Table of contents

We describe a simple mechanism of quantum friction for a particle moving parallel to a dielectric, based on a fully relativistic framework and the assumption of local equilibrium. The Cherenkov effect explains how the bare ground state becomes globally unstable and how fluctuations of the electromagnetic field and the particle's dipole are converted into pairs of excitations. Modeling the particle as a silver nano-sphere, we investigate the spectrum of the force and its velocity dependence. We find that the damping of the plasmon resonance in the silver particle has a relatively strong impact near the Cherenkov threshold velocity. We also present an expansion of the friction force near the threshold velocity for both damped and undamped particles.

In a recent publication [1] we have shown using a QED approach that, in the presence of a magnetic field, the quantum vacuum coupled to a chiral molecule provides a kinetic momentum directed along the magnetic field. Here we explain the physical mechanisms which operate in the transfer of momentum from the vacuum to the molecule. We show that the variation of the molecular kinetic energy originates from the magnetic energy associated with the vacuum correction to the magnetization of the molecule. We carry out a semiclassical calculation of the vacuum momentum and compare the result with the QED calculation.

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.

We consider how membrane fluctuations can modify the miscibility of lipid mixtures, that is to say how the phase diagram of a boundary-constrained membrane is modified when the membrane is allowed to fluctuate freely in the case of zero surface tension. In order for fluctuations to have an effect, the different lipid types must have differing Gaussian rigidities. We show, somewhat paradoxically, that fluctuation-induced interactions can be treated approximately in a mean-field type theory. Our calculations predict that, depending on the difference in bending and Gaussian rigidity of the lipids, membrane fluctuations can either favor or disfavor mixing.

We find the steady-state heat flow P between two classical harmonic oscillators having natural frequency ω₀, dynamically identical, damped, and acted on by Langevin forces appropriate, respectively, to temperatures T₁ and T₂ (with k_BT_1,2 ≫ ℏω₀). Retardation and relativistic effects are disregarded. Considered individually, each of the two normal modes of the joint system behaves as if it were in equilibrium at the average temperature (T₁ + T₂)/2, but the modes are correlated, and it is these correlations that govern P. From P one readily calculates the classical heat flow per unit area between two Drude-modelled half-spaces. It emerges that, by contrast to equilibrium statistical mechanics, theories of such steady-state systems must generally specify the mechanism they envisage for enforcing the nominally prescribed temperatures.

We study critical Casimir forces between planar walls and geometrically structured substrates within mean-field theory. As substrate structures, crenellated surfaces consisting of periodic arrays of rectangular crenels and merlons are considered. Within the widely used proximity force approximation, both the top surfaces of the merlons and the bottom surfaces of the crenels contribute to the critical Casimir force. However, for such systems the full, numerically determined critical Casimir forces deviate significantly from the pairwise addition formalism underlying the proximity force approximation. A first-order correction to the proximity force approximation is presented in terms of a step contribution arising from the critical Casimir interaction between a planar substrate and the right-angled steps of the merlons consisting of their upper and lower edges as well as their sidewalls.

We find the analytic expressions for the Casimir free energy, entropy and pressure at low temperature in the configuration of two parallel plates made of magnetodielectic material. The cases of constant and frequency-dependent dielectic permittivity and magnetic permeability of the plates are considered. Special attention is paid to the account of dc conductivity. It is shown that in the case of finite static dielectric permittivity and magnetic permeability the Nernst heat theorem for the Casimir entropy is satisfied. If the dc conductivity is taken into account, the Casimir entropy goes to a positive nonzero limit depending on the parameters of a system when the temperature vanishes, i.e. the Nernst theorem is violated. The experimental situation is also discussed.

This paper extends our recent study on Casimir friction forces for dielectric plates moving parallel to each other (Høye and Brevik 2014 Eur. Phys. J. D 68 61), to a 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 expected 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.

I consider a possibility of parametric amplification of the microwave vacuum field in a reentrant cavity enclosing a nonlinear crystal whose refractive index is modulated by periodic high-intensity short laser pulses. The main result is that the total number of created 'Casimir quanta' depends neither on the laser beam shape, nor on the duration or power of individual pulses, but it depends on the total energy of all the pulses, provided the duration of each pulse is much shorter than the period of field oscillations in the selected resonant mode. The scheme can be feasible if reliable materials with high nonlinear coefficients can be found.

Recent experimental realizations of the critical Casimir effect have been implemented by monitoring colloidal particles immersed in a binary liquid mixture near demixing and exposed to a chemically structured substrate. In particular, critical Casimir forces have been measured for surfaces consisting of stripes with periodically alternating adsorption preferences, forming chemical steps between them. Motivated by these experiments, we analyze the contribution of such chemical steps to the critical Casimir force for the film geometry and within the Ising universality class. By means of Monte Carlo simulations, mean-field theory and finite-size scaling analysis we determine the universal scaling function associated with the contribution to the critical Casimir force due to individual, isolated chemical steps facing a surface with homogeneous adsorption preference or with Dirichlet boundary condition. In line with previous findings, these results allow one to compute the critical Casimir force for the film geometry and in the presence of arbitrarily shaped, but wide stripes. In this latter limit the force decomposes into a sum of the contributions due to the two homogeneous parts of the surface and due to the chemical steps between the stripes. We assess this decomposition by comparing the resulting sum with actual simulation data for the critical Casimir force in the presence of a chemically striped substrate.

We consider the mechanical coupling between a two-dimensional Bose–Einstein condensate and a graphene sheet via the vacuum fluctuations of the electromagnetic field which are at the origin of the so-called Casimir–Polder potential. By deriving a self-consistent set of equations governing the dynamics of the condensate and the flexural (out-of-plane) modes of the graphene, we can show the formation of a new type of purely acoustic quasi-particle excitation, a quasi-polariton resulting from the coherent superposition of quanta of flexural and Bogoliubov modes.

Measurements of the Casimir force require the elimination of the electrostatic force between the surfaces. However, due to electrostatic patch potentials, the voltage required to minimize the total force may not be sufficient to completely nullify the electrostatic interaction. Thus, these surface potential variations cause an additional force, which can obscure the Casimir force signal. In this paper, we inspect the spatially varying surface potential of e-beamed, sputtered, sputtered and annealed, and template stripped gold surfaces with Heterodyne amplitude modulated Kelvin probe force microscopy (HAM-KPFM). It is demonstrated that HAM-KPFM improves the spatial resolution of surface potential measurements compared to amplitude modulated Kelvin probe force microscopy. We find that patch potentials vary depending on sample preparation, and that the calculated pressure can be similar to the pressure difference between Casimir force calculations employing the plasma and Drude models.

We formulate a method allowing us to confirm or exclude the alternative models of material properties at some definite confidence level in experiments on measuring the Casimir force. The method is based on the consideration of differences between the theoretical and mean measured quantities and the confidence intervals for these differences found at sufficiently high or low confidence probabilities. The developed method is applied to the data of four recent experiments on measuring the gradient of the Casimir force by means of a dynamic atomic force microscope. It is shown that in experiments with Au–Au and Ni–Ni test bodies, where the Drude model approach is excluded at a 95% confidence level, the plasma model approach agrees with the data at higher than 90% confidence. In experiments using an Au sphere interacting with either a Ni plate or a graphene-coated substrate, the measurement data agree with the common prediction of the Drude and plasma model approaches and theory using the polarization tensor at 90% and 80% confidence levels, respectively.

The dependence of the Casimir force on the frequency-dependent dielectric functions of interacting materials makes it possible to tailor the actuation dynamics of microactuators. The Casimir force is largest for metallic interacting systems due to the high absorption of conduction electrons in the far-infrared range. For less conductive systems, such as phase change materials or conductive silicon carbide, the reduced force offers the advantage of increased stable operation of MEMS devices against pull-in instabilities that lead to unwanted stiction. Bifurcation analysis with phase portraits has been used to compare the sensitivity of a model actuator when the optical properties are altered.

We consider and review the emergence of singular field fluctuations or energy densities at sharp boundaries or point-like field sources in the vacuum. The presence of singular energy densities of a field may be relevant from a conceptual point of view, because they contribute to the self-energy of the system. They could also generate significant gravitational effects. We first consider the case of the interface between a metallic boundary and the vacuum, and obtain the structure of the singular electric and magnetic energy densities at the interface through an appropriate limit from a dielectric to an ideal conductor. Then, we consider the case of a nondispersive and nondissipative point-like source of the electromagnetic field, described by its polarizability, and show that also in this case the electric and magnetic energy densities show a singular structure at the source position. We discuss how, in both cases, these singularities give an essential contribution to the electromagnetic self-energy of the system; moreover, they solve an apparent inconsistency between the space integral of the field energy density and the average value of the field Hamiltonian. The singular behavior we find is softened, or even eliminated, for boundaries fluctuating in space and for extended field sources. We discuss in detail the case in which a reflecting boundary is not fixed in space but is allowed to move around an equilibrium position, under the effect of quantum fluctuations of its position. Specifically, we consider the simple case of a 1D massless scalar field in a cavity with one fixed and one mobile wall described quantum-mechanically. We investigate how the possible motion of the wall changes the vacuum fluctuations and the energy density of the field, compared with the fixed-wall case. Also, we explicitly show how the fluctuating motion of the wall smears out the singular behaviour of the field energy density at the boundary.

The basic theory of temporal mechanical fluctuation induced systematic errors in Casimir force experiments is developed and applications of this theory to several experiments is reviewed. This class of systematic error enters in a manner similar to the usual surface roughness correction, but unlike the treatment of surface roughness for which an exact result requires an electromagnetic mode analysis, time dependent fluctuations can be treated exactly, assuming the fluctuation times are much longer than the zero point and thermal fluctuation correlation times of the electromagnetic field between the plates. An experimental method for measuring absolute distance with high bandwidth is also described and measurement data presented.

We present a variety of methods to derive the Casimir interaction in planar systems containing 2D layers. Examples where this can be of use is graphene, graphene-like layers and 2D electron gases. We present results for two free standing layers and for one layer above a substrate. The results can easily be extended to systems with a larger number of layers.

We study the Casimir–Polder interaction at finite temperatures between a polarizable small, anisotropic particle and a non-planar surface using a derivative expansion. We obtain the leading and the next-to-leading curvature corrections to the interaction for low and high temperatures. Explicit results are provided for the retarded limit in the presence of a perfectly conducting surface.

We compute the radiative heat transfer between two sheets of 2D Dirac materials, including topological Chern insulators and graphene, within the framework of the local approximation for the optical response of these materials. In this approximation, which neglects spatial dispersion, we derive both numerically and analytically the short-distance asymptotic of the near-field heat transfer in these systems, and show that it scales as the inverse of the distance between the two sheets. Finally, we discuss the limitations to the validity of this scaling law imposed by spatial dispersion in 2D Dirac materials.

The aim of this paper is to revisit the calculation of atom–surface quantum friction in the quantum field theory formulation put forward by Barton (2010 New J. Phys.12 113045). We show that the power dissipated into field excitations and the associated friction force depend on how the atom is boosted from being initially at rest to a configuration in which it is moving at constant velocity (v) parallel to the planar interface. In addition, we point out that there is a subtle cancellation between the one-photon and part of the two-photon dissipating power, resulting in a leading order contribution to the frictional power which goes as v⁴. These results are also confirmed by an alternative calculation of the average radiation force, which scales as v³.

We describe a superconducting Casimir apparatus inspired by a recently proposed setup involving magnetic surfaces (Bimonte G 2014 Phys. Rev. Lett.112 240401). The present setup consists of a superconducting Nb sphere and a flat gold plate including in its interior a superconducting Nb strip. The experimental scheme involves a differential measurement of the Casimir force at a point of the gold plate above the Nb strip and away from it. We show that similar to the previous setup, the superconducting system considered here implies widely different modulations of the Casimir force, depending on whether the thermal force is computed using the Drude or the plasma model, thus paving the way to an unambiguous discrimination between these alternative prescriptions.