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We reply to the "Comment on 'Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic mirrors.' " We believe the comment misrepresents our papers, and fails to provide a plausible resolution to the conflict between theory and experiment.

We examine the conditions of validity for the Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic plane mirrors. As in the previously studied case of nonmagnetic materials [Guérout et al., Phys. Rev. E 90, 042125 (2014)], we recover the usual expression for the lossy model of optical response, but not for the lossless plasma model. We also show that the modes associated with the Foucault currents play a crucial role in the limit of vanishing losses, in contrast to expectations.

We present a time-dependent quantum calculation of the van der Waals interaction between a pair of dissimilar atoms, one of which is initially excited while the other one is in its ground state. For small detuning, the interaction is predominantly mediated at all distances by the exchange of doubly resonant photons between the two atoms. We find that it presents both temporal and spatial oscillations. Spatially oscillating terms depend on the resonant frequencies of both atoms, while the frequency of the time oscillations is given by their detuning. We analyze the physical content of our findings and discuss to what extent previous conflicting stationary approaches provide compatible results. A proper account of causality is found essential in order to obtain the correct result.

Negative entropy has been known in Casimir systems for some time. For example, it can occur between parallel metallic plates modeled by a realistic Drude permittivity. Less well known is that negative entropy can occur purely geometrically, say between a perfectly conducting sphere and a conducting plate. The latter effect is most pronounced in the dipole approximation, which is reliable when the size of the sphere is small compared to the separation between the sphere and the plate. Therefore, here we examine cases where negative entropy can occur between two electrically and magnetically polarizable nanoparticles or atoms, which need not be isotropic, and between such a small object and a conducting plate. Negative entropy can occur even between two perfectly conducting spheres, between two electrically polarizable nanoparticles if there is sufficient anisotropy, between a perfectly conducting sphere and a Drude sphere, and between a sufficiently anisotropic electrically polarizable nanoparticle and a transverse magnetic conducting plate.

Negative values of the Casimir entropy occur quite frequently at low temperatures in arrangements of metallic objects. The physical reason lies either in the dissipative nature of the metals as is the case for the plane-plane geometry or in the geometric form of the objects involved. Examples for the latter are the sphere-plane and the sphere-sphere geometry, where negative Casimir entropies can occur already for perfect metal objects. After appropriately scaling out the size of the objects, negative Casimir entropies of geometric origin are particularly pronounced in the limit of large distances between the objects. We analyze this limit in terms of the different scattering channels and demonstrate how the negativity of the Casimir entropy is related to the polarization mixing arising in the scattering process. If all involved objects have a finite zero-frequency conductivity, the channels involving transverse electric modes are suppressed and the Casimir entropy within the large-distance limit is found to be positive.

We carefully reexamine the conditions of validity for the consistent derivation of the Lifshitz-Matsubara sum formula for the Casimir pressure between metallic plane mirrors. We recover the usual expression for the lossy Drude model but not for the lossless plasma model. We give an interpretation of this new result in terms of the modes associated with the Foucault currents, which play a role in the limit of vanishing losses, in contrast to common expectations.

The potential energy curves, permanent and transition dipole moments, and the static dipolar polarizability, of molecular ions composed of one alkali-metal atom and a strontium ion are determined with a quantum chemistry approach. The molecular ions are treated as effective two-electron systems and are treated using effective core potentials including core polarization, large gaussian basis sets, and full configuration interaction. In the perspective of upcoming experiments aiming at merging cold atom and cold ion traps, possible paths for radiative charge exchange, photoassociation of a cold lithium or rubidium atom and a strontium ion are discussed, as well as the formation of stable molecular ions.

We measure the Casimir force between a gold sphere and a silicon plate with nanoscale, rectangular corrugations with a depth comparable to the separation between the surfaces. In the proximity force approximation (PFA), both the top and bottom surfaces of the corrugations contribute to the force, leading to a distance dependence that is distinct from a flat surface. The measured Casimir force is found to deviate from the PFA by up to 10%, in good agreement with calculations based on scattering theory that includes both geometry effects and the optical properties of the material.

A new potential energy surface for the electronic ground state of the simplest triatomic anion H(3) (-) is determined for a large number of geometries. Its accuracy is improved at short and large distances compared to previous studies. The permanent dipole moment surface of the state is also computed for the first time. Nine vibrational levels of H(3) (-) and 14 levels of D(3) (-) are obtained, bound by at most approximately 70 and approximately 126 cm(-1), respectively. These results should guide the spectroscopic search of the H(3) (-) ion in cold gases (below 100K) of molecular hydrogen in the presence of H(-) ions.

The B1A1 electronic state of silylene (SiH2) is the second excited singlet state of the molecule and, like the analogous c state of methylene (CH2), it is quasilinear with symmetry 1sigmag+ at linearity. This state dissociates to Si(1D) + H2(1sigmag+). At equilibrium, the B state of SiH2 has an energy that we calculate to be 0.71 eV above that of the dissociation products. However, there is a barrier to dissociation that allows quasibound rovibrational levels to occur, and some have been observed recently [Y. Muramoto et al., J. Chem. Phys. 122, 154302 (2005)]. Starting with our analytical ab initio potential-energy surface, we adjusted it in a fitting to the experimental term values in order to determine the optimum potential-energy function in the bound region. This potential has a C2v equilibrium structure with a SiH bond length of 1.459 angstroms and a bond angle of 165.4 degrees; the barrier to linearity is only 129 cm(-1). Using the optimized potential-energy surface we calculate B-state term values, and using our calculated y and z dipole moment surfaces, we simulate the rotation-vibration spectrum of the state in order to assist in the detection of the matrix isolation spectrum.