Characterisation and representation of non-dissipative electromagnetic medium with a double light cone

We study Maxwell's equations on a 4-manifold N with a medium that is non-dissipative and has a linear and pointwise response. In this setting, the medium can be represented by a suitable (2,2)-tensor on the 4-manifold N. Moreover, in each cotangent space on N, the medium defines a Fresnel surface. Essentially, the Fresnel surface is a tensorial analogue of the dispersion equation that describes the response of the medium for signals in the geometric optics limit. For example, in isotropic medium the Fresnel surface is at each point a Lorentz light cone. In a recent paper, I. Lindell, A. Favaro and L. Bergamin introduced a condition that constrains the polarisation for plane waves. In this paper we show (under suitable assumptions) that a slight strengthening of this condition gives a pointwise characterisation of all medium tensors for which the Fresnel surface is the union of two distinct Lorentz null cones. This is for example the behaviour of uniaxial medium like calcite. Moreover, using the representation formulas from Lindell et al. we obtain a closed form representation formula that pointwise parameterises all medium tensors for which the Fresnel surface is the union of two distinct Lorentz null cones. Both the characterisation and the representation formula are tensorial and do not depend on local coordinates

On the concepts of radial and angular kinetic energies

We consider a general central-field system in D dimensions and show that the division of the kinetic energy into radial and angular parts proceeds differently in the wavefunction picture and the Weyl-Wigner phase-space picture. Thus, the radial and angular kinetic energies are different quantities in the two pictures, containing different physical information, but the relation between them is well defined. We discuss this relation and illustrate its nature by examples referring to a free particle and to a ground-state hydrogen atom.Comment: 10 pages, 2 figures, accepted by Phys. Rev.

Nonflammable, antistatic, and heat-sealable film

Antistatic, heat-sealable, nonflammable films prepared from polyvinylidene fluoride and polyvinylidene chloride resin

Extreme points of the set of density matrices with positive partial transpose

We present a necessary and sufficient condition for a finite dimensional density matrix to be an extreme point of the convex set of density matrices with positive partial transpose with respect to a subsystem. We also give an algorithm for finding such extreme points and illustrate this by some examples.Comment: 4 pages, 2 figure

Statistical properties of Klauder-Perelomov coherent states for the Morse potential

We present in this paper a realistic construction of the coherent states for the Morse potential using the Klauder-Perelomov approach . We discuss the statistical properties of these states, by deducing the Q- and P-distribution functions. The thermal expectations for the quantum canonical ideal gas of the Morse oscillators are also calculated

Formal Analysis of V2X Revocation Protocols

Research on vehicular networking (V2X) security has produced a range of security mechanisms and protocols tailored for this domain, addressing both security and privacy. Typically, the security analysis of these proposals has largely been informal. However, formal analysis can be used to expose flaws and ultimately provide a higher level of assurance in the protocols. This paper focusses on the formal analysis of a particular element of security mechanisms for V2X found in many proposals: the revocation of malicious or misbehaving vehicles from the V2X system by invalidating their credentials. This revocation needs to be performed in an unlinkable way for vehicle privacy even in the context of vehicles regularly changing their pseudonyms. The REWIRE scheme by Forster et al. and its subschemes BASIC and RTOKEN aim to solve this challenge by means of cryptographic solutions and trusted hardware. Formal analysis using the TAMARIN prover identifies two flaws with some of the functional correctness and authentication properties in these schemes. We then propose Obscure Token (OTOKEN), an extension of REWIRE to enable revocation in a privacy preserving manner. Our approach addresses the functional and authentication properties by introducing an additional key-pair, which offers a stronger and verifiable guarantee of successful revocation of vehicles without resolving the long-term identity. Moreover OTOKEN is the first V2X revocation protocol to be co-designed with a formal model.Comment: 16 pages, 4 figure

Segregation, precipitation, and \alpha-\alpha' phase separation in Fe-Cr alloys: a multi-scale modelling approach

Segregation, precipitation, and phase separation in Fe-Cr systems is investigated. Monte Carlo simulations using semiempirical interatomic potential, first-principles total energy calculations, and experimental spectroscopy are used. In order to obtain a general picture of the relation of the atomic interactions and properties of Fe-Cr alloys in bulk, surface, and interface regions several complementary methods has to be used. Using Exact Muffin-Tin Orbitals method the effective chemical potential as a function of Cr content (0-15 at.% Cr) is calculated for a surface, second atomic layer and bulk. At ~10 at.% Cr in the alloy the reversal of the driving force of a Cr atom to occupy either bulk or surface sites is obtained. The Cr containing surfaces are expected when the Cr content exceeds ~10 at.%. The second atomic layer forms about 0.3 eV barrier for the migration of Cr atoms between bulk and surface atomic layer. To get information on Fe-Cr in larger scales we use semiempirical methods. Using combined Monte Carlo molecular dynamics simulations, based on semiempirical potential, the precipitation of Cr into isolated pockets in bulk Fe-Cr and the upper limit of the solubility of Cr into Fe layers in Fe/Cr layer system is studied. The theoretical predictions are tested using spectroscopic measurements. Hard X-ray photoelectron spectroscopy and Auger electron spectroscopy investigations were carried out to explore Cr segregation and precipitation in Fe/Cr double layer and Fe_0.95Cr_0.05 and Fe_0.85Cr_0.15 alloys. Initial oxidation of Fe-Cr was investigated experimentally at 10^-8 Torr pressure of the spectrometers showing intense Cr_2O_3 signal. Cr segregation and the formation of Cr rich precipitates were traced by analysing the experimental spectral intensities with respect to annealing time, Cr content, and kinetic energy of the exited electron.Comment: 16 pages, 14 figures, 52 reference