9,346 research outputs found
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 with each , where
is a fixed positive definite matrix and a 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
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