On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.

Local and general anaesthesia do not influence outcome of transfemoral aortic valve implantation.

BACKGROUND There is great variability for the type of anaesthesia used during TAVI, with no clear consensus coming from comparative studies or guidelines. We sought to detect regional differences in the anaesthetic management of patients undergoing transcatheter aortic valve implantation (TAVI) in Europe and to evaluate the relationship between type of anaesthesia and in-hospital and 1year outcome. METHODS Between January 2011 and May 2012 the Sentinel European TAVI Pilot Registry enrolled 2807 patients treated via a transfemoral approach using either local (LA-group, 1095 patients, 39%) or general anaesthesia (GA-group, 1712 patients, 61%). RESULTS A wide variation in LA use was evident amongst the 10 participating countries. The use of LA has increased over time (from a mean of 37.5% of procedures in the first year, to 57% in last 6months, p<0.01). MI, major stroke as well as in-hospital death rate (7.0% LA vs 5.3% GA, p=0.053) had a similar incidence between groups, confirmed in multivariate regression analysis after adjusting for confounders. Dividing our population in tertiles according to the Log-EuroSCORE we found similar mortality under LA, whilst mortality was higher in the highest risk tertile under GA. Survival at 1year, compared by Kaplan-Meier analysis, was similar between groups (log-rank: p=0.1505). CONCLUSIONS Selection of anaesthesia appears to be more influenced by national practice and operator preference than patient characteristics. In the absence of an observed difference in outcomes for either approach, there is no compelling argument to suggest that operators and centres should change their anaesthetic practice.

Electronic band dispersion of graphene nanoribbons via Fourier-transformed scanning tunneling spectroscopy

The electronic structure of atomically precise armchair graphene nanoribbons of width N=7 (7-AGNRs) are investigated by scanning tunneling spectroscopy (STS) on Au(111). We record the standing waves in the local density of states of finite ribbons as a function of sample bias and extract the dispersion relation of frontier electronic states by Fourier transformation. The wave-vector-dependent contributions from these states agree with density functional theory calculations, thus enabling the unambiguous assignment of the states to the valence band, the conduction band, and the next empty band with effective masses of 0.41±0.08me,0.40±0.18me, and 0.20±0.03me, respectively. By comparing the extracted dispersion relation for the conduction band to corresponding height-dependent tunneling spectra, we find that the conduction band edge can be resolved only at small tip-sample separations and has not been observed before. As a result, we report a band gap of 2.37±0.06 eV for 7-AGNRs adsorbed on Au(111).