arXiv subjects

Johan S. Høye

Publications and source records attributed to Johan S. Høye.

At least 19 recordsLinked to original sources

arXiv2022

Individual ion species chemical potentials in the Mean Spherical Approximation

The Mean Spherical Approximation (MSA) is a commonly-used thermodynamic theory for computing the energetics of ions in the primitive model (i.e., charged hard-sphere ions in a background dielectric). For the excess chemical potential, however, the early MSA formulations (which were widely adopted) only included the terms needed to compute the mean excess chemical potential (or the mean activity coefficient). Other terms for the chemical potential $μ_i$ of individual species $i$ were not included because they sum to $0$ in the mean chemical potential. Here, we derive these terms to give a complete MSA formulation of the chemical potential. The result is a simple additive term for $μ_i$ that we show is a qualitative improvement over the previous MSA version. In addition, our derivation shows that the MSA's assumption of global charge neutrality is not strictly necessary, so that the MSA is also valid for systems close to neutrality.

cond-mat.stat-mech↗

arXiv2020

Casimir force between ideal metal plates in a chiral vacuum

We calculate the Casimir force between two parallel ideal metal plates when there is an intervening chiral medium present. Making use of methods of quantum statistical mechanics we show how the force can be found in a simple and compact way. The expression for the force is in agreement with that obtained recently by Q.-D. Jiang and F. Wilczek [Phys. Rev. B {\bf 99}, 125403 (2019)], in their case with the use of Green function methods.

quant-ph↗

arXiv2019

Uniform quantized electron gas: Radiation corrections

In this paper we analyze how radiation effects influence the correlation functions, the excess energy, and in turn the electron correlation energy of the quantized electron gas at temperature $T=0$. To that aim we resort to a statistical mechanical description of the quantum problem of electron correlations, based on the path integral formalism. In previous works we studied and found accurate results for the usual situation with the electrostatic Coulomb interaction. Here the additional problem with radiation is taken into account. This is facilitated by the equivalence to a dielectric fluid for which correlation functions for dipolar moments are established. From these functions follows the usual density-density (or charge-charge) correlation function needed for the longitudinal electrostatic problem, and in addition the one needed for the transverse radiation problem. While electrostatic excess energy is negative, the transverse one is positive. This quantity is small and decreases rapidly for decreasing densities. However, for high densities it approaches the electrostatic contribution, eventually becoming even larger. The part of the transverse energy from induced correlations turns out to be very small. Also, the non-local longitudinal and transverse dielectric constants of the electron gas are identified from the induced correlation functions.

cond-mat.stat-mech↗

arXiv2019

Casimir Friction Between a Magnetic and a Dielectric Material, in the Nonretarded Limit

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 {\bf 9}, 2078 (1974)]. 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 half-spaces sliding against each other. At the end explicit results are obtained both for finite and zero temperatures. We restrict ourselves to the nonretarded limit.

quant-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↗

arXiv2017

Critical properties of the hierarchical reference theory

The critical region of the hierarchical reference theory (HRT) is investigated further. This extends an earlier work by us where the critical properties of the HRT were concluded indirectly via another accurate but somewhat different theory, the self-consistent Ornstein-Zernike approximation (SCOZA), and numerical work. In the present work we perform our analysis directly upon the HRT partial differential equation to establish ordinary differential equations for the subleading scaling contributions. Again we find that the HRT critical indices in three dimensions are simple rational numbers.

cond-mat.stat-mech↗

arXiv2016

The uniform quantized electron gas revisited

In this work we continue and extend our recent work on the correlation energy of the quantized electron gas of uniform density at temperature $T=0$. As before we utilize the methods, properties, and results obtained by means of classical statistical mechanics. These were extended to quantized systems via the Feynman path integral formalism. The latter translates the quantum problem into a classical polymer problem in four dimensions. Again the well known RPA (random phase approximation) is recovered as a basic result which we then modify and improve upon. Here we will we focus upon thermodynamic self-consistency. Our numerical calculations exhibit a remarkable agreement with well known results of a standard parametrization of Monte Carlo correlation energies.

cond-mat.stat-mech↗

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↗

arXiv2016

Casimir Force between a Half-Space and a Plate of Finite Thickness

Zero-frequency Casimir theory is analyzed from different viewpoints, focusing on the Drude-plasma issue that turns up when one considers thermal corrections to the Casimir force. The problem is that the plasma model, although leaving out dissipation in the material, apparently gives the best agreement with recent experiments. We consider a dielectric plate separated from a dielectric half-space by a vacuum gap, both media being similar. We consider the following categories: (1) Making use of the statistical mechanical method developed by Høye and Brevik (1998), implying that the quantized electromagnetic field is replaced by interaction between dipole moments oscillating in harmonic potentials, we first verify that the Casimir force is in agreement with the Drude prediction. No use of Fresnel's reflection coefficients is made at this stage. (2) Then turning to the field theoretical description implying use of the reflection coefficients, we derive results in agreement with the forgoing when first setting the frequency equal to zero, before letting the permittivity becoming large. With the plasma relation the reflection coefficient for TE zero frequency modes depend on the component of the wave vector parallel to the surfaces and lies between 0 and 1. This contradicts basic electrostatic theory. (3) Turning to high permeability magnetic materials the TE zero frequency mode describes the static magnetic field in the same way as the TM zero frequency modes describe the static electric fields in electrostatics. With the plasma model magnetic fields, except for a small part, can not pass through metals. i.e.~metals effectively become superconductors. However, recent experimental results clearly favor the plasma model. We shortly discuss a possible explanation for this apparent conflict with electrostatics.

quant-ph↗

arXiv2016

Uniform quantized electron gas

In this work we study the correlation energy of the quantized electron gas of uniform density at temperature $T=0$. To do so we utilize methods from classical statistical mechanics. The basis for this is the Feynman path integral for the partition function of quantized systems. With this representation the quantum mechanical problem can be interpreted as, and is equivalent to, a classical polymer problem in four dimensions where the fourth dimension is imaginary time. Thus methods, results, and properties obtained in the statistical mechanics of classical fluids can be utilized. From this viewpoint we recover the well known RPA (random phase approximation). Then to improve it we in this work modify the RPA by requiring the corresponding correlation function to be such that electrons with equal spins can not be on the same position. Numerical evaluations are compared with well known results of a standard parameterization of Monte Carlo correlation energies.

cond-mat.stat-mech↗

arXiv2014

Casimir friction: Relative motion more generally

This paper extends our recent study on Casimir friction forces for dielectric plates moving parallel to each other [J. S. Høye and I. Brevik, Eur. Phys. J. D {\bf 68}, 61 (2014)], to the case where the plates are no longer restricted to rectilinear motion. Part of the mathematical formalism thereby becomes more cumbersome, but reduces in the end to the form that we could expect to be the natural one in advance. As an example, we calculate the Casimir torque on a planar disc rotating with constant angular velocity around its vertical symmetry axis next to another plate.

quant-ph↗

arXiv2014

Casimir friction at zero and finite temperatures

The Casimir friction problem for dielectric plates that move parallel to each other is treated by assuming one of the plates to be at rest. The other performs a closed loop motion in the longitudinal direction. Therewith by use of energy dissipation the formalism becomes more manageable and transparent than in the conventional setting where uniform sliding motion is assumed from $t=-\infty$ to $t=+\infty$. One avoids separating off a reversible interparticle force (independent of friction) from the total force. Moreover, the cases of temperatures $T=0$ and finite $T$ are treated on the same footing. For metal plates we find the friction force to be proportional to $v^3$ at $T=0$ while at finite $T$ it is proportional to $v$ for small $v$ as found earlier. Comparisons with earlier results of Pendry (1997, 2010) and Barton (2011) are made.

quant-ph↗

arXiv2013

Temperature Dependence of the Casimir Force

The Casimir force - at first a rather unexpected consequence of quantum electrodynamics - was discovered by Hendrik Casimir in Eindhoven in 1948. It predicts that two uncharged metal plates experience an attractive force because of the zero-point fluctuations of the electromagnetic field. The idea was tested experimentally in the 1950's and 1960's, but the results were not so accurate that one could make a definite conclusion regarding the existence of the effect. Evgeny Lifshitz expanded the theory in 1955 so as to deal with general dielectric media. Much experimental work has later been done to test the theory's predictions, especially with regards to the temperature dependence of the effect. The existence of the effect itself was verified beyond doubt by Sabisky and Anderson in 1973. Another quarter century had to pass before Lamoreaux and collaborators were able to confirm - or at least make plausible - the temperature dependence predicted by Lifshitz formula in combination with reasonable input data for the material's dispersive properties. The situation is not yet clear-cut, however; there are recent experiments indicating results in disagreement with those of Lamoreaux. In the present paper a brief review is given of the status of this research field.

quant-ph↗

arXiv2013

Critical region of D-dimensional spins: Extension and analysis of the hierarchical reference theory

The hierarchical reference theory (HRT) is generalized to spins of dimensionality $D$. Then its properties are investigated by both analytical and numerical evaluations for supercritical temperatures. The HRT is closely related to the self-consistent Ornstein-Zernike approximation (SCOZA) that was developed earlier for arbitrary $D$. Like the $D=1$ case we studied earlier, our investigation is facilitated by a situation where both HRT and SCOZA give identical results with a mean spherical model (MSM) behavior (i.e. $D=\infty$). However, for the more general situation we find that an additional intermediate term appears. With an interplay between leading and subleading contributions, simple rational numbers, independent of $D$ ($<\infty$), are found for the critical indices.

cond-mat.stat-mech↗

arXiv2013

Casimir Friction for Media of Finite Density

This work is a continuation of our papers from the last couple of years on the Casimir friction for a pair of particles at low relative velocity. The new element in the present analysis is to allow the media to be dense. Then the situation becomes more complex due to induced dipolar correlations, both within the two planes, and between the planes. We show that the structure of the problem can be simplified by regarding the two plates to be a generalized version of a pair of particles. The force is predicted to be very small, far beyond what is practically measurable.

quant-ph↗

arXiv2013

Casimir Friction Between Dense Polarizable Media

The present paper - a continuation of our recent series of papers on Casimir friction for a pair of particles at low relative particle velocity - extends the analysis so as to include dense media. The situation becomes in this case more complex due to induced dipolar correlations, both within planes, and between planes. We show that the structure of the problem can be simplified by regarding the two half-planes as a generalized version of a pair of particles. It turns out that macroscopic parameters such as permittivity suffice to describe the friction also in the finite density case. The expression for the friction force per unit surface area becomes mathematically well-defined and finite at finite temperature. We give numerical estimates, and compare them with those obtained earlier by Pendry (1997) and by Volokitin and Persson (2007). We also show in an appendix how the statistical methods that we are using, correspond to the field theoretical methods more commonly in use.

quant-ph↗

arXiv2012

Casimir Friction Force Between Polarizable Media

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 half-space, 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.

quant-ph↗

arXiv2011

Casimir Friction Force for Moving Harmonic Oscillators

Casimir friction is analyzed for a pair of dielectric particles in relative motion. We first adopt a microscopic model for harmonically oscillating particles at finite temperature T moving non-relativistically with constant velocity. We use a statistical-mechanical description where time-dependent correlations are involved. This description is physical and direct, and, in spite of its simplicity, is able to elucidate the essentials of the problem. This treatment elaborates upon, and extends, an earlier theory of ours back in 1992. The energy change Delta E turns out to be finite in general, corresponding to a finite friction force. In the limit of zero temperature the formalism yields, however, Delta E ->0, this being due to our assumption about constant velocity, meaning slowly varying coupling. For couplings varying more rapidly, there will also be a finite friction force at T=0. As second part of our work, we consider the friction problem using time-dependent perturbation theory. The dissipation, basically a second order effect, is obtainable with the use of first order theory, the reason being the absence of cross terms due to uncorrelated phases of eigenstates. The third part of the present paper is to demonstrate explicitly the equivalence of our results with those recently obtained by Barton (2010); this being not a trivial task since the formal results are seemingly quite different from each other.

quant-ph↗