Stochastic Green's function approach to disordered systems

Based on distributions of local Green's functions we present a stochastic approach to disordered systems. Specifically we address Anderson localisation and cluster effects in binary alloys. Taking Anderson localisation of Holstein polarons as an example we discuss how this stochastic approach can be used for the investigation of interacting disordered systems.Comment: 12 pages, 7 figures, conference proceedings: Progress in Nonequilibrium Green's Functions III, 22-26 August 2005, University of Kiel, German

Ergodicity breaking in a model showing many-body localization

We study the breaking of ergodicity measured in terms of return probability in the evolution of a quantum state of a spin chain. In the non ergodic phase a quantum state evolves in a much smaller fraction of the Hilbert space than would be allowed by the conservation of extensive observables. By the anomalous scaling of the participation ratios with system size we are led to consider the distribution of the wave function coefficients, a standard observable in modern studies of Anderson localization. We finally present a criterion for the identification of the ergodicity breaking (many-body localization) transition based on these distributions which is quite robust and well suited for numerical investigations of a broad class of problems.Comment: 5 pages, 5 figures, final versio

A single defect approximation for localized states on random lattices

Geometrical disorder is present in many physical situations giving rise to eigenvalue problems. The simplest case of diffusion on a random lattice with fluctuating site connectivities is studied analytically and by exact numerical diagonalizations. Localization of eigenmodes is shown to be induced by geometrical defects, that is sites with abnormally low or large connectivities. We expose a ``single defect approximation'' (SDA) scheme founded on this mechanism that provides an accurate quantitative description of both extended and localized regions of the spectrum. We then present a systematic diagrammatic expansion allowing to use SDA for finite-dimensional problems, e.g. to determine the localized harmonic modes of amorphous media.Comment: final version as published, 6 pages, 1 ps-figur

Anderson transition on the Cayley tree as a traveling wave critical point for various probability distributions

For Anderson localization on the Cayley tree, we study the statistics of various observables as a function of the disorder strength $W$ and the number $N$ of generations. We first consider the Landauer transmission $T_N$. In the localized phase, its logarithm follows the traveling wave form $\ln T_N \simeq \bar{\ln T_N} + \ln t^*$ where (i) the disorder-averaged value moves linearly $\bar{\ln (T_N)} \simeq - \frac{N}{\xi_{loc}}$ and the localization length diverges as $\xi_{loc} \sim (W-W_c)^{-\nu_{loc}}$ with $\nu_{loc}=1$ (ii) the variable $t^*$ is a fixed random variable with a power-law tail $P^*(t^*) \sim 1/(t^*)^{1+\beta(W)}$ for large $t^*$ with $0<\beta(W) \leq 1/2$, so that all integer moments of $T_N$ are governed by rare events. In the delocalized phase, the transmission $T_N$ remains a finite random variable as $N \to \infty$, and we measure near criticality the essential singularity $\bar{\ln (T)} \sim - | W_c-W |^{-\kappa_T}$ with $\kappa_T \sim 0.25$. We then consider the statistical properties of normalized eigenstates, in particular the entropy and the Inverse Participation Ratios (I.P.R.). In the localized phase, the typical entropy diverges as $(W-W_c)^{- \nu_S}$ with $\nu_S \sim 1.5$, whereas it grows linearly in $N$ in the delocalized phase. Finally for the I.P.R., we explain how closely related variables propagate as traveling waves in the delocalized phase. In conclusion, both the localized phase and the delocalized phase are characterized by the traveling wave propagation of some probability distributions, and the Anderson localization/delocalization transition then corresponds to a traveling/non-traveling critical point. Moreover, our results point towards the existence of several exponents $\nu$ at criticality.Comment: 28 pages, 21 figures, comments welcom

Properties of low-lying states in a diffusive quantum dot and Fock-space localization

Motivated by an experiment by Sivan et al. (Europhys. Lett. 25, 605 (1994)) and by subsequent theoretical work on localization in Fock space, we study numerically a hierarchical model for a finite many-body system of Fermions moving in a disordered potential and coupled by a two-body interaction. We focus attention on the low-lying states close to the Fermi energy. Both the spreading width and the participation number depend smoothly on excitation energy. This behavior is in keeping with naive expectations and does not display Anderson localization. We show that the model reproduces essential features of the experiment by Sivan et al.Comment: 4 pages, 3 figures, accepted for publication in Phys. Rev. Let

Analytic computation of the Instantaneous Normal Modes spectrum in low density liquids

We analytically compute the spectrum of the Hessian of the Hamiltonian for a system of N particles interacting via a purely repulsive potential in one dimension. Our approach is valid in the low density regime, where we compute the exact spectrum also in the localized sector. We finally perform a numerical analysis of the localization properties of the eigenfunctions.Comment: 4 RevTeX pages, 4 EPS figures. Revised version to appear on Phys. Rev. Let

Low cardiorespiratory fitness in people at risk for type 2 diabetes: early marker for insulin resistance

<p>Abstract</p> <p>Purpose</p> <p>There is a significant association between insulin resistance and low cardiorespiratory fitness in nondiabetic subjects. In a population with risk factors for type 2 diabetes (T2DM), before they are insulin resistant, we investigated low exercise capacity (VO2max) as an early marker of impaired insulin sensitivity in order to determine earlier interventions to prevent development of insulin resistance syndrome (IRS) and T2DM.</p> <p>Methods</p> <p>Cross-sectional analyses of data on 369 (78 men and 291 women) people at risk for IRS and T2DM, aged 45.6 +/- 10 years (20-65 years) old from the Community Diabetes Prevention Project in Minnesota were carried out. The cardiorespiratory fitness (VO2max) by respiratory gas exchange and bicycle ergometer were measured in our at risk non insulin resistant population and compared with a control group living in the same geographic area. Both groups were equally sedentary, matched for age, gender and BMI.</p> <p>Results</p> <p>The most prevalent abnormality in the study population was markedly low VO2max when compared with general work site screening control group, (n = 177; 137F; 40 M, mean age 40 ± 11 years; BMI = 27.8 ± 6.1 kg/m²). Individuals at risk for IRS and T2DM had a VO2max (22 ± 6 ml/kg/min) 15% lower than the control group VO2max (26 ± 9 ml/kg/min) (p < 0.001). It was foun that VO₂max was inversely correlated with HOMA-IR (r = -0.30, p < 0.0001).</p> <p>Conclusions</p> <p>Decreased VO2max is correlated with impaired insulin sensitivity and was the most prevalent abnormality in a population at risk for IRS and T2DM but without overt disease. This raises the possibility that decreased VO2 max is among the earliest indicators of IRS and T2DM therefore, an important risk factor for disease progression.</p

Localization Properties of the Periodic Random Anderson Model

We consider diagonal disordered one-dimensional Anderson models with an underlying periodicity. We assume the simplest periodicity, i.e., we have essentially two lattices, one that is composed of the random potentials and the other of non-random potentials. Due to the periodicity special resonance energies appear, which are related to the lattice constant of the non-random lattice. Further on two different types of behaviors are observed at the resonance energies. When a random site is surrounded by non-random sites, this model exhibits extended states at the resonance energies, whereas otherwise all states are localized with, however, an increase of the localization length at these resonance energies. We study these resonance energies and evaluate the localization length and the density of states around these energies.Comment: 4 page

Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach

The problem of electron--electron lifetime in a quantum dot is studied beyond perturbation theory by mapping it onto the problem of localization in the Fock space. We identify two regimes, localized and delocalized, corresponding to quasiparticle spectral peaks of zero and finite width, respectively. In the localized regime, quasiparticle states are very close to single particle excitations. In the delocalized state, each eigenstate is a superposition of states with very different quasiparticle content. A transition between the two regimes occurs at the energy $\simeq\Delta(g/\ln g)^{1/2}$, where $\Delta$ is the one particle level spacing, and $g$ is the dimensionless conductance. Near this energy there is a broad critical region in which the states are multifractal, and are not described by the Golden Rule.Comment: 13 pages, LaTeX, one figur

Aerobic Exercise Capacity and Pulmonary Function in Athletes With and Without Type 1 Diabetes

OBJECTIVE - To compare the aerobic exercise capacity and pulmonary function between athletes with and without type 1 diabetesRESEARCH DESIGN and METHODS - Fifty-one adult age-matched individuals were assessed in random order to the maximum volume of O(2) consumption (Vo(2 peak max)) (ml/kg/mm) anaerobic threshold (ml/kg/min) peak pulmonary ventilation (V(E)) heart rate (beats per mm) time to exhaustion (mm) forced vital capacity (FEV) (%) forced expiratory volume in the first second (FEV1) (%) total lung capacity (TLC) (%) and lung diffusion capacity for carbon monoxide (DL(CO)) (%) Individuals were 27 with type 1 diabetes 15 athletes (ADM) and 12 nonathletes (NADM) and 24 healthy individuals 12 ADM and 12 NADM Duration of diabetes was 14 6 +/- 6 2 and 15 2 +/- 6 7 years in ADM and NADM respectivelyRESULTS - Vo(2peal max) was higher in ADM than in NADM (P < 0 001) the anaerobic threshold was lower in subjects with type I diabetes than in control subjects (P < 0 001) FEV1 was lower m ADM than in other groups (NADM athletes control and nonathletes control P < 0 001)CONCLUSIONS - Aerobic capacity in subjects with type 1 diabetes with programmed exercise is similar to the capacity of normal athletes despite lower anaerobic threshold and FEV1Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Universidade Federal de São Paulo, Ctr Diabet, Dept Med, Div Endocrinol, São Paulo, BrazilUniversidade Federal de São Paulo, Phys Act & Sports Med Ctr, São Paulo, BrazilUniversidade Federal de São Paulo, Ctr Diabet, Dept Med, Div Endocrinol, São Paulo, BrazilUniversidade Federal de São Paulo, Phys Act & Sports Med Ctr, São Paulo, BrazilWeb of Scienc