On the uncertainty relations and squeezed states for the quantum mechanics on a circle

The uncertainty relations for the position and momentum of a quantum particle on a circle are identified minimized by the corresponding coherent states. The sqeezed states in the case of the circular motion are introduced and discussed in the context of the uncertainty relations.Comment: 4 figure

On the Strong Coupling Limit of the Faddeev-Hopf Model

The variational calculus for the Faddeev-Hopf model on a general Riemannian domain, with general Kaehler target space, is studied in the strong coupling limit. In this limit, the model has key similarities with pure Yang-Mills theory, namely conformal invariance in dimension 4 and an infinite dimensional symmetry group. The first and second variation formulae are calculated and several examples of stable solutions are obtained. In particular, it is proved that all immersive solutions are stable. Topological lower energy bounds are found in dimensions 2 and 4. An explicit description of the spectral behaviour of the Hopf map S^3 -> S^2 is given, and a conjecture of Ward concerning the stability of this map in the full Faddeev-Hopf model is proved.Comment: 21 pages, 0 figure

Coherent states on spheres

We describe a family of coherent states and an associated resolution of the identity for a quantum particle whose classical configuration space is the d-dimensional sphere S^d. The coherent states are labeled by points in the associated phase space T*(S^d). These coherent states are NOT of Perelomov type but rather are constructed as the eigenvectors of suitably defined annihilation operators. We describe as well the Segal-Bargmann representation for the system, the associated unitary Segal-Bargmann transform, and a natural inversion formula. Although many of these results are in principle special cases of the results of B. Hall and M. Stenzel, we give here a substantially different description based on ideas of T. Thiemann and of K. Kowalski and J. Rembielinski. All of these results can be generalized to a system whose configuration space is an arbitrary compact symmetric space. We focus on the sphere case in order to be able to carry out the calculations in a self-contained and explicit way.Comment: Revised version. Submitted to J. Mathematical Physic

Deposition and spectral performance of an inhomogeneous broadband wide-angular antireflective coating

The gradient index coatings and optical filters based on them are a challenge for fabrication. In a round-robin experiment basically the same hybrid antireflection coating for the visible spectral region has been deposited with three different techniques: electron beam evaporation, ion beam sputtering and radio frequency magnetron-sputtering. Spectral performances of such one-side and both-side coated samples have been compared with corresponding theoretical spectra of the designed profile. Also, reproducibility of each process is checked

Reduced elastogenesis: a clue to the arteriosclerosis and emphysematous changes in Schimke immuno-osseous dysplasia?

BACKGROUND: Arteriosclerosis and emphysema develop in individuals with Schimke immuno-osseous dysplasia (SIOD), a multisystem disorder caused by biallelic mutations in SMARCAL1 (SWI/SNF-related, matrix-associated, actin-dependent regulator of chromatin, subfamily a-like 1). However, the mechanism by which the vascular and pulmonary disease arises in SIOD remains unknown. METHODS: We reviewed the records of 65 patients with SMARCAL1 mutations. Molecular and immunohistochemical analyses were conducted on autopsy tissue from 4 SIOD patients. RESULTS: Thirty-two of 63 patients had signs of arteriosclerosis and 3 of 51 had signs of emphysema. The arteriosclerosis was characterized by intimal and medial hyperplasia, smooth muscle cell hyperplasia and fragmented and disorganized elastin fibers, and the pulmonary disease was characterized by panlobular enlargement of air spaces. Consistent with a cell autonomous disorder, SMARCAL1 was expressed in arterial and lung tissue, and both the aorta and lung of SIOD patients had reduced expression of elastin and alterations in the expression of regulators of elastin gene expression. CONCLUSIONS: This first comprehensive study of the vascular and pulmonary complications of SIOD shows that these commonly cause morbidity and mortality and might arise from impaired elastogenesis. Additionally, the effect of SMARCAL1 deficiency on elastin expression provides a model for understanding other features of SIOD

Calibrated Sub-Bundles in Non-Compact Manifolds of Special Holonomy

This paper is a continuation of math.DG/0408005. We first construct special Lagrangian submanifolds of the Ricci-flat Stenzel metric (of holonomy SU(n)) on the cotangent bundle of S^n by looking at the conormal bundle of appropriate submanifolds of S^n. We find that the condition for the conormal bundle to be special Lagrangian is the same as that discovered by Harvey-Lawson for submanifolds in R^n in their pioneering paper. We also construct calibrated submanifolds in complete metrics with special holonomy G_2 and Spin(7) discovered by Bryant and Salamon on the total spaces of appropriate bundles over self-dual Einstein four manifolds. The submanifolds are constructed as certain subbundles over immersed surfaces. We show that this construction requires the surface to be minimal in the associative and Cayley cases, and to be (properly oriented) real isotropic in the coassociative case. We also make some remarks about using these constructions as a possible local model for the intersection of compact calibrated submanifolds in a compact manifold with special holonomy.Comment: 20 pages; for Revised Version: Minor cosmetic changes, some paragraphs rewritten for improved clarit

Hadron beam test of a scintillating fibre tracker system for elastic scattering and luminosity measurement in ATLAS

A scintillating fibre tracker is proposed to measure elastic proton scattering at very small angles in the ATLAS experiment at CERN. The tracker will be located in so-called Roman Pot units at a distance of 240 m on each side of the ATLAS interaction point. An initial validation of the design choices was achieved in a beam test at DESY in a relatively low energy electron beam and using slow off-the-shelf electronics. Here we report on the results from a second beam test experiment carried out at CERN, where new detector prototypes were tested in a high energy hadron beam, using the first version of the custom designed front-end electronics. The results show an adequate tracking performance under conditions which are similar to the situation at the LHC. In addition, the alignment method using so-called overlap detectors was studied and shown to have the expected precision.Comment: 12 pages, 8 figures. Submitted to Journal of Instrumentation (JINST