Do single photons tunnel faster than light?

Experiments done in the early 1990's produced a surprising result: that single photons pass through a photonic tunnel barrier with a group velocity faster than the vacuum speed of light. Subsequent experiments with classical pulses have also revealed apparent superluminal group velocities as well as tunneling times that saturate with barrier length, a phenomenon known as the Hartman effect. In this paper we show that the measured delays are in fact cavity lifetimes as opposed to transit times. This interpretation resolves the Hartman paradox and shows that tunneling is not superluminal as widely believed.Comment: Invited Paper presented at the SPIE Conference "The Nature of Light: What are Photons?", San Diego, CA, August 26, 200

The Ultrarelativistic Kerr-Geometry and its Energy-Momentum Tensor

The ultrarelativistic limit of the Schwarzschild and the Kerr-geometry together with their respective energy-momentum tensors is derived. The approach is based on tensor-distributions making use of the underlying Kerr-Schild structure, which remains stable under the ultrarelativistic boost.Comment: 16 pages, (AMS-LaTeX), TUW-94-0

A LEED determination of the structures of Ru(001) and of CO/Ru(001)−(√3 × √3)R30°

The structures of Ru(001) and of the √3 × √3 R30° overlayer of CO on Ru(001) have been determined by LEED I–V measurements and comparison to calculations. Special attention was paid to accurate angular alignment, selection of a well-ordered portion of the surface, and avoidance of beam-induced changes of the CO layer. Five orders of reflexes over a range of 300 eV each were used for the clean surface and 7 orders over 200 eV each for the CO superstructure. For the clean surface, a slight contraction of the first layer spacing (by 2%) was found which gave r-factors of 0.04 (Zanazzi-Jona) and 0.16 (Pendry) for 5 non-degenerate beams. For the CO structure the most probable geometry is the on-top site with spacings d(Ru---C) = 2.0 ± 0.1 Åandd(C---O) = 1.10 ± 0.1 Å (rZJ = 0.21; rP = 0.51). The two threefold hollow and the bridge sites can be clearly excluded

Kinetics of the adsorption of atomic oxygen (N2O) on the Si(001)2x1 surface as revealed by the change in the surface conductance

The adsorption behaviour of N2O on the Si(001)2 × 1 surface at 300 K substrate temperature has been investigated by measuring in situ the surface conductance during the reaction process. For comparison we monitored in the same way the adsorption of O2 on the same surface which ultimately leads to the flat band situation. The adsorption of atomic oxygen as released by decomposition of the N2O molecule, in contrast with molecular oxygen, was found to result in an increase of the band bending. The difference in behaviour of the change of the surface conductance between the two solid-gas reactions can be explained by considering that the adsorption of O2 will also remove deep-lying backbond states in addition to the dangling bond (DB) and dimer bond (DM) related surface states. It is well known that only the DB and DM surface states are affected by N2O. The surface conductance measurements (SCM) presented in this paper complement our previous spectroscopic differential reflectivity measurements and Auger electron spectroscopic results for the system Si(001)2 × 1 + N2O; we have found evidence that the second step of the proposed three-stage adsorption process of atomic oxygen can be divided into two substages. From our SCM data we could derive that the distance between the valence band edge and the Fermi energy of the clean Si(001)2 × 1 surface is 0.32 ± 0.02 eV, which is in agreement with previous photoemission results