Random projections and the optimization of an algorithm for phase retrieval

Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule. For a general class of algorithms, where the basic iteration is specified by the difference map, solutions are associated with fixed points of the map, the attractive character of which determines the effectiveness of the algorithm. The behavior of the difference map near fixed points is controlled by the relative orientation of the tangent spaces of the two constraint subspaces employed by the map. Since the dimensionalities involved are always large in practical applications, it is appropriate to use random matrix theory ideas to analyze the average-case convergence at fixed points. Optimal values of the gamma parameters of the difference map are found which differ somewhat from the values previously obtained on the assumption of orthogonal tangent spaces.Comment: 15 page

Magnetic Properties of Undoped C60C_{60}

The Heisenberg antiferromagnet, which arises from the large $U$ Hubbard model, is investigated on the $C_{60}$ molecule and other fullerenes. The connectivity of $C_{60}$ leads to an exotic classical ground state with nontrivial topology. We argue that there is no phase transition in the Hubbard model as a function of $U/t$, and thus the large $U$ solution is relevant for the physical case of intermediate coupling. The system undergoes a first order metamagnetic phase transition. We also consider the S=1/2 case using perturbation theory. Experimental tests are suggested.Comment: 12 pages, 3 figures (included

Water as a trophic currency in dryland food webs

Water is essential for life on Earth, yet little is known about how water acts as a trophic currency, a unit of value in determining species interactions in terrestrial food webs. We tested the relative importance of groundwater and surface water in riparian food webs by manipulating their availability in dryland floodplains. Primary consumers (crickets) increased in abundance in response to added surface water and groundwater (contained in moist leaves), and predators (spiders and lizards) increased in abundance in response to added surface water, in spite of the presence of a river, an abundant water source. Moreover, the relative magnitude of organism responses to added water was greatest at the most arid site and lowest at the least arid site, mirroring cricket recruitment, which was greatest at the least arid site and lowest at the most arid site. These results suggest that water may be a key currency in terrestrial dryland food webs, which has important implications for predicting ecosystem responses to human‐ and climate‐related changes in hydrology and precipitation

Rules for Computing Symmetry, Density and Stoichiometry in a Quasi-Unit-Cell Model of Quasicrystals

The quasi-unit cell picture describes the atomic structure of quasicrystals in terms of a single, repeating cluster which overlaps neighbors according to specific overlap rules. In this paper, we discuss the precise relationship between a general atomic decoration in the quasi-unit cell picture atomic decorations in the Penrose tiling and in related tiling pictures. Using these relations, we obtain a simple, practical method for determining the density, stoichiometry and symmetry of a quasicrystal based on the atomic decoration of the quasi-unit cell taking proper account of the sharing of atoms between clusters.Comment: 14 pages, 8 figure

Atmospheric Channel Characteristics for Quantum Communication with Continuous Polarization Variables

We investigate the properties of an atmospheric channel for free space quantum communication with continuous polarization variables. In our prepare-and-measure setup, coherent polarization states are transmitted through an atmospheric quantum channel of 100m length on the roof of our institute's building. The signal states are measured by homodyne detection with the help of a local oscillator (LO) which propagates in the same spatial mode as the signal, orthogonally polarized to it. Thus the interference of signal and LO is excellent and atmospheric fluctuations are autocompensated. The LO also acts as spatial and spectral filter, which allows for unrestrained daylight operation. Important characteristics for our system are atmospheric channel influences that could cause polarization, intensity and position excess noise. Therefore we study these influences in detail. Our results indicate that the channel is suitable for our quantum communication system in most weather conditions.Comment: 6 pages, 4 figures, submitted to Applied Physics B following an invitation for the special issue "Selected Papers Presented at the 2009 Spring Meeting of the Quantum Optics and Photonics Section of the German Physical Society

RNA:protein ratio of the unicellular organism as a characteristic of phosphorous and nitrogen stoichiometry and of the cellular requirement of ribosomes for protein synthesis

Background Mean phosphorous:nitrogen (P:N) ratios and relationships of P:N ratios with the growth rate of organisms indicate a surprising similarity among and within microbial species, plants, and insect herbivores. To reveal the cellular mechanisms underling this similarity, the macromolecular composition of seven microorganisms and the effect of specific growth rate (SGR) on RNA:protein ratio, the number of ribosomes, and peptide elongation rate (PER) were analyzed under different conditions of exponential growth. Results It was found that P:N ratios calculated from RNA and protein contents in these particular organisms were in the same range as the mean ratios reported for diverse organisms and had similar positive relationships with growth rate, consistent with the growth-rate hypothesis. The efficiency of protein synthesis in microorganisms is estimated as the number of active ribosomes required for the incorporation of one amino acid into the synthesized protein. This parameter is calculated as the SGR:PER ratio. Experimental and theoretical evidence indicated that the requirement of ribosomes for protein synthesis is proportional to the RNA:protein ratio. The constant of proportionality had the same values for all organisms, and was derived mechanistically from the characteristics of the protein-synthesis machinery of the cell (the number of nucleotides per ribosome, the average masses of nucleotides and amino acids, the fraction of ribosomal RNA in the total RNA, and the fraction of active ribosomes). Impairment of the growth conditions decreased the RNA:protein ratio and increased the overall efficiency of protein synthesis in the microorganisms. Conclusion Our results suggest that the decrease in RNA:protein and estimated P:N ratios with decrease in the growth rate of the microorganism is a consequence of an increased overall efficiency of protein synthesis in the cell resulting from activation of the general stress response and increased transcription of cellular maintenance genes at the expense of growth related genes. The strong link between P:N stoichiometry, RNA:protein ratio, ribosomal requirement for protein synthesis, and growth rate of microorganisms indicated by the study could be used to characterize the N and P economy of complex ecosystems such as soils and the oceans

Quantum filtering of optical coherent states

We propose and experimentally demonstrate nondestructive and noiseless removal (filtering) of vacuum states from an arbitrary set of coherent states of continuous variable systems. Errors, i.e., vacuum states in the quantum information are diagnosed through a weak measurement, and on that basis, probabilistically filtered out. We consider three different filters based on on-off detection, phase stabilized, and phase randomized homodyne detection. We find that on-off detection, optimal in the ideal theoretical setting, is superior to the homodyne strategy also in a practical setting

Spin tunneling in the Kagom\'e antiferromagnet

The collective tunneling of a small cluster of spins between two degenerate ground state configurations of the Kagom\'{e}-lattice quantum Heisenberg antiferromagnet is \mbox{studied}. The cluster consists of the six spins on a hexagon of the lattice. The resulting tunnel splitting energy $\Delta$ is calculated in detail, including the prefactor to the exponential \exp(- \SSo / \hbar). This is done by setting up a coherent spin state path integral in imaginary time and evaluating it by the method of steepest descent. The hexagon tunneling problem is mapped onto a much simpler tunneling problem, involving only one collective degree of freedom, which can be treated by known methods. It is found that for half-odd-integer spins, the tunneling amplitude and the tunnel splitting energy are exactly zero, because of destructive interference between symmetry-related $(+)$-instanton and $(-)$-instanton tunneling paths. This destructive interference is shown to occur also for certain larger loops of spins on the Kagom\'{e} lattice. For small, integer spins, our results suggest that tunneling strongly competes with \mbox{in-plane} order-from-disorder selection effects; it constitutes a disordering mechanism that might drive the system into a partially disordered ground state, related to a spin nematic.Comment: 38 pages (RevTex), 8 figures upon request PRB921

Quantum spin models with exact dimer ground states

Inspired by the exact solution of the Majumdar-Ghosh model, a family of one-dimensional, translationally invariant spin hamiltonians is constructed. The exchange coupling in these models is antiferromagnetic, and decreases linearly with the separation between the spins. The coupling becomes identically zero beyond a certain distance. It is rigorously proved that the dimer configuration is an exact, superstable ground state configuration of all the members of the family on a periodic chain. The ground state is two-fold degenerate, and there exists an energy gap above the ground state. The Majumdar-Ghosh hamiltonian with two-fold degenerate dimer ground state is just the first member of the family. The scheme of construction is generalized to two and three dimensions, and illustrated with the help of some concrete examples. The first member in two dimensions is the Shastry-Sutherland model. Many of these models have exponentially degenerate, exact dimer ground states.Comment: 10 pages, 8 figures, revtex, to appear in Phys. Rev.