State reduction in quantum mechanics: A calculational example

The question is posed as to the role of the state reduction hypothesis in the passage of a molecular beam through a Stern-Gerlach apparatus of the ordinary sort, and of the sort proposed by Wigner, in which the beam is rejoined at the end of the apparatus. The effect of the magnetic field is calculated, as is the effect of a “detector” atom placed asymmetrically in the apparatus, and sensitive to the passage of the molecular beam nearby. It is shown that in the absence of the detector atom the rejoined beam is represented by a pure case density matrix. However, when the detector is present in one arm of our Stern-Gerlach apparatus, the beam is found to be in a statistical mixture approximating “reduction”, even if we never “look” at the detector atom. It is also seen that the beam density matrix is reduced to diagonal form even though it is not physically affected by the detector.     

Operator algebras and a theorem of Dieudonne

LetA be aC*-algebra with second dualA″. Let (φ _n)(n=1,...) be a sequence in the dual ofA such that limφ _n(a) exists for eacha εA. In general, this does not imply that limφ _n(x) exists for eachx εA″. But if limφ _n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ _n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem.     

XPS analysis of aluminum nitride films deposited by plasma source molecular beam epitaxy

Ten samples of crystalline aluminum nitride (AlN) film were deposited on sapphire and silicon substrates by a plasma source molecular beam method. The samples were analyzed using X‐ray photoelectron spectroscopy (XPS) depth profiling and high‐resolution X‐ray diffraction. Oxygen levels were observed to decrease exponentially from the surface into the bulk film. Aluminum, nitrogen and oxygen peaks were fitted with subpeaks in a consistent manner and the subpeaks were assigned to chemical states. AlN subpeaks were observed at 73.5 eV for Al2p and 396.4 eV for N1s. An N1s subpeak at 395.0 eV was assigned to N? N defects. No direct N? O bonds are assigned; rather it is proposed that an N? Al? O bond sequence is the source of higher binding energy N1s subpeaks. The observations in this study support a model in which oxygen is bound only to aluminum in the form of Al? O octahedral complexes dispersed or clustered throughout the main AlN matrix or as Al? O bonds on the crystal grain boundaries. The data also suggest that the AlN lattice parameters are related to oxygen content, since the c‐axis is observed to increase with increasing oxygen content. Copyright © 2008 John Wiley & Sons, Ltd.     

Molecular organization in SAMs used for neuronal cell growth

The attachment of cells onto solid supports is fundamental in the development of advanced biosensors or biochips. In this work, we characterize cortical neuron adhesion, growth, and distribution of an adhesive layer, depending on the molecular structure and composition . Neuronal networks are successfully grown on amino-terminated alkanethiol self-assembled monolayer (SAM) on a gold substrate without adhesion protein interfaces. Neuron adhesion efficiency was studied for amino-terminated, carboxy-terminated, and 1:1 mixed alkanethiol SAMs deposited on gold substrates. Atomic force microscopy and X-ray photoelectron spectroscopy were used to measure the roughness of gold substrate and thickness of SAM monolayers. Conformational ordering and ionic content of SAMs were characterized by vibrational sum frequency generation (VSFG) spectroscopy. Only pure amino-terminated SAMs provide efficient neuronal cell attachment. Ordering of the terminal amino groups does not affect efficiency of neuron adhesion. VSFG analysis shows that ordering of the terminal groups improves with decreasing surface roughness; however the number of gauche defects in alkane chains is independent of surface roughness. We monitor partial dissociation of carboxy groups in mixed SAMs that implies formation of NH3+ neighbors and appearance of catanionic structure. Such catanionic environment proved inefficient for neuron adhesion. Surface roughness of metal within the 0.7-2 nm range has little effect on the efficiency of neuron adhesion. This approach can be used to create new methods that help map structure-property relationships of biohybrid systems.     

Radial oscillations of neutron stars in strong magnetic fields

The eigen frequencies of radial pulsations of neutron stars are calculated in a strong magnetic field. At low densities we use the magnetic BPS equation of state (EOS) similar to that obtained by Lai and Shapiro while at high densities the EOS obtained from the relativistic nuclear mean field theory is taken and extended to include strong magnetic field. It is found that magnetized neutron stars support higher maximum mass whereas the effect of magnetic field on radial stability for observed neutron star masses is minimal.     

Analysis of short-wavelength charge-exchange lasers via plasma-gas beam clashing

The coupled particle and radiation rate equations have been solved for the population inversion and laser intensity which result when a plasma is incident on a vapor target. For the specific case of a helium plasma incident on a cesium vapor target, a laser intensity of order 10⁶W/cm² at 584A?is calculated. The numerical results are in basic agreement with a simple analytical model. Experimental considerations and progress are discussed.