Variety of idempotents in nonassociative algebras

In this paper, we study the variety of all nonassociative (NA) algebras from the idempotent point of view. We are interested, in particular, in the spectral properties of idempotents when algebra is generic, i.e. idempotents are in general position. Our main result states that in this case, there exist at least $n-1$ nontrivial obstructions (syzygies) on the Peirce spectrum of a generic NA algebra of dimension $n$. We also discuss the exceptionality of the eigenvalue $\lambda=\frac12$ which appears in the spectrum of idempotents in many classical examples of NA algebras and characterize its extremal properties in metrised algebras.Comment: 27 pages, 1 figure, submitte

Output of a pulsed atom laser

We study the output properties of a pulsed atom laser consisting of an interacting Bose-Einstein condensate (BEC) in a magnetic trap and an additional rf field transferring atoms to an untrapped Zeeman sublevel. For weak output coupling we calculate the dynamics of the decaying condensate population, of its chemical potential and the velocity of the output atoms analytically.Comment: 4 pages, RevTeX. Full ps file available on http://mpqibmr1.mpq.mpg.de:5000/~man

Disease-associated missense mutations in bestrophin-1 affect cellular trafficking and anion conductance

Bestrophin-1, an integral membrane protein encoded by the BEST1 gene, is localized predominantly to the basolateral membrane of the retinal pigment epithelium. Mutations in the BEST1 gene have been associated with Best vitelliforme macular dystrophy (BMD), a central retinopathy with autosomal dominant inheritance and variable penetrance. Over 120 disease-causing mutations are known, the majority of which result in amino acid substitutions within four mutational hot-spot regions in the highly conserved N-terminal half of the protein. Although initially thought to impair Cl⁻ channel function, the molecular pathology of BEST1 mutations is still controversial. We have analyzed the subcellular localization of 13 disease-associated BEST1 mutant proteins in polarized MDCK II cells, an established model of apical to basolateral protein sorting. Immunostaining demonstrated that nine of the 13 mutant proteins failed to integrate into the cell membrane. The defective proteins were predominantly retained in the cytoplasm, whereas wild-type bestrophin-1 revealed cell membrane localization. Functional analysis of I⁻ fluxes in HEK-293 cells showed that all mutants exhibited a significant reduction in anion conductance. Our data indicate that defective intracellular trafficking could be a common cause of BMD accompanied by impaired anion conductance, representing a loss of anion channel function that is probably due to mistargeting of mutant protein

Raman Topography and Strain Uniformity of Large-Area Epitaxial Graphene

We report results from two-dimensional Raman spectroscopy studies of large-area epitaxial graphene grown on SiC. Our work reveals unexpectedly large variation in Raman peak position across the sample resulting from inhomogeneity in the strain of the graphene film, which we show to be correlated with physical topography by coupling Raman spectroscopy with atomic force microscopy. We report that essentially strain free graphene is possible even for epitaxial graphene.Comment: 10 pages, 3 figure

Spatial coherence and density correlations of trapped Bose gases

We study first and second order coherence of trapped dilute Bose gases using appropriate correlation functions. Special attention is given to the discussion of second order or density correlations. Except for a small region around the surface of a Bose-Einstein condensate the correlations can be accurately described as those of a locally homogeneous gas with a spatially varying chemical potential. The degrees of first and second order coherence are therefore functions of temperature, chemical potential, and position. The second order correlation function is governed both by the tendency of bosonic atoms to cluster and by a strong repulsion at small distances due to atomic interactions. In present experiments both effects are of comparable magnitude. Below the critical temperature the range of the bosonic correlation is affected by the presence of collective quasi-particle excitations. The results of some recent experiments on second and third order coherence are discussed. It is shown that the relation between the measured quantities and the correlation functions is much weaker than previously assumed.Comment: RevTeX, 25 pages with 7 Postscript figure

Interference of Bose-Einstein condensates in momentum space

We suggest an experiment to investigate the linear superposition of two spatially separated Bose-Einstein condensates. Due to the coherent combination of the two wave functions, the dynamic structure factor, measurable through inelastic photon scattering at high momentum transfer $q$, is predicted to exhibit interference fringes with frequency period $\Delta\nu = q/md$ where $d$ is the distance between the condensates. We show that the coherent configuration corresponds to an eigenstate of the physical observable measured in the experiment and that the relative phase of the condensates is hence created through the measurement process.Comment: 4 pages and 2 eps figure

Raman spectra of epitaxial graphene on SiC and of epitaxial graphene transferred to SiO2

Raman spectra were measured for mono-, bi- and trilayer graphene grown on SiC by solid state graphitization, whereby the number of layers was pre-assigned by angle-resolved ultraviolet photoemission spectroscopy. It was found that the only unambiguous fingerprint in Raman spectroscopy to identify the number of layers for graphene on SiC(0001) is the linewidth of the 2D (or D*) peak. The Raman spectra of epitaxial graphene show significant differences as compared to micromechanically cleaved graphene obtained from highly oriented pyrolytic graphite crystals. The G peak is found to be blue-shifted. The 2D peak does not exhibit any obvious shoulder structures but it is much broader and almost resembles a single-peak even for multilayers. Flakes of epitaxial graphene were transferred from SiC onto SiO2 for further Raman studies. A comparison of the Raman data obtained for graphene on SiC with data for epitaxial graphene transferred to SiO2 reveals that the G peak blue-shift is clearly due to the SiC substrate. The broadened 2D peak however stems from the graphene structure itself and not from the substrate.Comment: 27 pages, 8 figure

A method for collective excitation of Bose-Einstein condensate

It is shown that by an appropriate modification of the trapping potential one may create collective excitation in cold atom Bose-Einstein condensate. The proposed method is complementary to earlier suggestions. It seems to be feasible experimentally --- it requires only a proper change in time of the potential in atomic traps, as realized in laboratories already.Comment: 4 pages, 4 figures; major revision, several references added, interacting particles case adde