Almost Sure Frequency Independence of the Dimension of the Spectrum of Sturmian Hamiltonians

We consider the spectrum of discrete Schr\"odinger operators with Sturmian potentials and show that for sufficiently large coupling, its Hausdorff dimension and its upper box counting dimension are the same for Lebesgue almost every value of the frequency.Comment: 12 pages, to appear in Commun. Math. Phy

Giant Optical Non-linearity induced by a Single Two-Level System interacting with a Cavity in the Purcell Regime

A two-level system that is coupled to a high-finesse cavity in the Purcell regime exhibits a giant optical non-linearity due to the saturation of the two-level system at very low intensities, of the order of one photon per lifetime. We perform a detailed analysis of this effect, taking into account the most important practical imperfections. Our conclusion is that an experimental demonstration of the giant non-linearity should be feasible using semiconductor micropillar cavities containing a single quantum dot in resonance with the cavity mode.Comment: 40 pages, 16 figures, accepted in Phys. Rev.

High-Resolution Measurements of the Dark Matter Halo of NGC 2976: Evidence for a Shallow Density Profile

We have obtained two-dimensional velocity fields of the dwarf spiral galaxy NGC 2976 in Halpha and CO. The high spatial (~75 pc) and spectral (13 km/s and 2 km/s, respectively) resolution of these observations, along with our multicolor optical and near-infrared imaging, allow us to measure the shape of the density profile of the dark matter halo with good precision. We find that the total (baryonic plus dark matter) mass distribution of NGC 2976 follows a rho_tot ~ r^(-0.27 +/- 0.09) power law out to a radius of 1.8 kpc, assuming that the observed radial motions provide no support. The density profile attributed to the dark halo is even shallower, consistent with a nearly constant density of dark matter over the entire observed region. A maximal disk fit yields an upper limit to the K-band stellar mass-to-light ratio (M*/L_K) of 0.09^{+0.15}_{-0.08} M_sun/L_sun,K (including systematic uncertainties), with the caveat that for M*/L_K > 0.19 M_sun/L_sun,K the dark matter density increases with radius, which is unphysical. Assuming 0.10 M_sun/L_sun,K < M*/L_K < 0.19 M_sun/L_sun,K, the dark matter density profile lies between rho_dm ~ r^-0.17 and rho_dm ~ r^-0.01. Therefore, independent of any assumptions about the stellar disk or the functional form of the density profile, NGC 2976 does not contain a cuspy dark matter halo. We also investigate some of the systematic effects that can hamper rotation curve studies, and show that 1) longslit rotation curves are far more vulnerable to systematic errors than two-dimensional velocity fields, 2) NGC 2976 contains large radial motions at small radii, and 3) the Halpha and CO velocity fields of NGC 2976 agree within their uncertainties. [slightly abridged]Comment: 30 pages, 4 tables, 13 figures (7 in color; Figures 1 and 3 are low-resolution to save space). Accepted for publication in ApJ. Version with full-resolution figures available at http://astro.berkeley.edu/~bolatto/ngc2976rotation.ps (46 MB

Lyapunov exponents for products of complex Gaussian random matrices

The exact value of the Lyapunov exponents for the random matrix product $P_N = A_N A_{N-1}...A_1$ with each $A_i = \Sigma^{1/2} G_i^{\rm c}$, where $\Sigma$ is a fixed $d \times d$ positive definite matrix and $G_i^{\rm c}$ a $d \times d$ complex Gaussian matrix with entries standard complex normals, are calculated. Also obtained is an exact expression for the sum of the Lyapunov exponents in both the complex and real cases, and the Lyapunov exponents for diffusing complex matrices.Comment: 15 page

Fourier Transform Scanning Tunneling Spectroscopy: the possibility to obtain constant energy maps and the band dispersion using a local measurement

We present here an overview of the Fourier Transform Scanning Tunneling spectroscopy technique (FT-STS). This technique allows one to probe the electronic properties of a two-dimensional system by analyzing the standing waves formed in the vicinity of defects. We review both the experimental and theoretical aspects of this approach, basing our analysis on some of our previous results, as well as on other results described in the literature. We explain how the topology of the constant energy maps can be deduced from the FT of dI/dV map images which exhibit standing waves patterns. We show that not only the position of the features observed in the FT maps, but also their shape can be explained using different theoretical models of different levels of approximation. Thus, starting with the classical and well known expression of the Lindhard susceptibility which describes the screening of electron in a free electron gas, we show that from the momentum dependence of the susceptibility we can deduce the topology of the constant energy maps in a joint density of states approximation (JDOS). We describe how some of the specific features predicted by the JDOS are (or are not) observed experimentally in the FT maps. The role of the phase factors which are neglected in the rough JDOS approximation is described using the stationary phase conditions. We present also the technique of the T-matrix approximation, which takes into account accurately these phase factors. This technique has been successfully applied to normal metals, as well as to systems with more complicated constant energy contours. We present results recently obtained on graphene systems which demonstrate the power of this technique, and the usefulness of local measurements for determining the band structure, the map of the Fermi energy and the constant-energy maps.Comment: 33 pages, 15 figures; invited review article, to appear in Journal of Physics D: Applied Physic

Measurement of the 58Ni(α, γ) 62Zn reaction and its astrophysical impact

Funding Details: PHY 08-22648, NSF, National Science Foundation; PHY 0969058, NSF, National Science Foundation; PHY 1102511, NSF, National Science FoundationCross section measurements of the 58Ni(α,γ)62Zn reaction were performed in the energy range Eα=5.5to9.5 MeV at the Nuclear Science Laboratory of the University of Notre Dame, using the NSCL Summing NaI(Tl) detector and the γ-summing technique. The measurements are compared to predictions in the statistical Hauser-Feshbach model of nuclear reactions using the SMARAGD code. It is found that the energy dependence of the cross section is reproduced well but the absolute value is overestimated by the prediction. This can be remedied by rescaling the α width by a factor of 0.45. Stellar reactivities were calculated with the rescaled α width and their impact on nucleosynthesis in type Ia supernovae has been studied. It is found that the resulting abundances change by up to 5% when using the new reactivities. © 2014 American Physical Society.Peer reviewe

Hidden dimers and the matrix maps: Fibonacci chains re-visited

The existence of cycles of the matrix maps in Fibonacci class of lattices is well established. We show that such cycles are intimately connected with the presence of interesting positional correlations among the constituent `atoms' in a one dimensional quasiperiodic lattice. We particularly address the transfer model of the classic golden mean Fibonacci chain where a six cycle of the full matrix map exists at the centre of the spectrum [Kohmoto et al, Phys. Rev. B 35, 1020 (1987)], and for which no simple physical picture has so far been provided, to the best of our knowledge. In addition, we show that our prescription leads to a determination of other energy values for a mixed model of the Fibonacci chain, for which the full matrix map may have similar cyclic behaviour. Apart from the standard transfer-model of a golden mean Fibonacci chain, we address a variant of it and the silver mean lattice, where the existence of four cycles of the matrix map is already known to exist. The underlying positional correlations for all such cases are discussed in details.Comment: 14 pages, 2 figures. Submitted to Physical Review

Recent results from the STAR spin program at RHIC

The STAR experiment uses polarized p+p collisions at RHIC to determine the contributions to the spin of the proton from gluon spin and from orbital angular momentum of the quarks and gluons. Selective STAR measurements of the longitudinal double spin asymmetry for inclusive jet and inclusive hadron production are presented here. In addition, we report measurements of the transverse spin asymmetry for di-jet production at mid-rapidity and the transverse single-spin asymmetry for forward pi0 productionComment: 4 pages, 5 figures, presented at GHP06 conferenc

Charge Deficiency, Charge Transport and Comparison of Dimensions

We study the relative index of two orthogonal infinite dimensional projections which, in the finite dimensional case, is the difference in their dimensions. We relate the relative index to the Fredholm index of appropriate operators, discuss its basic properties, and obtain various formulas for it. We apply the relative index to counting the change in the number of electrons below the Fermi energy of certain quantum systems and interpret it as the charge deficiency. We study the relation of the charge deficiency with the notion of adiabatic charge transport that arises from the consideration of the adiabatic curvature. It is shown that, under a certain covariance, (homogeneity), condition the two are related. The relative index is related to Bellissard's theory of the Integer Hall effect. For Landau Hamiltonians the relative index is computed explicitly for all Landau levels.Comment: 23 pages, no figure

Deep learning predicts function of live retinal pigment epithelium from quantitative microscopy.

Increases in the number of cell therapies in the preclinical and clinical phases have prompted the need for reliable and non-invasive assays to validate transplant function in clinical biomanufacturing. We developed a robust characterization methodology composed of quantitative bright-field absorbance microscopy (QBAM) and deep neural networks (DNNs) to non-invasively predict tissue function and cellular donor identity. The methodology was validated using clinical-grade induced pluripotent stem cell derived retinal pigment epithelial cells (iPSC-RPE). QBAM images of iPSC-RPE were used to train DNNs that predicted iPSC-RPE monolayer transepithelial resistance, predicted polarized vascular endothelial growth factor (VEGF) secretion, and matched iPSC-RPE monolayers to the stem cell donors. DNN predictions were supplemented with traditional machine learning algorithms that identified shape and texture features of single cells that were used to predict tissue function and iPSC donor identity. These results demonstrate non-invasive cell therapy characterization can be achieved with QBAM and machine learning