Ordered spectral statistics in 1D disordered supersymmetric quantum mechanics and Sinai diffusion with dilute absorbers

Some results on the ordered statistics of eigenvalues for one-dimensional random Schr\"odinger Hamiltonians are reviewed. In the case of supersymmetric quantum mechanics with disorder, the existence of low energy delocalized states induces eigenvalue correlations and makes the ordered statistics problem nontrivial. The resulting distributions are used to analyze the problem of classical diffusion in a random force field (Sinai problem) in the presence of weakly concentrated absorbers. It is shown that the slowly decaying averaged return probability of the Sinai problem, \mean{P(x,t|x,0)}\sim \ln^{-2}t, is converted into a power law decay, \mean{P(x,t|x,0)}\sim t^{-\sqrt{2\rho/g}}, where $g$ is the strength of the random force field and $\rho$ the density of absorbers.Comment: 10 pages ; LaTeX ; 4 pdf figures ; Proceedings of the meeting "Fundations and Applications of non-equilibrium statistical mechanics", Nordita, Stockholm, october 2011 ; v2: appendix added ; v3: figure 2.left adde

Sinai model in presence of dilute absorbers

We study the Sinai model for the diffusion of a particle in a one dimension random potential in presence of a small concentration $\rho$ of perfect absorbers using the asymptotically exact real space renormalization method. We compute the survival probability, the averaged diffusion front and return probability, the two particle meeting probability, the distribution of total distance traveled before absorption and the averaged Green's function of the associated Schrodinger operator. Our work confirms some recent results of Texier and Hagendorf obtained by Dyson-Schmidt methods, and extends them to other observables and in presence of a drift. In particular the power law density of states is found to hold in all cases. Irrespective of the drift, the asymptotic rescaled diffusion front of surviving particles is found to be a symmetric step distribution, uniform for $|x| < {1/2} \xi(t)$, where $\xi(t)$ is a new, survival length scale ($\xi(t)=T \ln t/\sqrt{\rho}$ in the absence of drift). Survival outside this sharp region is found to decay with a larger exponent, continuously varying with the rescaled distance $x/\xi(t)$. A simple physical picture based on a saddle point is given, and universality is discussed.Comment: 21 pages, 2 figure

Functionals of the Brownian motion, localization and metric graphs

We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of the Brownian motion arise in the study of electronic transport in weakly disordered metals (weak localization). Two aspects of the physics of the one-dimensional strong localization are reviewed : some properties of the scattering by a random potential (time delay distribution) and a study of the spectrum of a random potential on a bounded domain (the extreme value statistics of the eigenvalues). Then we mention several results concerning the diffusion on graphs, and more generally the spectral properties of the Schr\"odinger operator on graphs. The interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated. Finally, we consider a two-dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices. We recall the connection between spectral properties of this model and winding functionals of the planar Brownian motion.Comment: Review article. 50 pages, 21 eps figures. Version 2: section 5.5 and conclusion added. Several references adde

Nature of the bad metallic behavior of Fe_{1.06}Te inferred from its evolution in the magnetic state

We investigate with angle resolved photoelectron spectroscopy the change of the Fermi Surface (FS) and the main bands from the paramagnetic (PM) state to the antiferromagnetic (AFM) occurring below 72 K in Fe_{1.06}Te. The evolution is completely different from that observed in iron-pnictides as nesting is absent. The AFM state is a rather good metal, in agreement with our magnetic band structure calculation. On the other hand, the PM state is very anomalous with a large pseudogap on the electron pocket that closes in the AFM state. We discuss this behavior in connection with spin fluctuations existing above the magnetic transition and the correlations predicted in the spin-freezing regime of the incoherent metallic state

On the distribution of the Wigner time delay in one-dimensional disordered systems

We consider the scattering by a one-dimensional random potential and derive the probability distribution of the corresponding Wigner time delay. It is shown that the limiting distribution is the same for two different models and coincides with the one predicted by random matrix theory. It is also shown that the corresponding stochastic process is given by an exponential functional of the potential.Comment: 11 pages, four references adde

Ecological niche modelling of Hemipteran insects in Cameroon ; the paradox of a vector-borne transmission for Mycobacterium ulcerans, the causative agent of Buruli ulcer

Background: The mode of transmission of the emerging neglected disease Buruli ulcer is unknown. Several potential transmission pathways have been proposed, such as amoebae, or transmission through food webs. Several lines of evidence have suggested that biting aquatic insects, Naucoridae and Belostomatidae, may act as vectors, however this proposal remains controversial. Materials and methods: Herein, based on sampling in Cameroon, we construct an ecological niche model of these insects to describe their spatial distribution. We predict their distribution across West Africa, describe important environmental drivers of their abundance, and examine the correlation between their abundance and Buruli ulcer prevalence in the context of the Bradford-Hill guidelines. Results: We find a significant positive correlation between the abundance of the insects and the prevalence of Buruli ulcer. This correlation changes in space and time, it is significant in one Camerounese study region in (Akonolinga) and not other (Bankim). We discuss notable environmental differences between these regions. Conclusion: We interpret the presence of, and change in, this correlation as evidence (though not proof) that these insects may be locally important in the environmental persistence, or transmission, of Mycobacterium. ulcerans. This is consistent with the idea of M. ulcerans as a pathogen transmitted by multiple modes of infection, the importance of any one pathway changing from region to region, depending on the local environmental conditions

Breaking supersymmetry in a one-dimensional random Hamiltonian

The one-dimensional supersymmetric random Hamiltonian $H_{susy}=-\frac{d^2}{dx^2}+\phi^2+\phi'$, where $\phi(x)$ is a Gaussian white noise of zero mean and variance $g$, presents particular spectral and localization properties at low energy: a Dyson singularity in the integrated density of states (IDoS) $N(E)\sim1/\ln^2E$ and a delocalization transition related to the behaviour of the Lyapunov exponent (inverse localization length) vanishing like $\gamma(E)\sim1/|\ln{}E|$ as $E\to0$. We study how this picture is affected by breaking supersymmetry with a scalar random potential: $H=H_{susy}+V(x)$ where $V(x)$ is a Gaussian white noise of variance $\sigma$. In the limit $\sigma\ll{g}^3$, a fraction of states $N(0)\sim{g}/\ln^2(g^3/\sigma)$ migrate to the negative spectrum and the Lyapunov exponent reaches a finite value $\gamma(0)\sim{g}/\ln(g^3/\sigma)$ at E=0. Exponential (Lifshits) tail of the IDoS for $E\to-\infty$ is studied in detail and is shown to involve a competition between the two noises $\phi$ and $V$ whatever the larger is. This analysis relies on analytic results for $N(E)$ and $\gamma(E)$ obtained by two different methods: a stochastic method and the replica method. The problem of extreme value statistics of eigenvalues is also considered (distribution of the n-th excited state energy). The results are analyzed in the context of classical diffusion in a random force field in the presence of random annihilation/creation local rates.Comment: 33 pages, LaTeX, 13 eps figures ; 2nd version : refs. adde

Imaging Spectroscopy for Extrasolar Planet Detection

Coronagraphic imaging in combination with moderate to high spectral resolution may prove more effective in both detecting extrasolar planets and characterizing them than a standard coronagraphic imaging approach. We envisage an integral-field spectrograph coupled to a coronagraph to produce a 3D datacube. For the idealised case where the spectrum of the star is well-known and unchanging across the field, we discuss the utility of cross-correlation to seek the extrasolar planet signal, and describe a mathematical approach to completely eliminate stray light from the host star (although not its Poisson noise). For the case where the PSF is dominated by diffraction and scattering effects, and comprises a multitude of speckles within an Airy pattern typical of a space-based observation, we turn the wavelength dependence of the PSF to advantage and present a general way to eliminate the contribution from the star while preserving both the flux and spectrum of the extrasolar planet. We call this method `spectral deconvolution'. We illustrate the dramatic gains by showing an idealized simulation that results in a 20-sigma detection of a Jovian planet at 2 pc with a 2-m coronagraphic space telescope, even though the planet's peak flux is only 1% that of the PSF wings of the host star. This scales to detection of a terrestrial extrasolar planet at 2 pc with an 8-m coronagraphic Terrestrial Planet Finder (TPF) in ~7 hr (or less with appropriate spatial filtering). Data on the spectral characteristics of the extrasolar planet and hence on its atmospheric constituents and possible biomarkers are obtained naturally as part of this process.Comment: 62 pages 27 figures accepted for publication in Ap

Lithic technological responses to Late Pleistocene glacial cycling at Pinnacle Point Site 5-6, South Africa

There are multiple hypotheses for human responses to glacial cycling in the Late Pleistocene, including changes in population size, interconnectedness, and mobility. Lithic technological analysis informs us of human responses to environmental change because lithic assemblage characteristics are a reflection of raw material transport, reduction, and discard behaviors that depend on hunter-gatherer social and economic decisions. Pinnacle Point Site 5-6 (PP5-6), Western Cape, South Africa is an ideal locality for examining the influence of glacial cycling on early modern human behaviors because it preserves a long sequence spanning marine isotope stages (MIS) 5, 4, and 3 and is associated with robust records of paleoenvironmental change. The analysis presented here addresses the question, what, if any, lithic assemblage traits at PP5-6 represent changing behavioral responses to the MIS 5-4-3 interglacial-glacial cycle? It statistically evaluates changes in 93 traits with no a priori assumptions about which traits may significantly associate with MIS. In contrast to other studies that claim that there is little relationship between broad-scale patterns of climate change and lithic technology, we identified the following characteristics that are associated with MIS 4: increased use of quartz, increased evidence for outcrop sources of quartzite and silcrete, increased evidence for earlier stages of reduction in silcrete, evidence for increased flaking efficiency in all raw material types, and changes in tool types and function for silcrete. Based on these results, we suggest that foragers responded to MIS 4 glacial environmental conditions at PP5-6 with increased population or group sizes, 'place provisioning', longer and/or more intense site occupations, and decreased residential mobility. Several other traits, including silcrete frequency, do not exhibit an association with MIS. Backed pieces, once they appear in the PP5-6 record during MIS 4, persist through MIS 3. Changing paleoenvironments explain some, but not all temporal technological variability at PP5-6.Social Science and Humanities Research Council of Canada; NORAM; American-Scandinavian Foundation; Fundacao para a Ciencia e Tecnologia [SFRH/BPD/73598/2010]; IGERT [DGE 0801634]; Hyde Family Foundations; Institute of Human Origins; National Science Foundation [BCS-9912465, BCS-0130713, BCS-0524087, BCS-1138073]; John Templeton Foundation to the Institute of Human Origins at Arizona State Universit