The Gram Matrix of a PT-Symmetric Quantum System

The eigenstates of a diagonalizable PT-symmetric Hamiltonian satisfy unconventional completeness and orthonormality relations. These relations reflect the properties of a pair of bi-orthonormal bases associated with non-hermitean diagonalizable operators. In a similar vein, such a dual pair of bases is shown to possess, in the presence of PT symmetry, a Gram matrix of a particular structure: its inverse is obtained by simply swapping the signs of some its matrix elements.     

Mineralogical analysis of auriferous ores from the El Diamante mine, Colombia

X-ray diffraction (XRD), Mössbauer spectrometry (MS), secondary ions mass spectroscopy (SIMS) and laser-ablation microprobe–inductively coupled plasma–mass spectrometry (LAM–ICP–MS) were used to study mineral samples of Colombian auriferous ores collected from the “El Diamante” mine, located in the municipality of Guachavez-Nariño, in Colombia. The samples were prepared as polished thin sections and polished sections. From XRD data, quartz, sphalerite and pyrite were detected and their respective cell parameters were estimated. From MS analyses, pyrite, arsenopyrite and chalcopyrite were identified; their respective hyperfine parameters and respective texture were deduced. Multiple regions of approximately 200 × 200 μm in each sample were analyzed with SIMS; the occurrence of “invisible gold” associated mainly with pyrite and secondarily with arsenopyrite could thus be assigned. It was also found that pyrite is of the arsenious type. Spots from 30 to 40 μm in diameter were analyzed with LAM–ICP–MS for pyrite, arsenopyrite and sphalerite; Au is “homogeneously” distributed inside the structure of the arsenious pyrite and the arsenopyrite (not as inclusions); the chemical composition indicates similarities of this “invisible gold”, forming a solid solution with arsenious pyrite and arsenopyrite. One hundred nineteen and 62 ppm of ‘invisible gold’ was quantified in 21 spots analyzed on pyrite and in 14 spots on arsenopyrite, respectively.     

Adaption of a diffractometer for time‐resolved X‐ray resonant magnetic scattering

A new set‐up is presented to measure element‐selective magnetization dynamics using the ALICE chamber [Grabis et al. (2003), Rev. Sci. Instrum. 74 , 4048–4051] at the BESSY II synchrotron at the Helmholtz‐Zentrum Berlin. A magnetic‐field pulse serves as excitation, and the magnetization precession is probed by element‐selective X‐ray resonant magnetic scattering. With the use of single‐bunch‐generated X‐rays a temporal resolution well below 100 ps is reached. The ALICE diffractometer environment enables investigations of thin films, described here, multilayers and laterally structured samples in reflection or diffuse scattering geometry. The combination of the time‐resolved set‐up with a cryostat in the ALICE chamber will allow temperature‐dependent studies of precessional magnetization dynamics and of damping constants to be conducted over a large temperature range and for a large variety of systems in reflection geometry.     

Dipolar and quadrupolar detection using an FT-ICR MS setup at the MPIK Heidelberg

Dipolar and single-phase two-electrode quadrupolar detection schemes have been investigated at a Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) setup built for the KATRIN experiment at the Max-Planck-Institute for Nuclear Physics (MPIK) in Heidelberg. We present first experimental results of ⁷Li^?+? signals from a cylindrical Penning trap configuration for both detection schemes. While the prominent signal of the conventional dipolar detection scheme marks the reduced cyclotron frequency, the main signal for the quadrupolar detection appears at the sum of the reduced cyclotron frequency and the magnetron frequency. For ideal trapping fields, this sum frequency equals the ion cyclotron frequency ?? _c ?=?qB/(2??m). Sidebands due to the combined motions of the cyclotron mode and magnetron mode are observed by quadrupolar detection which allows the determination of the respective combinations of eigenfrequencies.     

Gold-surface binding of molecular switches studied by M?ssbauer spectroscopy

The nonanuclear coordination compound [Mo^IV{(CN)Fe^III(3-methyl-saldptn)}₈]Cl₄ exhibits multiple spin transitions (3-methyl-saldptn = N,N′-bis(3′′-methyl-2′′-hydroxy-benzyliden)-1,7-diamino-4-azaheptane). This spin crossover cluster is bound via a self-assembled monolayer onto a two dimensional array gold surface. M?ssbauer spectroscopy indicates that the thermally and optically induced spin crossover of the compound is maintained. Thereby, the foundation for its potential practical application (e.g. in the field of information storage) was laid.     

Chaotic inflation in supergravity with Heisenberg symmetry

We propose the introduction of a Heisenberg symmetry of the Kähler potential to solve the problems with chaotic inflation in supergravity, as a viable alternative to the use of shift symmetry. The slope of the inflaton potential emerges from a small Heisenberg symmetry breaking term in the superpotential. The modulus field of the Heisenberg symmetry is stabilized and made heavy with the help of the large vacuum energy density during inflation. The observable predictions are indistinguishable from those of typical chaotic inflation models, however the form of the inflationary superpotential considered here may be interpreted in terms of sneutrino inflation arising from certain classes of string theory.