The Anderson Model as a Matrix Model

In this paper we describe a strategy to study the Anderson model of an electron in a random potential at weak coupling by a renormalization group analysis. There is an interesting technical analogy between this problem and the theory of random matrices. In d=2 the random matrices which appear are approximately of the free type well known to physicists and mathematicians, and their asymptotic eigenvalue distribution is therefore simply Wigner's law. However in d=3 the natural random matrices that appear have non-trivial constraints of a geometrical origin. It would be interesting to develop a general theory of these constrained random matrices, which presumably play an interesting role for many non-integrable problems related to diffusion. We present a first step in this direction, namely a rigorous bound on the tail of the eigenvalue distribution of such objects based on large deviation and graphical estimates. This bound allows to prove regularity and decay properties of the averaged Green's functions and the density of states for a three dimensional model with a thin conducting band and an energy close to the border of the band, for sufficiently small coupling constant.Comment: 23 pages, LateX, ps file available at http://cpth.polytechnique.fr/cpth/rivass/articles.htm

Nearly optimal solutions for the Chow Parameters Problem and low-weight approximation of halfspaces

The \emph{Chow parameters} of a Boolean function $f: \{-1,1\}^n \to \{-1,1\}$ are its $n+1$ degree-0 and degree-1 Fourier coefficients. It has been known since 1961 (Chow, Tannenbaum) that the (exact values of the) Chow parameters of any linear threshold function $f$ uniquely specify $f$ within the space of all Boolean functions, but until recently (O'Donnell and Servedio) nothing was known about efficient algorithms for \emph{reconstructing} $f$ (exactly or approximately) from exact or approximate values of its Chow parameters. We refer to this reconstruction problem as the \emph{Chow Parameters Problem.} Our main result is a new algorithm for the Chow Parameters Problem which, given (sufficiently accurate approximations to) the Chow parameters of any linear threshold function $f$, runs in time \tilde{O}(n^2)\cdot (1/\eps)^{O(\log^2(1/\eps))} and with high probability outputs a representation of an LTF $f'$ that is \eps-close to $f$. The only previous algorithm (O'Donnell and Servedio) had running time \poly(n) \cdot 2^{2^{\tilde{O}(1/\eps^2)}}. As a byproduct of our approach, we show that for any linear threshold function $f$ over $\{-1,1\}^n$, there is a linear threshold function $f'$ which is \eps-close to $f$ and has all weights that are integers at most \sqrt{n} \cdot (1/\eps)^{O(\log^2(1/\eps))}. This significantly improves the best previous result of Diakonikolas and Servedio which gave a \poly(n) \cdot 2^{\tilde{O}(1/\eps^{2/3})} weight bound, and is close to the known lower bound of $\max\{\sqrt{n},$ (1/\eps)^{\Omega(\log \log (1/\eps))}\} (Goldberg, Servedio). Our techniques also yield improved algorithms for related problems in learning theory

Establishing a Connection Between Active Region Outflows and the Solar Wind: Abundance Measurements with EIS/Hinode

One of the most interesting discoveries of the X-ray Telescope and EUV Imaging Spectrometer (EIS) on board the Hinode solar observatory is the presence of persistent high temperature high speed outflows from the edges of active regions. Measurements by EIS indicate that the outflows reach velocities of 50 km/s with spectral line asymmetries approaching 200 km/s. It has been suggested that these outflows may lie on open field lines that connect to the heliosphere, and that they could potentially be a significant source of the slow speed solar wind. A direct link has been difficult to establish, however. In this letter, we use EIS measurements of spectral line intensities that are sensitive to changes in the relative abundance of Si and S as a result of the first ionization potential (FIP) effect, to measure the chemical composition in the outflow regions of AR 10978 over a period of 5 days in December 2007. We find that Si is always enhanced over S by a factor of 3--4. This is generally consistent with the enhancement factor of low FIP elements measured in-situ in the slow solar wind by non-spectroscopic methods. Plasma with a slow wind-like composition was therefore flowing from the edge of the active region for at least 5 days. Furthermore, on December 10--11, when the outflow from the western side was favorably oriented in the Earth direction, the Si/S ratio was found to match the value measured a few days later by ACE/SWICS. These results provide strong observational evidence for a direct connection between the solar wind, and the coronal plasma in the outflow regions.Comment: Version to be published in ApJ

Determinant Bounds and the Matsubara UV Problem of Many-Fermion Systems

It is known that perturbation theory converges in fermionic field theory at weak coupling if the interaction and the covariance are summable and if certain determinants arising in the expansion can be bounded efficiently, e.g. if the covariance admits a Gram representation with a finite Gram constant. The covariances of the standard many--fermion systems do not fall into this class due to the slow decay of the covariance at large Matsubara frequency, giving rise to a UV problem in the integration over degrees of freedom with Matsubara frequencies larger than some Omega (usually the first step in a multiscale analysis). We show that these covariances do not have Gram representations on any separable Hilbert space. We then prove a general bound for determinants associated to chronological products which is stronger than the usual Gram bound and which applies to the many--fermion case. This allows us to prove convergence of the first integration step in a rather easy way, for a short--range interaction which can be arbitrarily strong, provided Omega is chosen large enough. Moreover, we give - for the first time - nonperturbative bounds on all scales for the case of scale decompositions of the propagator which do not impose cutoffs on the Matsubara frequency.Comment: 29 pages LaTe

Theory of Weak Hypernuclear Decay

The weak nonmesonic decay of Lambda-hypernuclei is studied in the context of a one-meson-exchange model. Predictions are made for the decay rate, p/n stimulation ratio and the asymmetry in polarized hypernuclear decay.Comment: Standard 41 page Latex fil

The impact of midlife educational, work, health and family experiences on men's early retirement

Objectives. In empirical studies on predictors of retirement, midlife experiences have often remained implicit or been neglected. This study aims to improve our understanding of retirement by examining the impact of midlife educational, work, health, and family experiences on early retirement intentions and behavior. We distinguish theoretically and empirically between financial and nonfinancial preretirement factors through which midlife experiences could affect retirement. Methods. Using panel data of 1,229 Dutch male older workers, we estimated linear regression models to explain retirement intentions and logistic regression models to explain retirement behavior. Results. Midlife experiences in all studied life spheres are related to retirement intentions. Educational investments, job changes, late transitions into parenthood, and late divorces are associated with weaker intentions to retire early. Midlife health problems are related to stronger early retirement intentions. For midlife work and family experiences, the relationships are (partly) mediated by the preretirement financial opportunity structure. In the educational, work, and health spheres, the preretirement nonfinancial situation has a mediating effect. Only some of the predictors of retirement intentions also predicted retirement behavior. Discussion. Given the destandardization of life courses, information on distal life experiences might become even more important toward understanding retirement in the future. keywords: children; divorce; education; life course; retirement; work history

Design of an RSFQ Control Circuit to Observe MQC on an rf-SQUID

We believe that the best chance to observe macroscopic quantum coherence (MQC) in a rf-SQUID qubit is to use on-chip RSFQ digital circuits for preparing, evolving and reading out the qubit's quantum state. This approach allows experiments to be conducted on a very short time scale (sub-nanosecond) without the use of large bandwidth control lines that would couple environmental degrees of freedom to the qubit thus contributing to its decoherence. In this paper we present our design of a RSFQ digital control circuit for demonstrating MQC in a rf-SQUID. We assess some of the key practical issues in the circuit design including the achievement of the necessary flux bias stability. We present an "active" isolation structure to be used to increase coherence times. The structure decouples the SQUID from external degrees of freedom, and then couples it to the output measurement circuitry when required, all under the active control of RSFQ circuits. Research supported in part by ARO grant # DAAG55-98-1-0367.Comment: 4 pages. More information and publications at http://www.ece.rochester.edu:8080/users/sde/research/publications/index.htm

An Anomalous Extra Z Prime from Intersecting Branes with Drell-Yan and Direct Photons at the LHC

We quantify the impact of gauge anomalies at the Large Hadron Collider by studying the invariant mass distributions in Drell-Yan and in double prompt photon, using an extension of the Standard Model characterized by an additional anomalous U(1) derived from intersecting branes. The approach is rather general and applies to any anomalous abelian gauge current. Anomalies are cancelled using either the Wess-Zumino mechanism with suitable Peccei-Quinn-like interactions and a Stueckelberg axion, or by the Green-Schwarz mechanism. We compare predictions for the corresponding extra Z-prime to anomaly-free realizations such as those involving U(1)_{B-L}. We identify the leading anomalous corrections to both channels, which contribute at higher orders, and compare them against the next-to-next-to-leading order (NNLO) QCD background. Anomalous effects in these inclusive observables are found to be very small, far below the percent level and below the size of the typical QCD corrections quantified by NNLO K-factors.Comment: 46 pages, 36 figures, comments and citations adde

Forward modeling of emission in SDO/AIA passbands from dynamic 3D simulations

It is typically assumed that emission in the passbands of the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) is dominated by single or several strong lines from ions that under equilibrium conditions are formed in a narrow range of temperatures. However, most SDO/AIA channels also contain contributions from lines of ions that have formation temperatures that are significantly different from the "dominant" ion(s). We investigate the importance of these lines by forward modeling the emission in the SDO/AIA channels with 3D radiative MHD simulations of a model that spans the upper layer of the convection zone to the low corona. The model is highly dynamic. In addition, we pump a steadily increasing magnetic flux into the corona, in order to increase the coronal temperature through the dissipation of magnetic stresses. As a consequence, the model covers different ranges of coronal temperatures as time progresses. The model covers coronal temperatures that are representative of plasma conditions in coronal holes and quiet sun. The 131, 171, and 304 \AA{} AIA passbands are found to be least influenced by the so-called "non-dominant" ions, and the emission observed in these channels comes mostly from plasma at temperatures near the formation temperature of the dominant ion(s). On the other hand, the other channels are strongly influenced by the non-dominant ions, and therefore significant emission in these channels comes from plasma at temperatures that are different from the "canonical" values. We have also studied the influence of non-dominant ions on the AIA passbands when different element abundances are assumed (photospheric and coronal), and when the effects of the electron density on the contribution function are taken into account.Comment: 48 pages, 14 figures, accepted to be publish in Ap