Spectral isolation of naturally reductive metrics on simple Lie groups

We show that within the class of left-invariant naturally reductive metrics $\mathcal{M}_{\operatorname{Nat}}(G)$ on a compact simple Lie group $G$, every metric is spectrally isolated. We also observe that any collection of isospectral compact symmetric spaces is finite; this follows from a somewhat stronger statement involving only a finite part of the spectrum.Comment: 19 pages, new title and abstract, revised introduction, new result demonstrating that any collection of isospectral compact symmetric spaces must be finite, to appear Math Z. (published online Dec. 2009

Lifetimes of image-potential states on copper surfaces

The lifetime of image states, which represent a key quantity to probe the coupling of surface electronic states with the solid substrate, have been recently determined for quantum numbers $n\le 6$ on Cu(100) by using time-resolved two-photon photoemission in combination with the coherent excitation of several states (U. H\"ofer et al, Science 277, 1480 (1997)). We here report theoretical investigations of the lifetime of image states on copper surfaces. We evaluate the lifetimes from the knowledge of the self-energy of the excited quasiparticle, which we compute within the GW approximation of many-body theory. Single-particle wave functions are obtained by solving the Schr\"odinger equation with a realistic one-dimensional model potential, and the screened interaction is evaluated in the random-phase approximation (RPA). Our results are in good agreement with the experimentally determined decay times.Comment: 4 pages, 1 figure, to appear in Phys. Rev. Let

Self-energy of image states on copper surfaces

We report extensive calculations of the imaginary part of the electron self-energy in the vicinity of the (100) and (111) surfaces of Cu. The quasiparticle self-energy is computed by going beyond a free-electron description of the metal surface, either within the GW approximation of many-body theory or with inclusion, within the GW$\Gamma$ approximation, of short-range exchange-correlation effects. Calculations of the decay rate of the first three image states on Cu(100) and the first image state on Cu(111) are also reported, and the impact of both band structure and many-body effects on the electron relaxation process is discussed.Comment: 8 pages, 5 figures, to appear in Phys. Rev.

Osteochondritis dissecans and Osgood Schlatter disease in a family with Stickler syndrome

<p>Abstract</p> <p>Purpose</p> <p>Stickler syndrome is among the most common autosomal dominant connective tissue disorders but is often unrecognised and therefore not diagnosed by clinicians. Despite much speculation, the cause of osteochondrosis in general and osteochondritis dissecans (OCD) and Osgood Schlatter syndrome (OSS) in particular remain unclear. Etiological understanding is essential. We describe a pair of family subjects presented with OCD and OSS as a symptom complex rather than a diagnosis.</p> <p>Methods</p> <p>Detailed clinical and radiographic examinations were undertaken with emphasis on the role of MRI imaging. Magnetic resonance imaging may allow early prediction of articular lesion healing potential in patients with Stickler syndrome.</p> <p>Results</p> <p>The phenotype of Stickler syndrome can be diverse and therefore misleading. The expectation that the full clinical criteria of any given genetic disorder such as Stickler syndrome will always be present can easily lead to an underestimation of these serious inheritable disorders. We report here two family subjects, a male proband and his aunt (paternal sister), both presented with the major features of Stickler syndrome. Tall stature with marfanoid habitus, astigmatism/congenital vitreous abnormality and submucus cleft palate/cleft uvula, and enlarged painful joints with early onset osteoarthritis. Osteochondritis dissecans (OCD) and Osgood Schlatter syndrome (OSS) were the predominating joint abnormalities.</p> <p>Conclusion</p> <p>We observed that the nature of the articular and physeal abnormalities was consistent with a localised manifestation of a more generalised epiphyseal dysplasia affecting the weight-bearing joints. In these two patients, OCD and OSS appeared to be the predominant pathologic musculoskeletal consequences of an underlying Stickler's syndrome. It is empirical to consider generalised epiphyseal dysplasia as a major underlying causation that might drastically affect the weight-bearing joints.</p