Microscopic theory of the Casimir effect (original) (raw)

Theory of Casimir Forces without the Proximity-Force Approximation

Physical Review Letters, 2016

We analyze both the attractive and repulsive Casimir-Lifshitz forces recently reported in experimental investigations. By using a kinetic approach, we obtain the Casimir forces from the power absorbed by the materials. We consider collective material excitations through a set of relaxation times distributed in frequency according to a log-normal function. A generalized expression for these forces for arbitrary values of temperature is obtained. We compare our results with experimental measurements and conclude that the model goes beyond the proximity-force approximation.

Surprises in Theoretical Casimir Physics: Quantum Forces in Inhomogeneous Media

Despite more than half a century of theoretical work, the Casimir effect is still not as fully understood as some suppose. In this treatise, the author uncovers new puzzles and paradoxes concerning this mysterious phenomenon. In particular, he clearly demonstrates that the most sophisticated theories fail when confronted with dielectrics in which the refractive index is not uniform but gradually changes.

On Casimir forces for media with arbitrary dielectric properties

Revista Mexicana De Fisica, 2002

We derive an expression for the Casimir force between slabs with arbitrary dielectric properties characterized by their reflection coefficients. The formalism presented here is applicable to media with a local or a non-local dielectric response, an infinite or a finite width, inhomogeneous dissipative, etc. Our results reduce to the Lifshitz formula for the force between semi-infinite dielectric slabs by replacing the reflection coefficients by the Fresnel amplitudes.

Casimir force: an alternative treatment

2009

The Casimir force between two parallel uncharged closely spaced metallic plates is evaluated in ways alternatives to those usually considered in the literature. In a first approximation we take in account the suppressed quantum numbers of a cubic box, representing a cavity which was cut in a metallic block. We combine these ideas with those of the MIT bag model of hadrons, but adapted to nonrelativistic particles. In a second approximation we consider the particles occupying the energy levels of a Bohr atom, so that the Casimir force depends explicitly on the fine structure constant α. In both treatments, the mean energies which have explicit dependence on the particle mass and on the maximum occupied quantum number (related to the Fermi level of the system) at the beginning of the calculations, have these dependences mutually canceled at the end of them. Finally by comparing the averaged energies computed in both approximations, we are able to make an estimate of the value of the fine structure constant α.

Casimir forces between arbitrary compact objects

Journal of Physics A: Mathematical and Theoretical, 2008

We develop an exact method for computing the Casimir energy between arbitrary compact objects, both with boundary conditions for a scalar field and dielectrics or perfect conductors for the electromagnetic field. The energy is obtained as an interaction between multipoles, generated by quantum source or current fluctuations. The objects' shape and composition enter only through their scattering matrices. The result is exact when all multipoles are included, and converges rapidly. A low frequency expansion yields the energy as a series in the ratio of the objects' size to their separation. As examples, we obtain this series for two spheres with Robin boundary conditions for a scalar field and dielectric spheres for the electromagnetic field. The full interaction at all separations is obtained for spheres with Robin boundary conditions and for perfectly conducting spheres. Submitted to: J. Phys. A: Math. Gen. ‡ This presentation is based on work performed in collaboration with N. Graham and M. Kardar. For a complete exposition, see Refs. [6] and [7].

Casimir Effect: The Classical Limit

Annals of Physics, 2001

We analyze the high temperature (or classical) limit of the Casimir effect. A useful quantity which arises naturally in our discussion is the "relative Casimir energy", which we define for a configuration of disjoint conducting boundaries of arbitrary shapes, as the difference of Casimir energies between the given configuration and a configuration with the same boundaries infinitely far apart. Using path integration techniques, we show that the relative Casimir energy vanishes exponentially fast in temperature. This is consistent with a simple physical argument based on Kirchhoff's law. As a result the "relative Casimir entropy", which we define in an obviously analogous manner, tends, in the classical limit, to a finite asymptotic value which depends only on the geometry of the boundaries. Thus the Casimir force between disjoint pieces of the boundary, in the classical limit, is entropy driven and is governed by a dimensionless number characterizing the geometry of the cavity. Contributions to the Casimir thermodynamical quantities due to each individual connected component of the boundary exhibit logarithmic deviations in temperature from the behavior just described. These logarithmic deviations seem to arise due to our difficulty to separate the Casimir energy (and the other thermodynamical quantities) from the "electromagnetic" self-energy of each of the connected components of the boundary in a well defined manner. Our approach to the Casimir effect is not to impose sharp boundary conditions on the fluctuating field, but rather take into consideration its interaction with the plasma of "charge carriers" in the boundary, with the plasma frequency playing the role of a physical UV cutoff. This also allows us to analyze deviations from a perfect conductor behavior.

Non-Local Effects in the Casimir Force

AIP Conference Proceedings, 2005

Although the Casimir force, i.e., the force between the walls of a cavity due to the zero point and the thermal fluctuations of its electromagnetic field, was predicted half a century ago, it has only been measured with precision in the last decade. The possibility of comparing theory to experiment and the importance that Casimir forces might have on micro and nano machines has stimulated a renewed interest in their precise calculation for real materials. We show that the character of the cavity field is completely determined by the optical reflection amplitudes of the wall materials. Thus, we obtained an expression for the Casimir force which requires no assumption and no particular model for its walls. Thus, our results constitute a generalization of Lifshitz formula, applicable to a wide class of materials, which could be semi-infinite or finite, local or spatially dispersive, homogeneous or layered, dissipative or dissipationless, isotropic or anisotropic, etc. As an application, we evaluate the force between two metallic slabs accounting for the spatial dispersion of the dynamical response of their conduction electrons. A self-consistent jellium theory predicts a force that is significantly larger than that of a local theory at nanometric distances due to the fact that most of the screening charge at a metallic surface lies outside the nominal surface of the conductor and within vacuum.

The Casimir effect: some aspects

Brazilian Journal of Physics, 2006

We start this paper with a historical survey of the Casimir effect, showing that its origin is related to experiments on colloidal chemistry. We present two methods of computing Casimir forces, namely: the global method introduced by Casimir, based on the idea of zero-point energy of the quantum electromagnetic field, and a local one, which requires the computation of the energy-momentum stress tensor of the corresponding field. As explicit examples, we calculate the (standard) Casimir forces between two parallel and perfectly conducting plates and discuss the more involved problem of a scalar field submitted to Robin boundary conditions at two parallel plates. A few comments are made about recent experiments that undoubtedly confirm the existence of this effect. Finally, we briefly discuss a few topics which are either elaborations of the Casimir effect or topics that are related in some way to this effect as, for example, the influence of a magnetic field on the Casimir effect of charged fields, magnetic properties of a confined vacuum and radiation reaction forces on non-relativistic moving boundaries.

A critical discussion of different methods and models in Casimir effect

Journal of Physics Communications, 2022

The Casimir-Lifhitz force acts between neutral material bodies and is due to the fluctuations (around zero) of the electrical polarizations of the bodies. This force is a macroscopic manifestation of the van der Waals forces between atoms and molecules. In addition to being of fundamental interest, the Casimir-Lifshitz force plays an important role in surface physics, nanotechnology and biophysics. There are two different approaches in the theory of this force. One is centered on the fluctuations inside the bodies, as the source of the fluctuational electromagnetic fields and forces. The second approach is based on finding the eigenmodes of the field, while the material bodies are assumed to be passive and non-fluctuating. In spite of the fact that both approaches have a long history, there are still some misconceptions in the literature. In particular, there are claims that (hypothetical) materials with a strictly real dielectric function ε(ω) can give rise to fluctuational Casimir...

Finite-temperature Casimir effect in the presence of nonlinear dielectrics

Physical Review A, 2011

Starting from a Lagrangian, electromagnetic field in the presence of a nonlinear dielectric medium is quantized using path-integral techniques and correlation functions of different fields are calculated. The susceptibilities of the nonlinear medium are obtained and their relation to coupling functions are determined. Finally, the Casimir energy and force in the presence of a nonlinear medium at finite temperature is calculated.