The Casimir Effect for Generalized Piston Geometries

In this paper we study the Casimir energy and force for generalized pistons constructed from warped product manifolds of the type $I\times_{f}N$ where $I=[a,b]$ is an interval of the real line and $N$ is a smooth compact Riemannian manifold either with or without boundary. The piston geometry is obtained by dividing the warped product manifold into two regions separated by the cross section positioned at $R\in(a,b)$. By exploiting zeta function regularization techniques we provide formulas for the Casimir energy and force involving the arbitrary warping function $f$ and base manifold $N$.Comment: 16 pages, LaTeX. To appear in the proceedings of the Conference on Quantum Field Theory Under the Influence of External Conditions (QFEXT11). Benasque, Spain, September 18-24, 201

Casimir experiments showing saturation effects

We address several different Casimir experiments where theory and experiment disagree. First out is the classical Casimir force measurement between two metal half spaces; here both in the form of the torsion pendulum experiment by Lamoreaux and in the form of the Casimir pressure measurement between a gold sphere and a gold plate as performed by Decca et al.; theory predicts a large negative thermal correction, absent in the high precision experiments. The third experiment is the measurement of the Casimir force between a metal plate and a laser irradiated semiconductor membrane as performed by Chen et al.; the change in force with laser intensity is larger than predicted by theory. The fourth experiment is the measurement of the Casimir force between an atom and a wall in the form of the measurement by Obrecht et al. of the change in oscillation frequency of a 87 Rb Bose-Einstein condensate trapped to a fused silica wall; the change is smaller than predicted by theory. We show that saturation effects can explain the discrepancies between theory and experiment observed in all these cases.Comment: 10 pages, 11 figure

A generalized Kramers-Kronig transform for Casimir effect computations

Recent advances in experimental techniques now permit to measure the Casimir force with unprecedented precision. In order to achieve a comparable precision in the theoretical prediction of the force, it is necessary to accurately determine the electric permittivity of the materials constituting the plates along the imaginary frequency axis. The latter quantity is not directly accessible to experiments, but it can be determined via dispersion relations from experimental optical data. In the experimentally important case of conductors, however, a serious drawback of the standard dispersion relations commonly used for this purpose, is their strong dependence on the chosen low-frequency extrapolation of the experimental optical data, which introduces a significant and not easily controllable uncertainty in the result. In this paper we show that a simple modification of the standard dispersion relations, involving suitable analytic window functions, resolves this difficulty, making it possible to reliably determine the electric permittivity at imaginary frequencies solely using experimental optical data in the frequency interval where they are available, without any need of uncontrolled data extrapolations.Comment: 10 pages, 6 encapsulated figures. A few typos corrected, some references added. The new version matches the one accepted for publication on Phys. Rev.

Damping of bulk excitations over an elongated BEC - the role of radial modes

We report the measurement of Beliaev damping of bulk excitations in cigar shaped Bose Einstein condensates of atomic vapor. By using post selection, excitation line shapes of the total population are compared with those of the undamped excitations. We find that the damping depends on the initial excitation energy of the decaying quasi particle, as well as on the excitation momentum. We model the condensate as an infinite cylinder and calculate the damping rates of the different radial modes. The derived damping rates are in good agreement with the experimentally measured ones. The damping rates strongly depend on the destructive interference between pathways for damping, due to the quantum many-body nature of both excitation and damping products.Comment: 5 pages, 4 figure

Stochastic Quantization and Casimir Forces: Pistons of Arbitrary Cross Section

Recently, a method based on stochastic quantization has been proposed to compute the Casimir force and its fluctuations in arbitrary geometries. It relies on the spectral decomposition of the Laplacian operator in the given geometry. Both quantum and thermal fluctuations are considered. Here we use such method to compute the Casimir force on the plates of a finite piston of arbitrary cross section. Asymptotic expressions valid at low and high temperatures and short and long distances are obtained. The case of a piston with triangular cross section is analysed in detail. The regularization of the divergent stress tensor is described.Comment: 10 pages and 4 figures. Accepted for publication in the Proceedings of the tenth conference on Quantum Field Theory under the influence of external conditions - QFEXT'1

Critical adsorption and critical Casimir forces for geometrically structured confinements

We study the behavior of fluids, confined by geometrically structured substrates, upon approaching a critical point at T = Tc in their bulk phase diagram. As generic substrate structures periodic arrays of wedges and ridges are considered. Based on general renormalization group arguments we calculate, within mean field approximation, the universal scaling functions for order parameter profiles of a fluid close to a single structured substrate and discuss the decay of its spatial variation into the bulk. We compare the excess adsorption at corrugated substrates with the one at planar walls. The confinement of a critical fluid by two walls generates effective critical Casimir forces between them. We calculate corresponding universal scaling functions for the normal critical Casimir force between a flat and a geometrically structured substrate as well as the lateral critical Casimir force between two identically patterned substrates.Comment: 25 pages, 21 figure

Exact results for Casimir interactions between dielectric bodies: The weak-coupling or van der Waals Limit

In earlier papers we have applied multiple scattering techniques to calculate Casimir forces due to scalar fields between different bodies described by delta function potentials. When the coupling to the potentials became weak, closed-form results were obtained. We simplify this weak-coupling technique and apply it to the case of tenuous dielectric bodies, in which case the method involves the summation of van der Waals (Casimir-Polder) interactions. Once again exact results for finite bodies can be obtained. We present closed formulas describing the interaction between spheres and between cylinders, and between an infinite plate and a retangular slab of finite size. For such a slab, we consider the torque acting on it, and find non-trivial equilibrium points can occur.Comment: 4 pages, 3 figure

Material dependence of Casimir forces: gradient expansion beyond proximity

A widely used method for estimating Casimir interactions [H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)] between gently curved material surfaces at short distances is the proximity force approximation (PFA). While this approximation is asymptotically exact at vanishing separations, quantifying corrections to PFA has been notoriously difficult. Here we use a derivative expansion to compute the leading curvature correction to PFA for metals (gold) and insulators (SiO$_2$) at room temperature. We derive an explicit expression for the amplitude $\hat\theta_1$ of the PFA correction to the force gradient for axially symmetric surfaces. In the non-retarded limit, the corrections to the Casimir free energy are found to scale logarithmically with distance. For gold, $\hat\theta_1$ has an unusually large temperature dependence.Comment: 4 pages, 2 figure

Casimir repulsion in moving media

Casimir-Lifshitz interaction emerging from relative movement of layers in stratified dielectric media (e.g., non-uniformly moving fluids) is considered. It is shown that such movement may result in a repulsive Casimir-Lifshitz force exerted on the layers, with the simplest possible structure consisting of three adjacent layers of the same dielectric medium, where the middle one is stationary and the other two are sliding along a direction parallel to the interfaces of the layers.Comment: 22 pages, 10 figure

General theory of electromagnetic fluctuations near a homogeneous surface, in terms of its reflection amplitudes

We derive new general expressions for the fluctuating electromagnetic field outside a homogeneous material surface. The analysis is based on general results from the thermodynamics of irreversible processes, and requires no consideration of the material interior, as it only uses knowledge of the reflection amplitudes for its surface. Therefore, our results are valid for all homogeneous surfaces, including layered systems and metamaterials, at all temperatures. In particular, we obtain new formulae for the near-field region, which are important for interpreting the numerous current experiments probing proximity effects for macroscopic and/or microscopic bodies separated by small empty gaps. By use of Onsager's reciprocity relations, we obtain also the general symmetry properties that must be satisfied by the reflection matrix of any material.Comment: 5 page