Iver Brevik - Profile on Academia.edu (original) (raw)

Papers by Iver Brevik

Physics Letters B, May 1, 1999

Mass and decay spectra are calculated for quantum massive exitations of a piecewise uniform boson... more Mass and decay spectra are calculated for quantum massive exitations of a piecewise uniform bosonic string. The physical meaning of the critical temperatures characterising the radiation in the decay of a massive microstate in string theory is discussed. The composite string, in which the (relativistic) string is assumed to consist of two (or more) separately uniform pieces, is a variant of the conventional theory. This theory has been generalized and further studied from various points of view [1] - . The composite string model may serve as a useful two-dimensional field theoretical model. Usually, a two-dimensional field theory describes a particular classical solution of string theory by constructing a matter system. The vanishing total central charge of a system ensures the existence of a BRST operator, playing a crucial role in world-sheet and space-time gauge invariance. Such an operator can be interpreted as a generator of linearized gauge transformations, mixing ghosts and matter. It is very important that two-dimensional topological field theories (like ordinary string models) can sometimes be given space-time interpretations for which the usual decoupling of ghosts and matter does not hold. For example, three-dimensional Chern-Simons gauge theory can arise as a string theory . Relations between gauge fields and strings present fascinating and unanswered questions. The full answer to these questions is of great importance for theoretical physics. It will provide the true gauge degrees of freedom of the fundamental string theories, and therefore also of gravity . 1. In this paper we consider the motion of a two-piece classical string in flat D-dimensional space-time. Following the notation in we let

Physical review, Apr 19, 2019

The repulsive nature of the static Casimir force between two half-spaces, one perfectly dielectri... more The repulsive nature of the static Casimir force between two half-spaces, one perfectly dielectric and the other purely magnetic, has been known since Boyer's work [T. H. Boyer, Phys. Rev. A 9, 2078]. We here analyze the corresponding friction force in the magnetodielectric case. Our main method is that of quantum mechanical statistical mechanics. The basic model we introduce is a harmonic oscillator model: an electric dipole oscillating in the x direction and a magnetic one oscillating in the y direction, while their separation is in the z direction. This is then extended to particles with isotropic polarizabilities. We evaluate the friction force in a variety of cases: force between moving particles, between a moving particle and a half-plane, and between halfspaces sliding against each other. At the end explicit results are obtained both for finite and zero temperatures. We restrict ourselves to the nonretarded limit.

International Journal of Modern Physics, Apr 30, 2022

In the more than 100 years-old Abraham-Minkowski problem in macroscopic electrodynamics, the issu... more In the more than 100 years-old Abraham-Minkowski problem in macroscopic electrodynamics, the issue of how to observe the so-called Abraham term f Aterm = [(εµ -1)/c 2 ]∂/∂t(E × H) has been a main point. Such a measurement is rather delicate. Recent years have seen a number of beautiful experiments in radiation optics, but these experiments usually give no information about the Abraham term as this term simply fluctuates out. So one is left with somewhat indirect verifications of this force, as in the radiation pressure of Jones et al. in the 1950's, testing the radiation pressure on a mirror immersed in a dielectric liquid. Now, there is a different way to test the existence of f Aterm , namely to work with low (quasi-stationary) frequencies enabling one to observe the sinusoidal variation of the force directly. These kind of experiments were actually done by Walker et al. in 1he 1970's, using BaTiO3 as a high-frequency dielectric (permittivity ε ∼ 3600). The outcome of these experiments was convincing. Now, in recent years there have appeared dielectric materials with giant permittivities, of order 10 5 or even higher. It is therefore natural to consider the idea of Walker et al. anew, in order to test if this demanding experiment can be facilitated and give better accuracy. That is the main topic of the present paper. The positive outcome of these kinds of experiments clearly supports the Abraham energy-momentum tensor at low frequencies. The Minkowski tensor is unable to predict a torque at all. The low-frequency and the high-frequency regimes are in this way highly contrasted, as it is obvious that in optical experiments the Minkowski tensor is by far the simplest and most convenient one to use. We end this note by commenting upon the use of the Einstein-Laub tensor (1908) in explaining this experiment, and discuss also the influence from air friction.

International Journal of Modern Physics D, Aug 1, 2007

An explicit calculation is given of the entropy/energy ratio for the TM modes of the electromagne... more An explicit calculation is given of the entropy/energy ratio for the TM modes of the electromagnetic field in the half Einstein universe. This geometry provides a mathematically convenient and physically instructive example of how the electromagnetic and thermodynamic quantities behave as a function of the nondimensional parameter δ = 1/2πaT , a being the scale factor and T the temperature. On physical grounds (related to the relaxation time), it is the case of small δ's that is pertinent to thermodynamics. We find that as long as δ is small, the entropy/energy ratio behaves in the same way as for the TE modes. The entropy is thus bounded. The present kind of formalism makes it convenient to study also the influence from frequency dispersion. We discuss an example where a sharp cutoff dispersion relation can in principle truncate the electromagnetic oscillations in the Einstein cavity such that only the lowest mode survives.

International Journal of Geometric Methods in Modern Physics, Aug 8, 2018

We propose to describe the acceleration of the universe by introducing a model of two coupled flu... more We propose to describe the acceleration of the universe by introducing a model of two coupled fluids. We focus on the accelerated expansion at the early stages. The inflationary expansion is described in terms of a van der Waals equation of state for the cosmic fluid, when account is taken of bulk viscosity. We assume that there is a weak interaction between the van der Waals fluid and the second component (matter). The gravitational equations for the energy densities of the two components are solved for a homogeneous and isotropic Friedmann-Robertson-Walker universe, and analytic expressions for the Hubble parameter are obtained. The slow-roll parameters, the spectral index, and the tensor-to-scalar ratio are calculated and compared with the most recent astronomical data from the Planck satellite. Given reasonable restriction on the parameters, the agreement with observations is favorable.

Physical review, Jun 6, 2002

As recently found by Youm [hep-th/0201268], the entropy of the universe will no longer be express... more As recently found by Youm [hep-th/0201268], the entropy of the universe will no longer be expressible in the conventional Cardy-Verlinde form if one relaxes the radiation dominance state equation and instead assumes a more general equation of the form p = (γ -1)ρ, with γ a constant. We show that Youm's generalized entropy formula remains valid when the cosmic fluid is no longer ideal, but is allowed to possess a constant bulk viscosity ζ. We supply our analysis with some numerical estimates, thus calculating the scale factor a(t) for a k = 0 universe, and also calculate via a perturbative expansion in ζ the magnitude of the viscosity-induced correction to the scale factor if the universe is radiation dominated.

Physical review, Sep 9, 2019

In analog gravity the recent experiment of Drori et al. [Phys. Rev. Lett. 122, 010404 (2019)] is ... more In analog gravity the recent experiment of Drori et al. [Phys. Rev. Lett. 122, 010404 (2019)] is impressive, as it shows how the emission of two Hawking quanta emitted in opposite directions lead to measurable consequences in the medium's rest system in a straightforward way. This result raises however the following problem: how can this experiment be explained in terms of classical electrodynamics? There must necessarily exist such an explanation (the experiment is after all classical); otherwise classical electrodynamics would be an incomplete theory. This is the main topic of the present paper. We propose that the measured effect is a demonstration of the spacelike character of the Minkowski four-momentum. Moreover, we extend the discussion by analyzing a Gedanken experiment (making use of the Kerr effect as a formal agency), to illustrate the transition from subluminal to superluminal phenomena in a straightforward way. Finally, we emphasize the close relationship that exists between the spacelike Minkowski momentum and the anomalous Doppler effect.

International Journal of Modern Physics, May 10, 2003

The holographic principle in a radiation dominated universe is extended to incorporate the case o... more The holographic principle in a radiation dominated universe is extended to incorporate the case of a bulk-viscous cosmic fluid. This corresponds to a nonconformally invariant theory. Generalization of the Cardy-Verlinde entropy formula to the viscous case appears to be possible from a formal point of view, although we question on physical grounds the manner in which the Casimir energy is evaluated in this case. Also, we consider an observation recently made by Youm, namely that the entropy of the universe is no longer expressible in the conventional Cardy-Verlinde form if one relaxes the radiation dominance equation of state and instead merely assumes that the pressure is proportional to the energy density. We show that Youm's generalized entropy formula remains valid when the cosmic fluid is no longer ideal, but endowed with a constant bulk viscosity.

Physical review, Sep 6, 2016

We construct various self-similar configurations using parallel δ-function plates and show that i... more 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 the 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.

Physical review, May 26, 2017

From energy considerations there is reason to expect that the work done by Casimir forces during ... more From energy considerations there is reason to expect that the work done by Casimir forces during a slow displacement of the parallel plates reflects the free energy of the surface tension of the adjacent surfaces. We show this explicitly, for a one-component ionic fluid or plasma with q c as ionic charge, where the particles are neutralized by a uniform continuous oppositely charged background. For two equal half-planes, the surface-associated free energy for one half-plane turns out to be just one half of the total Casimir energy for the conventional Casimir setup. We also comment, from a wider perspective, on the intriguing possibility that knowledge about the magnitude of the surface tension coefficient obtained from statistical mechanics or experiments may give insight into the value of the conventional cutoff time-splitting parameter τ = tt ′ occurring in quantum field theory. A simple analysis suggests that the minimal distance τ c is of the order of atomic dimensions, which is a physically natural result.

International Journal of Modern Physics D, Nov 1, 2005

We discuss a modified form of gravity implying that the action contains a power α of the scalar c... more We discuss a modified form of gravity implying that the action contains a power α of the scalar curvature. Coupling with the cosmic fluid is assumed. As equation of state for the fluid, we take the simplest version where the pressure is proportional to the density. Based upon a natural ansatz for the time variation of the scale factor, we show that the equations of motion are satisfied for general α. Also the condition of conservation of energy and momentum is satisfied. Moreover, we investigate the case where the fluid is allowed to possess a bulk viscosity, and find the noteworthy fact that consistency of the formalism requires the bulk viscosity to be proportional to the power (2α -1) of the scalar expansion. In Einstein's gravity, where α = 1, this means that the bulk viscosity is proportional to the scalar expansion. This mathematical result is of physical interest; as discussed recently by the present authors, there exists in principle a viscositydriven transition of the fluid from the quintessence region into the phantom region, implying a future Big Rip singularity.

Physica Scripta, Aug 25, 2010

Finite temperature Casimir theory of the Dirichlet scalar field is developed, assuming that there... more Finite temperature Casimir theory of the Dirichlet scalar field is developed, assuming that there is a conventional Casimir setup in physical space with two infinitely large plates separated by a gap R and in addition an arbitrary number q of extra compacified dimensions. As a generalization of earlier theory, we assume in the first part of the paper that there is a scalar 'refractive index' N filling the whole of the physical space region. After presenting general expressions for free energy and Casimir forces we focus on the low temperature case, as this is of main physical interest both for force measurements and also for issues related to entropy and the Nernst theorem. Thereafter, in the second part we analyze dispersive properties, assuming for simplicity q = 1, by taking into account dispersion associated with the first Matsubara frequency only. The medium-induced contribution to the free energy, and pressure, is calculated at low temperatures.

European Physical Journal D, 2011

This paper is a second in a series devoted to the study of a twooscillator system in linear relat... more This paper is a second in a series devoted to the study of a twooscillator system in linear relative motion (the first one published as a letter in Europhys. Lett. 91, 60003 (2010)). The main idea behind considering this kind of system is to use it as a simple model for Casimir friction. In the present paper we extend our previous theory so as to obtain the change in the oscillator energy to second order in the perturbation, even though we employ first order perturbation theory only. The results agree with, and confirm, our earlier results obtained via different routes. The friction force is finite at finite temperatures, whereas in the case of two oscillators moving with constant relative velocity the force becomes zero at zero temperature, due to slowly varying coupling.

Physical review, Sep 26, 2002

We address the localization of gravity on the Friedmann-Robertson-Walker type brane embedded in e... more We address the localization of gravity on the Friedmann-Robertson-Walker type brane embedded in either AdS 5 or dS 5 bulk space, and derive two definite limits between which the value of the bulk cosmological constant has to lie in order to localize the graviton on the brane. The lower limit implies that the brane should be either dS 4 or 4d Minkowski in the AdS 5 bulk. The positive upper limit indicates that the gravity can be trapped also on curved brane in the dS 5 bulk space. Some implications to recent cosmological scenarios are also discussed.

International Journal of Modern Physics, Mar 20, 2002

The Casimir mutual free energy F for a system of two dielectric concentric nonmagnetic spherical ... more The Casimir mutual free energy F for a system of two dielectric concentric nonmagnetic spherical bodies is calculated, at arbitrary temperatures. Whereas F has recently been evaluated for the special case of metals (refractive index n = ∞), here analogous results are presented for dielectrics, and shown graphically when n = 2.0. Our calculational method relies upon quantum statistical mechanics. The Debye expansions for the Riccati-Bessel functions when carried out to a high order are found to be very useful in practice (thereby overflow/underflow problems are easily avoided), and also to give accurate results even for the lowest values of l. Another virtue of the Debye expansions is that the limiting case of metals becomes quite amenable to an analytical treatment in spherical geometry. We first discuss the zero-frequency TE mode problem from a mathematical viewpoint and then, as physical input, invoke the actual dispersion relations. The result of our analysis, based upon adoption of the Drude dispersion relation as the most correct one at low frequencies, is that the zero-frequency TE mode does not contribute for a metal.

European Physical Journal D, Jun 1, 2012

This work is a continuation of our recent series of papers on Casimir friction, for a pair of par... more This work is a continuation of our recent series of papers on Casimir friction, for a pair of particles of low relative particle velocity. Each particle is modeled as a simple harmonic oscillator. Our basic method, as before, is the use of quantum mechanical statistical mechanics, involving the Kubo formula, at finite temperature. In this work we begin by analyzing the Casimir friction between two particles polarizable in all spatial directions, this being a generalization of our study in EPL 91, 60003 (2010), which was restricted to a pair of particles with longitudinal polarization only. For simplicity the particles are taken to interact via the electrostatic dipole-dipole interaction. Thereafter, we consider the Casimir friction between one particle and a dielectric halfspace, and also the friction between two dielectric half-spaces. Finally, we consider general polarizabilities (beyond the simple one-oscillator form), and show how friction occurs at finite temperature when finite frequency regions of the imaginary parts of polarizabilities overlap.

International Journal of Modern Physics D, Jul 1, 2019

We analyze gravitational waves propagating in an isotropic cosmic fluid endowed with a bulk visco... more We analyze gravitational waves propagating in an isotropic cosmic fluid endowed with a bulk viscosity ζ and a shear viscosity η, assuming these coefficients to vary with fluid density ρ as ρ λ , with λ = 1/2 favored by experimental evidence. We give the general governing equation for the gravitational waves, and focus thereafter on two examples. The first concerns waves in the very late universe, close to the Big Rip, where the fate of the comic fluid is dependent highly on the values of the parameters. Our second example considers the very early universe, the lepton era; the motivation for this choice being that the microscopical bulk viscosity as calculated from statistical mechanics is then at maximum. We find that the gravitational waves on such an underlying medium are damped, having a decay constant equal to the inverse of the conformal Hubble parameter. Our results turn out to be in good agreement with other viscosity-based approaches.

Physical review, Aug 9, 2018

The Casimir force between two parallel thick plates, one perfectly dielectric, the other purely m... more 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 9, 2078]. Its most characteristic property is that it is repulsive. The problem is actually delicate and counterintuitive. In the present paper we analyze the problem by first considering the simple harmonic oscillator model introduced by us earlier [J. S. Høye et al., Phys. Rev. E 67, 056116 (2003); Phys. Rev. A 94, 032113 ( )]. 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.

Physical Review A, Jun 28, 2010

Critical experimental tests of the time-dependent Abraham force in phenomenological electrodynami... more Critical experimental tests of the time-dependent Abraham force in phenomenological electrodynamics are scarce. In this paper we analyze the possibility of making use of intensity-modulated whispering gallery modes in a microresonator for this purpose. Systems of this kind appear attractive, as the strong concentration of electromagnetic fields near the rim of the resonator serves to enhance the Abraham torque exerted by the field. We analyze mainly spherical resonators, although as an introductory step we consider also the cylinder geometry. The order of magnitude of the Abraham torques are estimated by inserting reasonable and common values for the various input parameters. As expected, the predicted torques turn out to be very small, although probably not beyond any reach experimentally. Our main idea is essentially a generalization of the method used by G. B. Walker et al. [Can. J. Phys. 53, 2577 (1975)] for low-frequency fields, to the optical case.

International Journal of Modern Physics D, May 1, 2006

We consider a modified form of gravity in which the action contains a power α of the scalar curva... more We consider a modified form of gravity in which the action contains a power α of the scalar curvature. It is shown how the presence of a bulk viscosity in a spatially flat universe may drive the cosmic fluid into the phantom region (w < -1) and thus into a Big Rip singularity, even if it lies in the quintessence region (w > -1) in the non-viscous case. The condition for this to occur is that the bulk viscosity contains the power (2α -1) of the scalar expansion. Two specific examples are discussed in detail. The present paper is a generalization of the recent investigation dealing with barrier crossing in Einstein's gravity: I.