Repulsive Casimir–Polder forces from cosmic strings

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 on 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 show that for an isotropic polarizability tensor the force is always repulsive. At large separations between the microparticle and the string, the force varies inversely with the fifth power of the distance. In the non-retarded regime, corresponding to separations smaller than the relevant transition wavelengths, the force decays with the inverse fourth power of the distance. In the case of anisotropic polarizability, the dependence of the Casimir–Polder potential on the orientation of the polarizability tensor principal axes also leads to a moment of force acting on the particle.     

Thermal Casimir versus Casimir-Polder forces: equilibrium and nonequilibrium forces

We critically discuss whether and under what conditions Lifshitz theory may be used to describe thermal Casimir-Polder forces on atoms or molecules. An exact treatment of the atom-field coupling reveals that for a ground-state atom (molecule), terms associated with virtual-photon absorption lead to a deviation from the traditional Lifshitz result; they are identified as a signature of nonequilibrium dynamics. Even the equilibrium force on a thermalized atom (molecule) may be overestimated when using the ground-state polarizability instead of its thermal counterpart.     

Casimir-Polder interaction of atoms with magnetodielectric bodies

A general theory of the Casimir-Polder interaction of single atoms with dispersing and absorbing magnetodielectric bodies is presented, which is based on QED in linear, causal media. Both ground-state and excited atoms are considered. Whereas the Casimir-Polder force acting on a ground-state atom can conveniently be derived from a perturbative calculation of the atom-field coupling energy, an atom in an excited state is subject to transient force components that can only be fully understood by a dynamical treatment based on the body-assisted vacuum Lorentz force. The results show that the Casimir-Polder force can be influenced by the body-induced broadening and shifting of atomic transitions — an effect that is not accounted for within lowest-order perturbation theory. The theory is used to study the Casimir-Polder force of a ground-state atom placed within a magnetodielectric multilayer system, with special emphasis on thick and thin plates as well as a planar cavity consisting of two thick plates. It is shown how the competing attractive and repulsive force components related to the electric and magnetic properties of the medium, respectively, can — for sufficiently strong magnetic properties — lead to the formation of potential walls and wells.     

Measurement of the tensor electric polarizability of a deuteron in storage rings

When an electric field of resonant frequency acts on a deuteron beam in a storage ring, the tensor electric polarizability stimulates buildup of the vertical polarization of the beam (the Baryshevsky effect). This effect allows high-precision measurement of the tensor electric polarizability of the deuteron, which contains important information about spin-dependent nuclear forces. The general formulas describing the Baryshevsky effect are derived. It is shown that doubling of the resonant frequency leads to dramatic enhancement of the effect.     

Wightman function and scalar Casimir densities for a wedge with two cylindrical boundaries

Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are investigated for a massive scalar field with general curvature coupling parameter inside a wedge with two coaxial cylindrical boundaries. It is assumed that the field obeys Dirichlet boundary condition on bounding surfaces. The application of a variant of the generalized Abel-Plana formula enables to extract from the expectation values the contribution corresponding to the geometry of a wedge with a single shell and to present the interference part in terms of exponentially convergent integrals. The local properties of the vacuum are investigated in various asymptotic regions of the parameters. The vacuum forces acting on the boundaries are presented as the sum of self-action and interaction terms. It is shown that the interaction forces between the separate parts of the boundary are always attractive. The generalization to the case of a scalar field with Neumann boundary condition is discussed.     

Closed-form solution for a pair of touching cylindrical conductors in an external electric field

We give expressions for the electric potential and field around two conducting cylinders in contact, in closed form and in terms of elementary functions. The polarizability tensor, and hence the torque acting on the cylinder pair, follow from these results. The surface charge density, and the total charge per unit length on each cylinder, can also be evaluated in closed form. The equal and opposite forces on the two cylinders are found in the case of equal cylinder radii.     

Atoms near magnetodielectric bodies: van der Waals energy and the Casimir-Polder force

Based on macroscopic QED in linear, causal media, a consistent theory for the Casimir-Polder force acting on an atom positioned near dispersing and absorbing magnetodielectric bodies is presented. The perturbative result for the van der Waals energy is shown to exhibit interesting new features in the presence of magnetodielectric bodies. To go beyond perturbation theory, we start with the center-of-mass equation of motion and derive a dynamical expression for the Casimir-Polder force acting on an atom prepared in an arbitrary electronic state. For a nondriven atom in the weak coupling regime, the force as a function of time is shown to be a superposition of force components that are related to the electronic density matrix elements at a chosen time. These force components depend on the position-dependent polarizability of the atom, which correctly accounts for the body-induced level shifts and broadenings.     

二维静态时空中Dirac场的重正化能动张量和Casimir效应

在一般渐近平直的二维静态黑洞时空中,利用重正化能动张量的一般性质, 对位于两“平行板”间满足Dirichlet条件的无质量Dirac场的重正化能动张量的真空期待值进行了分析和计算, 得到了一般表达式.利用该表达式可以给出各种具体渐近平直二维静态黑洞时空中的相应Casimir力.对于重正化能动张量及Casimir力与真空态定义(包括Boulware 真空态、Hartle-Hawking真空态和Unrum真空态三种情况)、Hawking辐射和反常迹的关系分别进行了讨论，给出了相应的表达式和计算结果. 关键词： 能动张量 Casimir 效应 黑洞 真空态     

Local field in liquid dielectrics: A two-parameter mean field approach

In the molecular field approximation, one derives an expression of the static dielectric constant of an isotropic liquid involving renormalized expressions of the molecular dipole and polarizability. The long-range moderate attractive forces are treated as a perturbation of the short-range intense repulsions, so that two parameters λ and η describe the short-range correlations and the long-range order, respectively. On the condition of a superposition hypothesis, the model is compared in its hard-sphere limit (λ=0, η=1) with the available experimental data about a series of organic liquids and with Onsager's continuum approach.     

Casimir–Polder potential for a metallic cylinder in cosmic string spacetime

Casimir–Polder potential is investigated for a polarizable microparticle in the geometry of a straight cosmic string with a metallic cylindrical shell. The electromagnetic field Green tensor is evaluated on the imaginary frequency axis. The expressions for the Casimir–Polder potential is derived in the general case of anisotropic polarizability for the both interior and exterior regions of the shell. The potential is decomposed into pure string and shell-induced parts. The latter dominates for points near the shell, whereas the pure string part is dominant near the string and at large distances from the shell. For the isotropic case and in the region inside the shell the both pure string and shell-induced parts in the Casimir–Polder force are repulsive with respect to the string. In the exterior region the shell-induced part of the force is directed toward the cylinder whereas the pure string part remains repulsive with respect to the string. At large distances from the shell the total force is repulsive.     

Electromagnetic Casimir densities for a wedge with a coaxial cylindrical shell

Vacuum expectation values of the field square and the energy-momentum tensor for the electromagnetic field are investigated for the geometry of a wedge with a coaxial cylindrical boundary. All boundaries are assumed to be perfectly conducting, and both regions inside and outside the shell are considered. By using the generalized Abel–Plana formula, the vacuum expectation values are presented in the form of the sum of two terms. The first one corresponds to the geometry of the wedge without the cylindrical shell, and the second term is induced by the presence of the shell. The vacuum energy density induced by the shell is negative for the interior region and positive for the exterior region. The asymptotic behavior of the vacuum expectation values are investigated in various limiting cases. It is shown that the vacuum forces acting on the wedge sides due to the presence of the cylindrical boundary are always attractive. PACS 03.70.+k     

Fermionic vacuum polarization in compactified cosmic string spacetime

We investigate the fermionic condensate and the vacuum expectation value (VEV) of the energy-momentum tensor for a charged massive fermionic field in the geometry of a cosmic string compactified along its axis. In addition, we assume the presence of two types of magnetic fluxes: a flux running along the cosmic string and another enclosed by the compact dimension. These fluxes give rise to Aharanov–Bohm-like effects on the VEVs. The VEVs are decomposed into two parts corresponding to the geometry of a straight cosmic string without compactification plus a topological part induced by the compactification of the string axis. Both contributions are even periodic functions of the magnetic fluxes with period equal to the flux quantum. The vacuum energy density is equal to the radial stress for the parts corresponding to the straight cosmic string and the topological one. Moreover, the axial stress is equal to the energy density for the parts corresponding to the straight cosmic string; however, for massive fermionic fields this does not occur for the topological contributions. With respect to the dependence on the magnetic fluxes, both the fermionic condensate and the vacuum energy density, can be either positive or negative. Moreover, for points near the string, the main contribution to the VEVs comes from the straight cosmic string part, whereas at large distances the topological ones dominate. In addition to the local characteristics of the vacuum state, we also evaluate the part in the topological Casimir energy induced by the string.     

Polarization of vacuum of quantum fields in the Aaronov-Bohm external field. II

A spinor field interacting with the Aaronov-Bohm external field is examined. Analytical expressions for the vacuum average components of the energy-momentum tensor are derived. Dependences of the components of energymomentum tensor of the spinor field in the vacuum state on the distance and field strength are investigated. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 3–8, April, 2006.     

Extended string field theory for massless higher-spin fields

We propose a new gauge field theory which is an extension of ordinary string field theory by assembling multiple state spaces of the bosonic string. The theory includes higher-spin fields in its massless spectrum together with the infinite tower of massive fields. From the theory, we can easily extract the minimal gauge-invariant quadratic action for tensor fields with any symmetry. As examples, we explicitly derive the gauge-invariant actions for some simple mixed symmetric tensor fields. We also construct covariantly gauge-fixed action by extending the method developed for string field theory.     

Local field anisotropy in Langmuir-Blodgett films of cadmium arachidate

Lorentz tensor and local field tensor components for uniaxial Langmuir-Blodgett films of cadmium arachidate from 3 to 100 nm thick on silver, polymethyl methacrylate, and glass substrates have been experimentally determined using the data on the film refractive index dispersion in the visible range. The constraints from below on the mean value and anisotropy of the molecular polarizability caused by the intermolecular interactions in the film have been established.     

Nonlocal properties of dynamical three-body Casimir-Polder forces

We consider the three-body Casimir-Polder interaction between three atoms during their dynamical self-dressing. We show that the time-dependent three-body Casimir-Polder interaction energy displays nonlocal features related to quantum properties of the electromagnetic field and to the nonlocality of spatial field correlations. We discuss the measurability of this intriguing phenomenon and its relation with the usual concept of stationary three-body forces.     

Modified weak energy condition for the energy momentum tensor in quantum field theory

The weak energy condition is known to fail in general when applied to expectation values of the energy momentum tensor in flat space quantum field theory. It is shown how the usual counter arguments against its validity are no longer applicable if the states |ψ〉 for which the expectation value is considered are restricted to a suitably defined subspace. A possible natural restriction on |ψ〉 is suggested and illustrated by two quantum mechanical examples based on a simple perturbed harmonic oscillator Hamiltonian. The proposed alternative quantum weak energy condition is applied to states formed by the action of the scalar, vector and the energy momentum tensor operators on the vacuum. We assume conformal invariance in order to determine almost uniquely three-point functions involving the energy momentum tensor in terms of a few parameters. The positivity conditions lead to non-trivial inequalities for these parameters. They are satisfied in free field theories, except in one case for dimensions close to two. Further restrictions on |ψ〉 are suggested which remove this problem. The inequalities which follow from considering the state formed by applying the energy momentum tensor to the vacuum are shown to imply that the coefficient of the topological term in the expectation value of the trace of the energy momentum tensor in an arbitrary curved space background is positive, in accord with calculations in free field theories.     

Elastic dipoles in the model of single-crystal and amorphous copper

The characteristic values of the elastic polarizability tensor components of point defects in crystalline and amorphous copper, which determine changes in the elasticity tensor components upon introduction of defects, have been found using the molecular dynamics method. A relation of the elastic polarizability tensor with the main parameter of the interstitialcy theory, i.e., shear susceptibility, has been established. An analysis of the elastic polarizability tensors of defects in crystalline and amorphous copper has demonstrated that, in a noncrystalline structure, there are specific atomic configurations that under deformation manifest themselves similarly to elastic dipoles (interstitial atoms in a dumbbell configuration) in single-crystal copper.     

Manifestation of tensor magnetic polarizability of the deuteron in storage ring experiments

It was previously shown that the tensor magnetic polarizability of the deuteron causes the spin rotation with two frequencies and experiences beating for polarized deuteron beams in storage rings. We confirm an existence of this effect and derive general formulae describing deuteron spin dynamics. It is found that an initially tensor polarized deuteron beam can acquire a final horizontal vector polarization of order of 1%. This effect allows to measure the tensor magnetic polarizability of the deuteron in storage ring experiments.     

Born expansion of the Casimir–Polder interaction of a ground-state atom with dielectric bodies

Within leading-order perturbation theory, the Casimir–Polder potential of a ground-state atom placed within an arbitrary arrangement of dispersing and absorbing linear bodies can be expressed in terms of the polarizability of the atom and the scattering Green tensor of the body-assisted electromagnetic field. Based on a Born series of the Green tensor, a systematic expansion of the Casimir–Polder potential in powers of the electric susceptibilities of the bodies is presented. The Born expansion is used to show how and under which conditions the Casimir–Polder force can be related to microscopic many-atom van der Waals forces, for which general expressions are presented. As an application, the Casimir–Polder potentials of an atom near a dielectric ring and an inhomogeneous dielectric half space are studied and explicit expressions are presented that are valid up to second order in the susceptibility. PACS 12.20.-m; 34.50.Dy; 34.20.-b; 42.50.Nn