arXiv subjects

Iver Brevik

Publications and source records attributed to Iver Brevik.

At least 55 records · Page 3Linked to original sources

arXiv2018

Analysis of Recent Interpretations of the Abraham-Minkowski Problem

The 100-year-long problem concerning the correct form of the electromagnetic energy-momentum tensor in continuous media (usually called the Abraham-Minkowski problem) continues to attract interest. We provide a critical analysis of interpretations presented in the literature on this topic recently, in two cases - one real experiment on radiation pressure A. Kundu {\it et al.}, Scient. Reports {\bf 7}, 42538 (2017), and one computer experiment M. Partanen {\it et al.}, Phys. Rev. A {\bf 95}, 063850 (2017).

physics.optics↗

arXiv2018

Remarks on the Casimir force for magnetodielectric media

Boyer showed that a perfect electrically conducting slab repels a perfect magnetically conducting slab, in contrast to the attractive Casimir force between two identical perfect electrically/magnetically conducting slabs. To gain insight for the difference between the Boyer force and the Casimir force, we present the derivation of the Boyer force using the stress tensor method and then using the method of variation in dielectric. The Green dyadic, in terms of electric and magnetic Green's functions, is presented for an electric medium filling half of space and another magnetic medium filling another half of space such that the two half-spaces are parallel and separated by a distance $a$. We make the observation that the spectral distribution of scattering in a Boyer cavity is that of Fermi-Dirac type, while the spectral distribution of scattering in a Casimir cavity is that of Bose-Einstein type. Based on this observation we conclude that the difference between the Boyer force and the Casimir force is governed by the statistics of the possible scattering in the respective cavities.

physics.class-ph↗

arXiv2018

Repulsive Casimir Force

The Casimir force between two parallel thick plates, one perfectly dielectric, the other purely magnetic, has been calculated long ago by Boyer [T. H. Boyer, Phys. Rev. A {\bf 9}, 2078 (1974)]. Its most characteristic property is that it is repulsive. The problem is actually delicate and counterintuitive, since it implies, for instance, that in the boundary layer of the electric plate the square $E^2$ of the electric field becomes a negative quantity. In the present paper we analyze the problem by first considering the simple harmonic oscillator model introduced by us earlier [J. S. Høye {\it et al.}, Phys. Rev. E {\bf 67}, 056116 (2003); Phys. Rev. A {\bf 94}, 032113 (2016)]. Extension of this model shows how the repulsive behavior can be understood on a microscopic basis, due to the duality between canonical and mechanical momenta in presence of the electromagnetic vector potential. This duality corresponds to the TM and TE modes in electrodynamics. We analyze the generalized Boyer case where the permittivities and permeabilities of the parallel plates are arbitrary. In this respect we first find the induced interaction between a pair of particles with given electric and magnetic polarizabilities and then find it for a pair of parallel plates. The method used for our evaluations is the statistical mechanical one that we have introduced and applied earlier. Whether the pair of particles or plates attract or repel each other depends on their polarizabilities or permittivities and permeabilities respectively. For equal particles or equal plates there is always attraction.

quant-ph↗

arXiv2018

Radiation Forces and the Abraham-Minkowski Problem

Recent years have witnessed a number of beautiful experiments in radiation optics. Our purpose with this mini-review is to highlight some developments of radiation pressure physics in general, and thereafter to focus on the importance of the mentioned experiments in regard to the classic Abraham-Minkowski problem. That means, what is the "correct" expression for electromagnetic momentum density in continuous matter. In our opinion one sees relatively often that authors over-interpret the importance of their experimental findings with respect to the momentum problem. Most of these experiments are actually unable to discriminate between these energy-momentum tensors at all, since they can be easily described in terms of force expressions that are common for Abraham and Minkowski. Moreover, we emphasize the inherent ambiguity in applying formal conservation principles to the radiation field in a dielectric, the reason being that the electromagnetic field in matter is only a subsystem which has to be supplemented by the mechanical subsystem to be closed. Finally, we make some suggestions regarding the connection between macroscopic electrodynamics and the Casimir effect, suggesting that there is a limit for the magnitudes of cutoff parameters in QFT related to surface tension in ordinary hydromechanics.

physics.class-ph↗

arXiv2018

Fluid sensitive nanoscale switching with quantum levitation controlled by $α$-Sn/$β$-Sn phase transition

We analyse the Lifshitz pressure between silica and tin separated by a liquid mixture of bromobenzene and chlorobenzene. We show that the phase transition from semimetallic $α$-Sn to metallic $β$-Sn can switch Lifshitz forces from repulsive to attractive. This effect is caused by the difference in dielectric functions of $α$-Sn and $β$-Sn, giving both attractive and repulsive contributions to the total Lifshitz pressure at different frequency regions controlled by the composition of the intervening liquid mixture. In this way, one may be able to produce phase transition-controlled quantum levitation in liquid medium.

cond-mat.other↗

arXiv2018

Casimir Energies for Isorefractive or Diaphanous Balls

It is familiar that the Casimir self-energy of a homogeneous dielectric ball is divergent, although a finite self-energy can be extracted through second order in the deviation of the permittivity from the vacuum value. The exception occurs when the speed of light inside the spherical boundary is the same as that outside, so the self-energy of a perfectly conducting spherical shell is finite, as is the energy of a dielectric-diamagnetic sphere with $\varepsilonμ=1$, a so-called isorefractive or diaphanous ball. Here we re-examine that example, and attempt to extend it to an electromagnetic $δ$-function sphere, where the electric and magnetic couplings are equal and opposite. Unfortunately, although the energy expression is superficially ultraviolet finite, additional divergences appear that render it difficult to extract a meaningful result in general, but some limited results are presented.

hep-th↗

arXiv2018

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↗

arXiv2017

Casimir energy of Sierpinski triangles

Using scaling arguments and the property of self-similarity we derive the Casimir energies of Sierpinski triangles and Sierpinski rectangles. The Hausdorff-Besicovitch dimension (fractal dimension) of the Casimir energy is introduced and the Berry-Weyl conjecture is discussed for these geometries. We propose that for a class of fractals, comprising of compartmentalized cavities, it is possible to establish a finite value to the Casimir energy even while the Casimir energy of the individual cavities consists of divergent terms.

hep-th↗

arXiv2017

Effective Polarisability Models

Theories for the effective polarisability of a small particle in a medium are presented using different levels of approximation: we consider the virtual cavity, real cavity and the hard-sphere models as well as a continuous interpolation of the latter two. We present the respective hard-sphere and cavity radii as obtained from density-functional simulations as well as the resulting effective polarisabilities at discrete Matsubara frequencies. This enables us to account for macroscopic media in van der Waals interactions between molecules in water and their Casimir-Polder interaction with an interface.

physics.chem-ph↗

arXiv2017

Casimir-Polder energy for axially symmetric systems

We develop a formalism suitable for studying Maxwell's equations in the presence of a medium that is axially symmetric, in particular with respect to Casimir-Polder interaction energies. As an application, we derive the Casimir-Polder interaction energy between an electric $δ$-function plate and an anisotropically polarizable molecule for arbitrary orientations of the principal axes of polarizabilities of the molecule. We show that in the perfect conductor limit for the plate the interaction is insensitive to the orientation of the polarizabilities of the molecule. We obtain the Casimir-Polder energy between an electric $δ$-function sphere and an anisotropically polarizable molecule, again for arbitrary orientations of the principal axes of polarizabilities of the molecule. We derive results when the polarizable molecule is either outside the sphere, or inside the sphere. We present the perfectly conducting limit for the $δ$-function sphere, and also the interaction energy for the special case when the molecule is at the center of the sphere. Our general proposition is that the Casimir-Polder energy between a dielectric body with axial symmetry and an unidirectionally polarizable molecule placed on the axis with its polarizability parallel to the axis gets non-zero contribution only from the $m=0$ azimuth mode. This feature in conjunction with the property that the $m=0$ mode separates into transverse electric and transverse magnetic modes allows the evaluation of Casimir-Polder energies for axially symmetric systems in a relatively easy manner.

physics.class-ph↗

arXiv2017

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↗

arXiv2017

Viscous Cosmology for Early- and Late-Time Universe

From a hydrodynamicist's point of view the inclusion of viscosity concepts in the macroscopic theory of the cosmic fluid would appear most natural, as an ideal fluid is after all an abstraction (excluding special cases such as superconductivity). Making use of modern observational results for the Hubble parameter plus standard Friedmann formalism, we may extrapolate the description of the universe back in time up to the inflationary era, or we may go to the opposite extreme and analyze the probable ultimate fate of the universe. In this review we discuss a variety of topics in cosmology when it is enlarged in order to contain a bulk viscosity. Various forms of this viscosity, when expressed in terms of the fluid density or the Hubble parameter, are discussed. Furthermore, we consider homogeneous as well as inhomogeneous equations of state. We investigate viscous cosmology in the early universe, examining the viscosity effects on the various inflationary observables. Additionally, we study viscous cosmology in the late universe, containing current acceleration and the possible future singularities, and we investigate how one may even unify inflationary and late-time acceleration. Finally, we analyze the viscosity-induced crossing through the quintessence-phantom divide, we examine the realization of viscosity-driven cosmological bounces, and we briefly discuss how the Cardy-Verlinde formula is affected by viscosity.

gr-qc↗

arXiv2017

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↗

arXiv2017

Entropy Production in a Lepton-Photon Universe

We look at the entropy production during the lepton era in the early Universe by using a model where we exclude all particles except the leptons and photons. We assume a temperature dependent viscosity as calculated recently by one of us (Husdal 2016) with use of relativistic kinetic theory. We consider only the bulk viscosity, the shear viscosity being omitted because of spatial isotropy. The rate of entropy production is highest just before the neutrinos decouple. Our results show that the increase in entropy during the lepton era is quite small, about 0.071 % at a decoupling temperature of $T=10^{10}~\mathrm{K}$. This result is slightly smaller than that obtained earlier by Caderni and Fabbri (1977). After the neutrino decoupling, when the Universe has entered the photon era, kinetic-theory arguments no longer support the appearance of a bulk viscosity. At high temperatures and a stable particle ratio, entropy production (d$σ$/d$T$) goes as $T^{-8}$, with the total entropy ($Δσ$) increasing as $T^{-7}$. These rates go slightly down just before the neutrinos decouple, where $Δσ\propto T^{-6.2}$.

astro-ph.CO↗

arXiv2016

Characteristic Properties of Two Different Viscous Cosmology Models for the Future Universe

We analyze characteristic properties of two different cosmological models: (i) a one-component dark energy model where the bulk viscosity $ζ$ is associated with the fluid as a whole, and (ii) a two-component model where $ζ$ is associated with a dark matter component $ρ_{\rm m}$ only, the dark energy component considered inviscid. Shear viscosity is omitted. We assume throughout the simple equation of state $p=wρ$, with $w$ a constant. In the one-component model we consider two possibilities, either to take $ζ$ proportional to the scalar expansion (equivalent to the Hubble parameter), in which case the evolution becomes critically dependent on the value of the small constant $α=1+w$ and the magnitude of $ζ$. Second, we consider the case $ζ=~$const., where a de Sitter final stage is reached in the future. In the two-component model we consider only the case where the dark matter viscosity $ζ_{\rm m}$ is proportional to the square of $ρ_{\rm m}$, where again a de Sitter form is found in the future. In this latter case the formalism is supplemented by a phase space analysis. As a general result of our considerations we suggest that a value $ζ_0\sim 10^6~$Pa s for the present viscosity is reasonable, and that the two-component model seems to be favored.

gr-qc↗

arXiv2016

Minkowski Momentum Resulting from a Vacuum-Medium Mapping Procedure, and a Brief Review of Minkowski Momentum Experiments

A discussion is given on the interpretation and physical importance of the Minkowski momentum in macroscopic electrodynamics (essential for the Abraham-Minkowski problem). We focus on the following two facets: (1) Adopting a simple dielectric model where the refractive index $n$ is constant, we demonstrate by means of a mapping procedure how the electromagnetic field in a medium can be mapped into a corresponding field in vacuum. This mapping was presented many years ago [I. Brevik and B. Lautrup, Mat. Fys. Medd. Dan. Vid. Selsk {\bf 38}(1), 1 (1970)], but is apparently not well known. A characteristic property of this procedure is that it shows how natural the Minkowski energy-momentum tensor fits into the canonical formalism. Especially the spacelike character of the electromagnetic total four-momentum for a radiation field (implying negative electromagnetic energy in some inertial frames), so strikingly demonstrated in the Cherenkov effect, is worth attention. (2) Our second objective is to give a critical analysis of some recent experiments on electromagnetic momentum. Care must here be taken in the interpretations: it is easy to be misled and conclude that an experiment is important for the energy-momentum problem, while what is demonstrated experimentally is merely the action of the Abraham-Minkowski force acting in surface layers or inhomogeneous regions. The Abraham-Minkowski force is common for the two energy-momentum tensors and carries no information about field momentum. As a final item, we propose an experiment that might show the existence of the Abraham force at high frequencies. This would eventually be a welcome optical analogue to the classic low-frequency 1975 Lahoz-Walker experiment.

quant-ph↗

arXiv2016

Casimir energies of self-similar plate configurations

We construct various self-similar configurations using parallel $δ$-function plates and show that it is possible to evaluate the Casimir interaction energy of these configurations using the idea of self-similarity alone. We restrict our analysis to interactions mediated by a scalar field, but the extension to electromagnetic field is immediate. Our work unveils an easy and powerful method that can be easily employed to calculate the Casimir energies of a class of self-similar configurations. As a highlight, in an example, we determine the Casimir interaction energy of a stack of parallel plates constructed by positioning $δ$-function plates at the points constituting the Cantor set, a prototype of a fractal. This, to our knowledge, is the first time that the Casimir energy of a fractal configuration has been reported. Remarkably, the Casimir energy of some of the configurations we consider turn out to be positive, and a few even have zero Casimir energy. For the case of positive Casimir energy that is monotonically decreasing as the stacking parameter increases the interpretation is that the pressure of vacuum tends to inflate the infinite stack of plates. We further support our results, derived using the idea of self-similarity alone, by rederiving them using the Green's function formalism. These expositions gives us insight into the connections between the regularization methods used in quantum field theories and regularized sums of divergent series in number theory.

hep-th↗

arXiv2016

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↗