International Journal of Modern Physics A

For the vacuum interaction of a sphere in front of a plane, both obeying conductor boundary conditions, we consider the approximation of small separation. We derive the next-to-leading order of the asymptotic expansion in the separation-to-radius ratio ε. This correction is of order ε. In opposite to the scalar cases it contains also contributions proportional to logarithms in first and second order, ε ln ε and ε(ln ε)². We compare this result with the available findings of numerical and experimental approaches.

The properties of fluctuation induced interactions like van der Waals and Casimir-Lifshitz forces are of interest in a plethora of fields ranging from biophysics to nanotechnology. Here we describe a general approach to compute these interactions. It is based on a combination of methods from statistical physics and scattering theory. We showcase how it is exquisitely suited to analyze a variety of previously unexplored phenomena. Examples are given to show how the interplay of geometry and material properties helps to understand and control these forces.

We consider semitransparent pistons in the presence of extra dimensions. It is shown that the piston is always attracted to the closest wall irrespective of details of the geometry and topology of the extra dimensions and of the cross section of the piston. Furthermore, we evaluate the zeta regularized determinant for this configuration.

We present the scattering approach which is nowadays the best tool for describing the Casimir force in realistic experimental configurations. After reminders on the simple geometries of 1d space and specular scatterers in 3d space, we discuss the case of stationary arbitrarily shaped mirrors in electromagnetic vacuum. We then review specific calculations based on the scattering approach, dealing for example with the forces or torques between nanostructured surfaces and with the force between a plane and a sphere. In these various cases, we account for the material dependence of the forces, and show that the geometry dependence goes beyond the trivial Proximity Force Approximation often used for discussing experiments.

We measure the Casimir force gradient between silicon surfaces with nanoscale, rectangular corrugations and a gold sphere attached to a micromechanical torsional oscillator. By comparing the force gradients on the corrugated surfaces to that on a smooth, flat surface of the same material, we demonstrate that the Casimir force deviates from the value expected from the pairwise additive approximation and the proximity force approximation. The observed deviation qualitatively agrees with calculations that take into account the interplay between finite conductivity and geometry effects. However, the agreement is not exact, possibly due to uncertainties in the optical properties of the silicon substrate.

We describe our latest results in the separation dependence of the Casimir interaction in the sphere-plane geometry for two Au-coated surfaces. All results are obtained by measuring the change in the resonant frequency of a sensitive microelectromechanical torsional oscillator as the separation between the sphere and the plane is changed. By means of the proximity force approximation, the change in resonant frequency yields the Casimir pressure between two parallel plates at the same separation. We present results for a new sample at room temperature, where the dielectric function has been measured in the 190-825 nm range. We show that the results of the Casimir force in this sample and in previous samples are virtually indistinguishable. Furthermore, the observed differences between measured and tabulated optical properties data do not show any effect on the calculation of the Casimir interaction. We also present results of the measurement of the Casimir force between a sphere and a plane at 300, 77, 4.2 and 2.1 K. While low temperature results are noisier than room temperature ones, precluding a direct exclusion of either the Drude or the plasma model, the average of the measurements coincide at all temperatures.

We present a short overview of the recent efforts of our group in the design of high precision Casimir force setups. We first describe our Atomic Force Microscope based technique that allows one to simultaneously and continuously calibrate the instrument, compensate for a residual electrostatic potential, measure the Casimir force, and, in the presence of a fluid in the gap between the interacting surfaces, measure the hydrodynamic force. Then we briefly discuss a new force sensor that adapts well to Casimir force measurements in critical environments.

Some experimental features of the recent lateral Casimir force measurement are discussed. A brief experimental overview, along with the related analysis to obtain calibration constants is presented. The data show the diffraction like coherent scattering from the corrugated surfaces.

By engineering the boundary conditions of electromagnetic fields between material interfaces, one can dramatically change the Casimir-Lifshitz force between surfaces as a result of the modified zero-point energy density of the system. Repulsive interactions between macroscopic bodies occur when their dielectric responses obey a particular inequality, as pointed out by Dzyaloshinskii, Lifshitz, and Pitaevskii. We discuss experimental verification of this behavior as well as a description of how this can be used to develop a scheme for quantum levitation. Based on these concepts, we discuss the possible development of a new class of devices based on ultra-low static friction and the ability to sort objects based on their dielectric functions.

Macroscopic quantum vacuum and modern theories of gravitation share the strong interplay between geometry and physical phenomena. We review selected issues related to the accuracy of the measurement of Casimir forces with particular emphasis on the implications for the search of non-Newtonian gravitational forces in the micrometer range. We then discuss the interplay of the Higgs particle with gravitation, arguing that spectroscopic shifts in atomic transitions due to the modifications of the vacuum expectation value of the Higgs field in regions with strong curvature of space-time may be of conceptual and observational relevance.

The wedge geometry closed by a circular-cylindrical arc is a nontrivial generalization of the cylinder, which may have various applications. If the radial boundaries are not perfect conductors, the angular eigenvalues are only implicitly determined. When the speed of light is the same on both sides of the wedge, the Casimir energy is finite, unlike the case of a perfect conductor, where there is a divergence associated with the corners where the radial planes meet the circular arc. We advance the study of this system by reporting results on the temperature dependence for the conducting situation. We also discuss the appropriate choice of the electromagnetic energy-momentum tensor.

We discuss Casimir phenomena which are dominated by long-range fluctuations. A prime example is given by "geothermal" Casimir phenomena where thermal fluctuations in open Casimir geometries can induce significantly enhanced thermal corrections. We illustrate the underlying mechanism with the aid of the inclined-plates configuration, giving rise to enhanced power-law temperature dependences compared to the parallel-plates case. In limiting cases, we find numerical evidence even for fractional power laws induced by long-range fluctuations. We demonstrate that thermal energy densities for open geometries are typically distributed over length scales of 1/T. As an important consequence, approximation methods for thermal corrections based on local energy-density estimates such as the proximity-force approximation are expected to become unreliable even at small surface separations.

We investigate the Casimir pressure between two parallel plates made of magnetic materials at nonzero temperature. It is shown that for real magnetodielectric materials only the magnetic properties of ferromagnets can influence the Casimir pressure. This influence is accomplished through the contribution of the zero-frequency term of the Lifshitz formula. The possibility of the Casimir repulsion through the vacuum gap is analyzed depending on the model used for the description of the dielectric properties of the metal plates.

The Lifshitz theory and its modifications are discussed with respect to the Nernst heat theorem and the experimental data of several recent experiments. An analysis of all available information leads to the conclusion that some concepts of statistical physics might need reconsideration.

It is shown that the violation of the positiveness of the entropy due to the Casimir-Lifshitz interaction claimed in several papers is an artifact related to an improper interpretation of the "Casimir entropy", which actually is a difference of two positive terms. It is explained that at definite condition this "Casimir entropy" must be negative. A direct derivation of the low temperature behavior of the "Casimir entropy" of a metallic surface in conditions of the anomalous skin effect is given and singular temperature dependency of this quantity is discussed. In conclusion a hydrodynamic example of the entropy of a liquid film is considered. It occurs that the entropy of a film of finite thickness and a liquid half-space behave differently at T → 0.

This article addresses the discrepancies between theoretical and experimental results obtained for the thermal Casimir effect. Here we test the possibility that saturation effects may be the root of the problems. We present graphs that describe the numerical derivations in great detail.

We give a re-interpretation of an 'entropy defect' in the electromagnetic Casimir effect. The electron gas in a perfect crystal is an electromagnetically disordered system whose entropy contains a finite Casimir-like contribution. The Nernst theorem (third law of thermodynamics) is not applicable.

The attractive branch of the interaction potentials with the surface of gold have been computed for a large variety of atomic systems: the hydrogen atom, noble gases (He, Ne, Ar, Kr, Xe), alkali atoms (Li, Na, K, Rb, Cs) and alkaline atoms (Be, Mg, Ca, Sr, Ba). The results include highly accurate dynamic polarizabilities for the helium atom calculated using a variational method and explicitly correlated wavefunctions. For other atoms considered we used the data available in the literature. The interaction potentials include both the effects of retardation of the electromagnetic interactions and a realistic representation of the optical response function of gold (beyond the approximation of a perfect conductor). An explicit comparison of our result to the interaction between an atom and a perfect conductor is given.

A basic property of the Casimir force is that, in most cases, it is attractive. The quest for workable configurations which exhibit repulsion is, at the same time, important and difficult, both in the nanophysics laboratory (e.g. to avoid stickness) and at cosmological scales (to account for the accelerated expansion of our universe). We shall here report on some configurations which exhibit the two signs of the Casimir force in function of the distance, and also on some alternatives to Einsteinian gravitation with the eventual aim to try to get around the cosmological constant problem.

Quantum field theory allows for the suppression of vacuum fluctuations, leading to sub-vacuum phenomena. One of these is the appearance of local negative energy density. Selected aspects of negative energy will be reviewed, including the quantum inequalities which limit its magnitude and duration. However, these inequalities allow the possibility that negative energy and related effects might be observable. Some recent proposals for experiments to search for sub-vacuum phenomena will be discussed. Fluctuations of the energy density around its mean value will also be considered, and some recent results on a probability distribution for the energy density in two dimensional spacetime are summarized.

In vacuum energy calculations with an ultraviolet cutoff, divergences arise that clearly are related to the physics of boundaries. We point out how to find the cut-off energy density and pressure most directly from a Green function. Then we discuss three apparent paradoxes arising in this work that are in various stages of resolution.

The Schwinger effect is the non-perturbative production of electron-positron pairs when an external electric field is applied to the quantum electrodynamical (QED) vacuum. The inherent instability of the vacuum in an electric field was one of the first non-trivial predictions of QED, but the effect is so weak that it has not yet been directly observed. However, there are exciting new developments in ultra-high intensity lasers, which may bring us to the verge of this extreme ultra-relativistic regime. This necessitates a fresh look at both experimental and theoretical aspects of the Schwinger effect. I describe some new theoretical ideas aimed at making this elusive effect observable, by careful shaping of the laser pulses, much as is done [in a different intensity regime] in the fast-developing field of atto-science.

The well-known formula det (A · B) = det A · det B can be easily proved for finite dimensional matrices but it may be incorrect for the functional determinants of differential operators, including the ones which are relevant for Quantum Field Theory applications. Considerable work has been done to prove that this equality can be violated, but in all previously known cases the difference could be reduced to renormalization ambiguity. We present the first example, where the difference between the two functional determinants is a nonlocal expression and therefore can not be explained by the renormalization ambiguity. Moreover, through the use of other even dimensions we explain the origin of this difference at qualitative level.

The trace anomaly of conformal matter implies the existence of massless scalar poles in physical amplitudes involving the stress-energy tensor. These poles may be described by a local effective action with massless scalar fields, which couple to classical sources, contribute to gravitational scattering processes, and can have long range gravitational effects at macroscopic scales. In an effective field theory approach, the effective action of the anomaly is an infrared relevant term that should be added to the Einstein-Hilbert action of classical General Relativity to take account of macroscopic quantum effects. The additional scalar degrees of freedom contained in this effective action may be understood as responsible for both the Casimir effect in flat spacetime and large quantum backreaction effects at the horizon scale of cosmological spacetimes. These effects of the trace anomaly imply that the cosmological vacuum energy is dynamical, and its value depends on macroscopic boundary conditions at the cosmological horizon scale, rather than sensitivity to the extreme ultraviolet Planck scale.