How does Casimir energy fall? IV. Gravitational interaction of regularized quantum vacuum energy

Several years ago we demonstrated that the Casimir energy for perfectly reflecting and imperfectly reflecting parallel plates gravitated normally, that is, obeyed the equivalence principle. At that time the divergences in the theory were treated only formally, without proper regularization, and the coupling to gravity was limited to the canonical energy-momentum-stress tensor. Here we strengthen the result by removing both of those limitations. We consider, as a toy model, massless scalar fields interacting with semitransparent ($\delta$-function) potentials defining parallel plates, which become Dirichlet plates for strong coupling. We insert space and time point-split regulation parameters, and obtain well-defined contributions to the self- energy of each plate, and the interaction energy between the plates. (This self-energy does not vanish even in the conformally-coupled, strong-coupled limit.) We also compute the local energy density, which requires regularization near the plates. In general, the energy density includes a surface energy that resides precisely on the boundaries. This energy is also regulated. The gravitational interaction of this well-defined system is then investigated, and it is verified that the equivalence principle is satisfied.Comment: 14 pages, 4 figure

Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors

We show that any pair of real symmetric tensors \BGve and \BGm can be realized as the effective electric permittivity and effective magnetic permeability of a metamaterial at a given fixed frequency. The construction starts with two extremely low loss metamaterials, with arbitrarily small microstructure, whose existence is ensured by the work of Bouchitt{\'e} and Bourel and Bouchitt\'e and Schweizer, one having at the given frequency a permittivity tensor with exactly one negative eigenvalue, and a positive permeability tensor, and the other having a positive permittivity tensor, and a permeability tensor having exactly one negative eigenvalue. To achieve the desired effective properties these materials are laminated together in a hierarchical multiple rank laminate structure, with widely separated length scales, and varying directions of lamination, but with the largest length scale still much shorter than the wavelengths and attenuation lengths in the macroscopic effective medium.Comment: 12 pages, no figure

On the Temperature Dependence of the Casimir Effect

The temperature dependence of the Casimir force between a real metallic plate and a metallic sphere is analyzed on the basis of optical data concerning the dispersion relation of metals such as gold and copper. Realistic permittivities imply, together with basic thermodynamic considerations, that the transverse electric zero mode does not contribute. This results in observable differences with the conventional prediction, which does not take this physical requirement into account. The results are shown to be consistent with the third law of thermodynamics, as well as being consistent with current experiments. However, the predicted temperature dependence should be detectable in future experiments. The inadequacies of approaches based on {\it ad hoc} assumptions, such as the plasma dispersion relation and the use of surface impedance without transverse momentum dependence, are discussed.Comment: 14 pages, 3 eps figures, revtex4. New version includes clarifications and new reference. Accepted for publication in Phys. Rev.

Pathway to a Compact SASE FEL Device

Newly developed high peak power lasers have opened the possibilities of driving coherent light sources operating with laser plasma accelerated beams and wave undulators. We speculate on the combination of these two concepts and show that the merging of the underlying technologies could lead to new and interesting possibilities to achieve truly compact, coherent radiator devices

Mode-by-mode summation for the zero point electromagnetic energy of an infinite cylinder

Using the mode-by-mode summation technique the zero point energy of the electromagnetic field is calculated for the boundary conditions given on the surface of an infinite solid cylinder. It is assumed that the dielectric and magnetic characteristics of the material which makes up the cylinder $(\epsilon_1, \mu_1)$ and of that which makes up the surroundings $(\epsilon_2, \mu_2)$ obey the relation $\epsilon_1\mu_1= \epsilon_2\mu_2$. With this assumption all the divergences cancel. The divergences are regulated by making use of zeta function techniques. Numerical calculations are carried out for a dilute dielectric cylinder and for a perfectly conducting cylindrical shell. The Casimir energy in the first case vanishes, and in the second is in complete agreement with that obtained by DeRaad and Milton who employed a Green's function technique with an ultraviolet regulator.Comment: REVTeX, 16 pages, no figures and tables; transcription error in previous version corrected, giving a zero Casimir energy for a tenuous cylinde

The Adler Function for Light Quarks in Analytic Perturbation Theory

The method of analytic perturbation theory, which avoids the problem of ghost-pole type singularities and gives a self-consistent description of both spacelike and timelike regions, is applied to describe the "light" Adler function corresponding to the non-strange vector channel of the inclusive decay of the $\tau$ lepton. The role of threshold effects is investigated. The behavior of the quark-antiquark system near threshold is described by using a new relativistic resummation factor. It is shown that the method proposed leads to good agreement with the ``experimental'' Adler function down to the lowest energy scale.Comment: 13 pages, one ps figure, REVTe

How does Casimir energy fall? III. Inertial forces on vacuum energy

We have recently demonstrated that Casimir energy due to parallel plates, including its divergent parts, falls like conventional mass in a weak gravitational field. The divergent parts were suitably interpreted as renormalizing the bare masses of the plates. Here we corroborate our result regarding the inertial nature of Casimir energy by calculating the centripetal force on a Casimir apparatus rotating with constant angular speed. We show that the centripetal force is independent of the orientation of the Casimir apparatus in a frame whose origin is at the center of inertia of the apparatus.Comment: 8 pages, 2 figures, contribution to QFEXT07 proceeding

Neural Networks for Modeling and Control of Particle Accelerators

We describe some of the challenges of particle accelerator control, highlight recent advances in neural network techniques, discuss some promising avenues for incorporating neural networks into particle accelerator control systems, and describe a neural network-based control system that is being developed for resonance control of an RF electron gun at the Fermilab Accelerator Science and Technology (FAST) facility, including initial experimental results from a benchmark controller.Comment: 21 p

Calculation of the Casimir Force between Similar and Dissimilar Metal Plates at Finite Temperature

The Casimir pressure is calculated between parallel metal plates, containing the materials Au, Cu, or Al. Our motivation for making this calculation is the need of comparing theoretical predictions, based on the Lifshitz formula, with experiments that are becoming gradually more accurate. In particular, the finite temperature correction is considered, in view of the recent discussion in the literature on this point. A special attention is given to the case where the difference between the Casimir pressures at two different temperatures, T=300 K and T=350 K, is involved. This seems to be a case that will be experimentally attainable in the near future, and it will be a critical test of the temperature correction.Comment: 23 latex pages, 12 figures. Introductory section expanded, 4 new references. To appear in J. Phys. A: Math. Ge