smooth geometry.     

Finite temperature Casimir effect in spacetime with extra compactified dimensions

In this Letter, we derive the explicit exact formulas for the finite temperature Casimir force acting on a pair of parallel plates in the presence of extra compactified dimensions within the framework of Kaluza–Klein theory. Using the piston analysis, we show that at any temperature, the Casimir force due to massless scalar field with Dirichlet boundary conditions on the plates is always attractive and the effect of extra dimensions becomes stronger when the size or number of the extra dimensions increases. These properties are not affected by the explicit geometry and topology of the Kaluza–Klein space.     

The physical meaning of Fermi coordinates

Fermi coordinates (FC) are supposed to be the natural extension of Cartesian coordinates for an arbitrary moving observer in curved space-time. Since their construction cannot be done on the whole space or even in the whole past of the observer we examine which construction principles are responsible for this effect and how they may be modified. A proposal for a modification is made and applied to the observer with constant acceleration in the two- and four-dimensional Minkowski space. The two-dimensional case shows some surprising similarities to Kruskal space which generalize those found by Rindler for the outer region of Kruskal space and the Rindler wedge. In perturbational approaches the modification also leads to different predictions for certain physical systems. As an example we consider atomic interferometry and derive the deviation of the acceleration-induced phase shift from the standard result in Fermi coordinates.     

HORIZONS AND GENERATING FUNCTIONALS FOR THE TEMPERATURE GREEN FUNCTIONS

The generating functional approach to Green functions in the thermal equilibrium is used to explore the geometrical origin of the temperatures of the quantum fields in the Rindler space-time and black hole spacetimes. It is shown that under the transformation from Minkowski space to the Rindler space the path integral representation for the Euclidean generating functionals of Green functions at zero temperature would transform into the corresponding ones of the quantum fields at a certain finite temperature, and the Minkowski vacuum state would have the same properties as that of the quantum mixed state at the same temperatfire. All thermal Green functions for the mixed state are given. Similar results would be obtained for the Schwarzschild, the Reissner-NordstrOm and the Kerr black holes and whereupon the Hawking temperature for the black holes would have geometrical origin as well as that in the Rindler spacetime. The various density operators of the mixed states at the Hawking temperature for the black hole sacetimes are specified.     

Unruh effect and holography

We study the Unruh effect on the dynamics of quarks and mesons in the context of AdS₅/CFT₄ correspondence. We adopt an AdS₅ metric with the boundary Rindler horizon extending into a bulk Rindler-like horizon, which yields the thermodynamics with Unruh temperature verified by computing the boundary stress tensor. We then embed in it a probe fundamental string and a D7 brane in such a way that they become the dual of an accelerated quark and a meson in Minkowski space, respectively. Using the standard procedure of holographic renormalization, we calculate the chiral condensate, and also the spectral functions for both the accelerated quark and meson. Especially, we extract the corresponding strength of random force of the Langevin dynamics and observe that it can characterize the phase transition of meson melting. This result raises an issue toward a formulation of complementarity principle for the Rindler horizon. We find most of the dynamical features are qualitatively similar to the ones in the thermal bath dual to the AdS black hole background, though they could be quite different quantitatively.     

Electrodynamics of hyperbolically accelerated charges V. The field of a charge in the Rindler space and the Milne space

We describe the electromagnetic field of a uniformly accelerated charge in its co-moving Rindler frame. It is shown that the electrical field lines coincide with the trajectories of photons. The self force of a charged particle at rest in Rindler space, and the increase of its weight due to its charge, is calculated. The general case of an accelerated charge in Rindler space is also considered. It is shown that the electrical field inside a uniformly charged spherical shell can be used as a measure of it 4-acceleration. A result that has earlier been deduced in a different way by Fugmann and Kretzschmar is confirmed, namely that the intensity of radiation from a point charge instantaneously at rest in an accelerated frame is proportional to the square of the relative acceleration of the charge and the observer. In particular it is shown that a freely falling charge in Rindler space radiates in accordance with Larmor’s formula. In this case the radiation energy is taken from the Schott energy. The energy of the electromagnetic field is analysed from the point of view of the Hirayama-separation, which generalizes the Teitelboim-separation to non-inertial frames, of the field in a bound part and an unbound part. A detailed account, with reference to the Rindler frame, of the field energy and particle energy is given for the case of a charge entering and leaving a region with hyperbolic motion. We also consider the electromagnetic field of a uniformly accelerated charge with reference to the Milne frame, which covers a different part of spacetime than the Rindler frame. The radiating part of the electromagnetic field is found in the Milne sector of spacetime.     

Critical casimir effect and wetting by helium mixtures

We have measured the contact angle of the interface of phase-separated 3He-4He mixtures against a sapphire window. We have found that this angle is finite and does not tend to zero when the temperature approaches T(t), the temperature of the tricritical point. On the contrary, it increases with temperature. This behavior is a remarkable exception to what is generally observed near critical points, i.e., "critical point wetting." We propose that it is a consequence of the "critical Casimir effect" which leads to an effective attraction of the 3He-4He interface by the sapphire near T(t).     

Anomalous temperature dependence of the Casimir force for thin metal films

Within the framework of the Drude dispersive model, we predict an unusual nonmonotonic temperature dependence of the Casimir force for thin metal films. For certain conditions, this force decreases with temperature due to the decrease of the metallic conductivity, whereas the force increases at high temperatures due to the increase of the thermal radiation pressure. We consider the attraction of a film to: either (i) a bulk ideal metal with a planar boundary, or (ii) a bulk metal sphere (lens). The experimental observation of the predicted decreasing temperature dependence of the Casimir force can put an end to the long-standing discussion on the role of the electron relaxation in the Casimir effect.     

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.