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Kimball A. Milton

Publications and source records attributed to Kimball A. Milton.

At least 37 records · Page 2Linked to original sources

Casimir-Polder forces in inhomogeneous backgrounds

Casimir-Polder interactions are considered in an inhomogeneous, dispersive background. We consider both the interaction between a polarizable atom and a perfectly conducting wall, and between such an atom and a plane interface between two different inhomogeneous dielectric media. Renormalization is achieved by subtracting the interaction with the local inhomogeneous medium by itself. The results are expressed in general form, and generalize the Dzyaloshinskii-Lifshitz-Pitaevskii interaction between a spatially homogeneous dielectric interface and a polarizable atom.

quant-ph↗

The Statistical Atom

This review is the updated and enlarged version of a talk delivered by J. S. on the occasion of the 1982 meeting of Nobel laureates at Lindau, and of talks given by B.-G. E. at several West German universities and Max Planck institutes in 1984.

quant-ph↗

Quantum Electromagnetic Stress Tensor in an Inhomogeneous Medium

Continuing a program of examining the behavior of the vacuum expectation value of the stress tensor in a background which varies only in a single direction, we here study the electromagnetic stress tensor in a medium with permittivity depending on a single spatial coordinate, specifically, a planar dielectric half-space facing a vacuum region. There are divergences occurring that are regulated by temporal and spatial point-splitting, which have a universal character for both transverse electric and transverse magnetic modes. The nature of the divergences depends on the model of dispersion adopted. And there are singularities occurring at the edge between the dielectric and vacuum regions, which also have a universal character, depending on the structure of the discontinuities in the material properties there. Remarks are offered concerning renormalization of such models, and the significance of the stress tensor. The ambiguity in separating "bulk" and "scattering" parts of the stress tensor is discussed.

hep-th↗

Distance-dependent sign-reversal in the Casimir-Lifshitz torque

The Casimir-Lifshitz torque between two biaxially polarizable anisotropic planar slabs is shown to exhibit a non-trivial sign-reversal in its rotational sense. The critical distance $a_c$ between the slabs that marks this reversal is characterized by the frequency $ω_c\!\sim \!c/2a_c$ at which the in-planar polarizabilities along the two principal axes are equal. The two materials seek to align their principal axes of polarizabilities in one direction below $a_c$, while above $a_c$ their axes try to align rotated perpendicular relative to their previous minimum energy orientation. The sign-reversal disappears in the nonretarded limit. Our perturbative result, derived for the case when the differences in the relative polarizabilities are small, matches excellently with the exact theory for uniaxial materials. We illustrate our results for black phosphorus and phosphorene.

cond-mat.mes-hall↗

Electromagnetic $δ$-function sphere

We develop a formalism to extend our previous work on the electromagnetic $δ$-function plates to a spherical surface. The electric ($λ_e$) and magnetic ($λ_g$) couplings to the surface are through $δ$-function potentials defining the dielectric permittivity and the diamagnetic permeability, with two anisotropic coupling tensors. The formalism incorporates dispersion. The electromagnetic Green's dyadic breaks up into transverse electric and transverse magnetic parts. We derive the Casimir interaction energy between two concentric $δ$-function spheres in this formalism and show that it has the correct asymptotic flat plate limit. We systematically derive expressions for the Casimir self-energy and the total stress on a spherical shell using a $δ$-function potential, properly regulated by temporal and spatial point-splitting, which are different from the conventional temporal point-splitting. In strong coupling, we recover the usual result for the perfectly conducting spherical shell but in addition, there is an integrated curvature-squared divergent contribution. For finite coupling, there are additional divergent contributions; in particular, there is a familiar logarithmic divergence occurring in the third order of the uniform asymptotic expansion that renders it impossible to extract a unique finite energy except in the case of an isorefractive sphere, which translates into $λ_g=-λ_e$.

hep-th↗

Lifshitz interaction can promote ice growth at water-silica interfaces

At air-water interfaces, the Lifshitz interaction by itself does not promote ice growth. On the contrary, we find that the Lifshitz force promotes the growth of an ice film, up to 1-8 nm thickness, near silica-water interfaces at the triple point of water. This is achieved in a system where the combined effect of the retardation and the zero frequency mode influences the short-range interactions at low temperatures, contrary to common understanding. Cancellation between the positive and negative contributions in the Lifshitz spectral function is reversed in silica with high porosity. Our results provide a model for how water freezes on glass and other surfaces.

cond-mat.other↗

Presence of negative entropies in Casimir interactions

Negative entropy in connection with the Casimir effect at uniform temperature is a phenomenon rooted in the circumstance that one is describing a nonclosed system, or only part of a closed system. In this paper we show that the phenomenon is not necessarily restricted to electromagnetic theory, but can be derived from the quantum theory of interacting harmonic oscillators, most typically two oscillators interacting not directly but indirectly via a third one. There are two such models, actually analogous to the transverse magnetic (TM) and transverse electric (TE) modes in electrodynamics. These mechanical models in their simplest version were presented some years ago, by J. S. Høye et al., Physical Review E {\bf 67}, 056116 (2003). In the present paper we re-emphasize the physical significance of the mechanical picture, and extend the theory so as to include the case where there are several mediating oscillators, instead of only one. The TE oscillator exhibits negative entropy. Finally, we show explicitly how the interactions via the electromagnetic field contain the two oscillator models.

quant-ph↗

Negative Entropies in Casimir and Casimir-Polder Interactions

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

quant-ph↗

Stress tensor for a scalar field in a spatially varying background potential: Divergences, "renormalization," anomalies, and Casimir forces

Motivated by a desire to understand quantum fluctuation energy densities and stress within a spatially varying dielectric medium, we examine the vacuum expectation value for the stress tensor of a scalar field with arbitrary conformal parameter, in the background of a given potential that depends on only one spatial coordinate. We regulate the expressions by incorporating a temporal-spatial cutoff in the (imaginary) time and transverse-spatial directions. The divergences are captured by the zeroth- and second-order WKB approximations. Then the stress tensor is "renormalized" by omitting the terms that depend on the cutoff. The ambiguities that inevitably arise in this procedure are both duly noted and restricted by imposing certain physical conditions; one result is that the renormalized stress tensor exhibits the expected trace anomaly. The renormalized stress tensor exhibits no pressure anomaly, in that the principle of virtual work is satisfied for motions in a transverse direction. We then consider a potential that defines a wall, a one-dimensional potential that vanishes for $z<0$ and rises like $z^α$, $α>0$, for $z>0$. The full finite stress tensor is computed numerically for the two cases where explicit solutions to the differential equation are available, $α=1$ and 2. The energy density exhibits an inverse linear divergence as the boundary is approached from the inside for a linear potential, and a logarithmic divergence for a quadratic potential. Finally, the interaction between two such walls is computed, and it is shown that the attractive Casimir pressure between the two walls also satisfies the principle of virtual work (i.e., the pressure equals the negative derivative of the energy with respect to the distance between the walls).

hep-th↗

Anisotropic contribution to the van der Waals and the Casimir-Polder energies for CO$_2$ and CH$_4$ molecules near surfaces and thin films

In order to understand why carbon dioxide (CO$_2$) and methane (CH$_4$) molecules interact differently with surfaces, we investigate the Casimir-Polder energy of a linearly polarizable CO$_2$ molecule and an isotropically polarizable CH$_4$ molecule in front of an atomically thin gold film and an amorphous silica slab. We quantitatively analyze how the anisotropy in the polarizability of the molecule influences the van der Waals contribution to the binding energy of the molecule.

cond-mat.mes-hall↗

Casimir-Polder repulsion: Three-body effects

In this paper we study an archetypical scenario in which repulsive Casimir-Polder forces between an atom or molecule and two macroscopic bodies can be achieved. This is an extension of previous studies of the interaction between a polarizable atom and a wedge, in which repulsion occurs if the atom is sufficiently anisotropic and close enough to the symmetry plane of the wedge. A similar repulsion occurs if such an atom passes a thin cylinder or a wire. An obvious extension is to compute the interaction between such an atom and two facing wedges, which includes as a special case the interaction of an atom with a conducting screen possessing a slit, or between two parallel wires. To this end we further extend the electromagnetic multiple-scattering formalism for three-body interactions. To test this machinery we reinvestigate the interaction of a polarizable atom between two parallel conducting plates. In that case, three-body effects are shown to be small, and are dominated by three- and four-scattering terms. The atom-wedge calculation is illustrated by an analogous scalar situation, described in the Appendix. The wedge-wedge-atom geometry is difficult to analyze because this is a scale-free problem. But it is not so hard to investigate the three-body corrections to the interaction between an anisotropic atom or nanoparticle and a pair of parallel conducting cylinders, and show that the three-body effects are very small and do not affect the Casimir-Polder repulsion at large distances between the cylinders. Finally, we consider whether such highly anisotropic atoms needed for repulsion are practically realizable. Since this appears rather difficult to accomplish, it may be more feasible to observe such effects with highly anisotropic nano particles.

quant-ph↗

Geometric origin of negative Casimir entropies: A scattering-channel analysis

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.

quant-ph↗

Casimir torque in weak coupling

In this paper, dedicated to Johan Høye on the occasion of his 70th birthday, we examine manifestations of Casimir torque in the weak-coupling approximation, which allows exact calculations so that comparison with the universally applicable, but generally uncontrolled, proximity force approximation may be made. In particular, we examine Casimir energies between planar objects characterized by $δ$-function potentials, and consider the torque that arises when angles between the objects are changed. The results agree very well with the proximity force approximation when the separation distance between the objects is small compared with their sizes. In the opposite limit, where the size of one object is comparable to the separation distance, the shape dependence starts becoming irrelevant. These calculations are illustrative of what to expect for the torques between, for example, conducting planar objects, which eventually should be amenable to both improved theoretical calculation and experimental verification.

hep-th↗

Investigations of the torque anomaly in an annular sector. II. Global calculations, electromagnetic case

Recently, it was suggested that there was some sort of breakdown of quantum field theory in the presence of boundaries, manifesting itself as a torque anomaly. In particular, Fulling et al. used the finite energy-momentum-stress tensor in the presence of a perfectly conducting wedge, calculated many years ago by Deutsch and Candelas, to compute the torque on one of the wedge boundaries, where the latter was cutoff by integrating the torque density down to minimum lower radius greater than zero. They observed that that torque is not equal to the negative derivative of the energy obtained by integrating the energy density down to the same minimum radius. This motivated a calculation of the torque and energy in an annular sector obtained by the intersection of the wedge with two coaxial cylinders. In a previous paper we showed that for the analogous scalar case, which also exhibited a torque anomaly in the absence of the cylindrical boundaries, the point-split regulated torque and energy indeed exhibit an anomaly, unless the point-splitting is along the axis direction. In any case, because of curvature divergences, no unambiguous finite part can be extracted. However, that ambiguity is linear in the wedge angle; if the condition is imposed that the linear term be removed, the resulting torque and energy is finite, and exhibits no anomaly. In this paper, we demonstrate the same phenomenon takes place for the electromagnetic field, so there is no torque anomaly present here either. This is a nontrivial generalization, since the anomaly found by Fulling et al. is linear for the Dirichlet scalar case, but nonlinear for the conducting electromagnetic case.

hep-th↗

Investigations of the torque anomaly in an annular sector. I. Global calculations, scalar case

In an attempt to understand a recently discovered torque anomaly in quantum field theory with boundaries, we calculate the Casimir energy and torque of a scalar field subject to Dirichlet boundary conditions on an annular sector defined by two coaxial cylinders intercut by two planes through the axis. In this model the particularly troublesome divergence at the cylinder axis does not appear, but new divergences associated with the curved boundaries are introduced. All the divergences associated with the volume, the surface area, the corners, and the curvature are regulated by point separation either in the direction of the axis of the cylinder or in the (Euclidean) time; the full divergence structure is isolated, and the remaining finite energy and torque are extracted. Formally, only the regulator based on axis splitting yields the expected balance between energy and torque. Because of the logarithmic curvature divergences, there is an ambiguity in the linear dependence of the energy on the wedge angle; if the terms constant and linear in this angle are removed by a process of renormalization, the expected torque-energy balance is preserved.

hep-th↗

Casimir interaction energies for magneto-electric δ-function plates

We present boundary conditions for the electromagnetic fields on a δ-function plate, having both electric and magnetic properties, sandwiched between two magneto-electric semi-infinite half spaces. The optical properties for an isolated δ-function plate are shown to be independent of the longitudinal material properties of the plate. The Casimir-Polder energy between an isotropically polarizable atom and a magneto-electric δ-function plate is attractive for a purely electric δ-function plate, repulsive for a purely magnetic δ-function plate, and vanishes for the simultaneous perfect conductor limit of both electric and magnetic properties of the δ-function plate. The interaction energy between two identical δ-function plates is always attractive. It can be attractive or repulsive when the plates have electric and magnetic properties interchanged and reproduces Boyer's result for the interaction energy between perfectly conducting electric and magnetic plates. The change in the Casimir-Polder energy in the presence of a δ-function plate on a magneto-electric substrate is substantial when the substrate is a weak dielectric.

hep-th↗

Three-body Casimir-Polder interactions

As part of our program to develop the description of three-body effects in quantum vacuum phenomena, we study the three-body interaction of two anisotropically polarizable atoms with a perfect electrically conducting plate, a generalization of earlier work. Three- and four-scattering effects are important, and lead to nonmonotonic behavior.

quant-ph↗

Electromagnetic semitransparent $δ$-function plate: Casimir interaction energy between parallel infinitesimally thin plates

We derive boundary conditions for electromagnetic fields on a $δ$-function plate. The optical properties of such a plate are shown to necessarily be anisotropic in that they only depend on the transverse properties of the plate. We unambiguously obtain the boundary conditions for a perfectly conducting $δ$-function plate in the limit of infinite dielectric response. We show that a material does not "optically vanish" in the thin-plate limit. The thin-plate limit of a plasma slab of thickness $d$ with plasma frequency $ω_p^2=ζ_p/d$ reduces to a $δ$-function plate for frequencies ($ω=iζ$) satisfying $ζd \ll \sqrt{ζ_p d} \ll 1$. We show that the Casimir interaction energy between two parallel perfectly conducting $δ$-function plates is the same as that for parallel perfectly conducting slabs. Similarly, we show that the interaction energy between an atom and a perfect electrically conducting $δ$-function plate is the usual Casimir-Polder energy, which is verified by considering the thin-plate limit of dielectric slabs. The "thick" and "thin" boundary conditions considered by Bordag are found to be identical in the sense that they lead to the same electromagnetic fields.

hep-th↗