Casimir and Casimir-Polder repulsion have been known for more than 50 years. The general "Lifshitz" configuration of parallel semi-infinite dielectric slabs permits if they are separated by a fluid that has value permittivity is intermediate between those the slabs. This was indirectly confirmed in 1970s, directly Capasso's group recently. It also many years electrically magnetically polarizable bodies can experience repulsive quantum vacuum force. More amenable to practical application...

Doubt continues to linger over the reality of quantum vacuum energy. There is some question whether fluctuating fields gravitate at all, or do so anomalously. Here we show that, for simple case parallel conducting plates, associated Casimir energy gravitates just as required by equivalence principle, and that therefore inertial gravitational masses a system possessing ${E}_{c}$ are both ${E}_{c}/{c}^{2}$. This result disproves recent claims in literature. We clarify pitfalls calculation can...

The formation and growth of ice particles, particularly on the surfaces spherical water droplets, bear profound implications for localized weather systems global climate. Herein, we develop a theoretical framework nucleation minuscule establishing that $10\sim5000\rm\ nm$ droplets can considerably increase in volume, making substantial contribution to within mist, fog, or even cloud systems. We reveal Casimir-Lifshitz (van der Waals) interaction these is robust enough stimulate both ice-cold...

In earlier papers, we have applied multiple-scattering techniques to calculate Casimir forces due scalar fields between different bodies described by delta function potentials. When the coupling potentials became weak, closed-form results were obtained. We simplify this weak-coupling technique and apply it case of tenuous dielectric bodies, in which method involves summation van der Waals (Casimir-Polder) interactions. Once again, exact for finite can be present closed formulas describing...

The Casimir interaction between two concentric corrugated cylinders provides the mechanism for noncontact gears. To this end, we calculate torque such cylinders, described by $\ensuremath{\delta}$-potentials, which interact through a scalar field. We derive analytic expressions case when corrugation amplitudes are small in comparison to wavelengths. explicit results Dirichlet case, and exact weak coupling limit, leading order. approach corresponding of parallel plates limit large radii...

We derive boundary conditions for electromagnetic fields on a $\delta$-function plate. The optical properties of such plate are shown to necessarily be anisotropic in that they only depend the transverse unambiguously obtain perfectly conducting limit infinite dielectric response. show material does not "optically vanish" thin-plate limit. plasma slab thickness $d$ with frequency $\omega_p^2=\zeta_p/d$ reduces frequencies ($\omega=i\zeta$) satisfying $\zeta d \ll \sqrt{\zeta_p d} 1$. Casimir...

Although repulsive effects have been predicted for quantum vacuum forces between bodies with nontrivial electromagnetic properties, such as a perfect electric conductor and magnetic conductor, realistic repulsion seems difficult to achieve. Repulsion is possible if the medium has permittivity in value intermediate those of two bodies, but this may not be useful configuration. Here, inspired by recent numerical work, we initiate analytic calculations Casimir-Polder interaction an atom...

It has been demonstrated that quantum vacuum energy gravitates according to the equivalence principle, at least for finite Casimir energies associated with perfectly conducting parallel plates. We here add further support this conclusion by considering semitransparent plates, is, δ-function potentials, acting on a massless scalar field, in spacetime defined Rindler coordinates (τ, x, y, ξ). Fixed ξ such represents uniform acceleration. calculate force systems consisting of one or two plates...

Recently, the topic of Casimir repulsion has received a great deal attention, largely because possibility technological application. The general subject long history, going back to self-repulsion conducting spherical shell and between perfect electric conductor magnetic conductor. it been observed that can be achieved ordinary bodies, provided sufficient anisotropy is present. For example, an anisotropic polarizable atom repelled near aperture in plate. Here, we provide new examples this...

Several years ago we demonstrated that the Casimir energy for perfectly reflecting and imperfectly parallel plates gravitated normally, is, obeyed equivalence principle. At time divergences in theory were treated only formally, without proper regularization, coupling to gravity was limited canonical energy-momentum-stress tensor. Here strengthen result by removing both of those limitations. We consider, as a toy model, massless scalar fields interacting with semitransparent...

The Casimir-Lifshitz torque between two biaxially polarizable anisotropic planar slabs is shown to exhibit a nontrivial sign reversal in its rotational sense. critical distance a_{c} the that marks this characterized by frequency ω_{c}∼c/2a_{c} at which in-planar polarizabilities along principal axes are equal. materials seek align their of one direction below a_{c}, while above try rotated perpendicular relative previous minimum energy orientation. disappears nonretarded limit. Our...

We calculate the lateral Casimir force between corrugated parallel plates, described by $\ensuremath{\delta}$-function potentials, interacting through a scalar field, using multiple scattering formalism. The contributions to energy due uncorrugated plates is treated as background from outset. derive leading- and next-to-leading-order contribution for case when corrugation amplitudes are small in comparison wavelengths. present explicit results terms of finite integrals Dirichlet limit, exact...

Continuing a program of examining the behavior vacuum expectation value stress tensor in background which varies only single direction, we here study electromagnetic medium with permittivity depending on spatial coordinate, specifically, planar dielectric half-space facing region. There are divergences occurring that regulated by temporal and point-splitting, have universal character for both transverse electric magnetic modes. The nature depends model dispersion adopted. And there...

Motivated by a desire to understand quantum fluctuation energy densities and stress within spatially varying dielectric medium, we examine the vacuum expectation value for tensor of scalar field with arbitrary conformal parameter, in background given potential that depends on only one spatial coordinate. We regulate expressions incorporating temporal-spatial cutoff (imaginary) time transverse-spatial directions. The divergences are captured zeroth- second-order WKB approximations. Then is...

It has been increasingly becoming clear that Casimir and Casimir‐Polder entropies may be negative in certain regions of temperature separation. In fact, the occurrence entropy seems to a nearly ubiquitous phenomenon. This is most highlighted quantum vacuum interaction nanoparticle with conducting plate or between two nanoparticles. argued this phenomenon does not violate physical intuition, since total entropy, including self‐entropies nanoparticle, should positive. New calculations, seem...

It has been demonstrated, using variational methods, that quantum vacuum energy gravitates according to the equivalence principle, at least for finite Casimir energies associated with perfectly conducting parallel plates. This conclusion holds independently of orientation We review these arguments and add further support this by considering semitransparent plates, is, δ-function potentials, acting on a massless scalar field, in spacetime defined Rindler coordinates. calculate force systems...

We have recently demonstrated that Casimir energy due to parallel plates, including its divergent parts, falls like conventional mass in a weak gravitational field. The parts were suitably interpreted as renormalizing the bare masses of plates. Here, we corroborate our result regarding inertial nature by calculating centripetal force on apparatus rotating with constant angular speed. show is independent orientation frame whose origin at center inertia apparatus.

We develop a formalism to extend our previous work on the electromagnetic $\ensuremath{\delta}$-function plates spherical surface. The electric (${\ensuremath{\lambda}}_{e}$) and magnetic (${\ensuremath{\lambda}}_{g}$) couplings surface are through potentials defining dielectric permittivity diamagnetic permeability, with two anisotropic coupling tensors. incorporates dispersion. Green's dyadic breaks up into transverse parts. derive Casimir interaction energy between concentric spheres in...

In this paper we continue our program of computing Casimir self-entropies idealized electrical bodies. Here consider an electromagnetic $\ensuremath{\delta}$-function sphere (``semitransparent sphere'') whose electric susceptibility has a transverse polarization with arbitrary strength. Dispersion is incorporated by plasma-like model. the strong-coupling limit, perfectly conducting spherical shell realized. We compute entropy for both low and high temperatures. The self-entropy negative as...

Various applications of the multiple scattering technique to calculating Casimir energy are described. These include interaction between dilute bodies various sizes and shapes, temperature dependence, interactions with multilayered corrugated bodies, new examples exactly solvable separable bodies.

In order to understand why carbon dioxide $({\mathrm{CO}}_{2})$ and methane $({\mathrm{CH}}_{4})$ molecules interact differently with surfaces, we investigate the Casimir-Polder energy of a linearly polarizable ${\mathrm{CO}}_{2}$ molecule an isotropically ${\mathrm{CH}}_{4}$ in front atomically thin gold film amorphous silica slab. We quantitatively analyze how anisotropy polarizability influences van der Waals contribution binding molecule.

Despite suggestions to the contrary, we show in this paper that usual dispersive form of electromagnetic energy density must be used derive Lifshitz force between parallel dielectric media. This conclusion follows from general quantum vacuum energy, which is basis multiple-scattering formalism. As an illustration, explicitly formula for interaction semispaces, including dispersion, starting expression total system. The issues constancy plates and observability electrostrictive forces are...

In this paper we study an archetypical scenario in which repulsive Casimir-Polder forces between atom or molecule and two macroscopic bodies can be achieved. This is extension of previous studies the interaction a polarizable wedge, repulsion occurs if sufficiently anisotropic close enough to symmetry plane wedge. A similar such passes thin cylinder wire. An obvious compute facing wedges, includes as special case with conducting screen possessing slit, parallel wires. To end further extend...

We analyze the Lifshitz pressure between silica and tin separated by a liquid mixture of bromobenzene chlorobenzene. show that phase transition from semimetallic $\ensuremath{\alpha}\ensuremath{-}\mathrm{Sn}$ to metallic $\ensuremath{\beta}\ensuremath{-}\mathrm{Sn}$ can switch forces repulsive attractive. This effect is caused difference in dielectric functions $\ensuremath{\beta}\ensuremath{-}\mathrm{Sn}$, giving both attractive contributions total different frequency regions controlled...