Correlated metallic two particle bound states in quasiperiodic chains

Single particle states in a chain with quasiperiodic potential show a metal-insulator transition upon the change of the potential strength. We consider two particles with local interaction in the single particle insulating regime. The two particle states change from being localized to delocalized upon an increase of the interaction strength to a nonperturbative finite value. At even larger interaction strength the states become localized again. This transition of two particle bound states into a correlated metal is due to a resonant mixing of the noninteracting two particle eigenstates. In the discovered correlated metal states two particles move coherently together through the whole chain, therefore contributing to a finite conductivity.Comment: 4 pages, 4 figure

Exponential localization in one-dimensional quasiperiodic optical lattices

We investigate the localization properties of a one-dimensional bichromatic optical lattice in the tight binding regime, by discussing how exponentially localized states emerge upon changing the degree of commensurability. We also review the mapping onto the discrete Aubry-Andre' model, and provide evidences on how the momentum distribution gets modified in the crossover from extended to exponentially localized states. This analysis is relevant to the recent experiment on Anderson localization of a noninteracting Bose-Einstein condensate in a quasiperiodic optical lattice [G. Roati et al., Nature 453, 895 (2008)].Comment: 13 pages, 6 figure

R-matrix approach to integrable systems on time scales

A general unifying framework for integrable soliton-like systems on time scales is introduced. The $R$-matrix formalism is applied to the algebra of $\delta$-differential operators in terms of which one can construct infinite hierarchy of commuting vector fields. The theory is illustrated by two infinite-field integrable hierarchies on time scales which are difference counterparts of KP and mKP. The difference counterparts of AKNS and Kaup-Broer soliton systems are constructed as related finite-field restrictions.Comment: 21 page

The relationship between meat disgust and meat avoidance—A chicken-and-egg problem

This is the final version. Available from Frontiers Media via the DOI in this record. Data availability statement: The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found below: https://osf.io/ vkcef/?view_only=aea15b1ad2e44e899191e2699161894b.Feelings of disgust toward meat have been researched for at least 30 years, but so far the causal relationship that may link meat disgust and meat consumption has remained elusive. Two possible pathways have been proposed in previous literature: the more common pathway seems to be that meat disgust is developed after a transition to vegetarianism, potentially via the process of moralization and recruitment of (moral) disgust. Other accounts suggest the existence of a second pathway in which disgust initiates the avoidance of meat and this can be explained by existing theories of disgust functioning as a pathogen avoidance mechanism and meat serving as a pathogen cue. However, the evidence base for either relationship remains thin and to our knowledge no research has examined whether temporary meat abstention can lead to increases in meat disgust, as the first pathway suggests. We measured meat disgust and meat intake in n = 40 meat eaters before and after attempting a meat-free diet for 1 month (while taking part in the annual vegan campaign Veganuary). Although most participants lapsed to eating meat during this period, we found that reductions in meat intake during the month were predictive of increases in meat disgust afterwards. This supports the view that meat disgust is expressed as a result of meat avoidance in meat eaters. Implications for theoretical understanding of the relationship between meat disgust and meat avoidance, as well as the development of disgust based interventions are discussed.University of Exete

On the critical level-curvature distribution

The parametric motion of energy levels for non-interacting electrons at the Anderson localization critical point is studied by computing the energy level-curvatures for a quasiperiodic ring with twisted boundary conditions. We find a critical distribution which has the universal random matrix theory form ${\bar P}(K)\sim |K|^{-3}$ for large level-curvatures $|K|$ corresponding to quantum diffusion, although overall it is close to approximate log-normal statistics corresponding to localization. The obtained hybrid distribution resembles the critical distribution of the disordered Anderson model and makes a connection to recent experimental data.Comment: 4 pages, 3 figure

Spreading of waves in nonlinear disordered media

We analyze mechanisms and regimes of wave packet spreading in nonlinear disordered media. We predict that wave packets can spread in two regimes of strong and weak chaos. We discuss resonance probabilities, nonlinear diffusion equations, and predict a dynamical crossover from strong to weak chaos. The crossover is controlled by the ratio of nonlinear frequency shifts and the average eigenvalue spacing of eigenstates of the linear equations within one localization volume. We consider generalized models in higher lattice dimensions and obtain critical values for the nonlinearity power, the dimension, and norm density, which influence possible dynamical outcomes in a qualitative way.Comment: 24 pages, 3 figures. arXiv admin note: text overlap with arXiv:0901.441

Wehrlites from continental mantle monitor the passage and degassing of carbonated melts

Continental rifting has been linked to the thinning and destruction of cratonic lithosphere and to the release of enough CO2 to impact the global climate. This fundamental plate tectonic process facilitates the infiltration and mobilisation of smallvolume carbonated melts, which may interact with mantle peridotite to form wehrlite through the reaction: enstatite thorn dolomite (melt) = forsterite thorn diopside thorn CO2 (vapour). Application to mantle xenolith suites from various rifts and basins shows that 2.9 to 10.2 kg CO2 are released per 100 kg of wehrlite formed. For the Eastern Rift (Africa), this results in estimated CO2 fluxes of 6.5 +/- 4.1 Mt yr(-1), similar to estimates of mantle contributions based on surficial CO2 surveys. Thus, wehrlite-bearing xenolith suites can be used to monitor present and past CO2 mobility through the continental lithosphere, ultimately with diffuse degassing to the atmosphere. They may also reveal the CO2 flux in lithospheric provinces where carbonated melts or continent-scale rifts are not observed at the surface.This work and collaborationwere stimulated by an invitation to SA and GMY to present at the Deep Carbon Observatory’s Deep Carbon 2019: Launching the Next Decade of Deep Carbon Science meeting in Washington DC (USA), and by an Alexander von Humboldt Fellowship to GMY, which we gratefully acknowledge. It was written while SA was funded through German Research Foundation fellowship AU356/11

On Max-Stable Processes and the Functional D-Norm

We introduce a functional domain of attraction approach for stochastic processes, which is more general than the usual one based on weak convergence. The distribution function G of a continuous max-stable process on [0,1] is introduced and it is shown that G can be represented via a norm on functional space, called D-norm. This is in complete accordance with the multivariate case and leads to the definition of functional generalized Pareto distributions (GPD) W. These satisfy W=1+log(G) in their upper tails, again in complete accordance with the uni- or multivariate case. Applying this framework to copula processes we derive characterizations of the domain of attraction condition for copula processes in terms of tail equivalence with a functional GPD. \delta-neighborhoods of a functional GPD are introduced and it is shown that these are characterized by a polynomial rate of convergence of functional extremes, which is well-known in the multivariate case.Comment: 22 page

Correlation function of weakly interacting bosons in a disordered lattice

One of the most important issues in disordered systems is the interplay of the disorder and repulsive interactions. Several recent experimental advances on this topic have been made with ultracold atoms, in particular the observation of Anderson localization, and the realization of the disordered Bose-Hubbard model. There are however still questions as to how to differentiate the complex insulating phases resulting from this interplay, and how to measure the size of the superfluid fragments that these phases entail. It has been suggested that the correlation function of such a system can give new insights, but so far little experimental investigation has been performed. Here, we show the first experimental analysis of the correlation function for a weakly interacting, bosonic system in a quasiperiodic lattice. We observe an increase in the correlation length as well as a change in shape of the correlation function in the delocalization crossover from Anderson glass to coherent, extended state. In between, the experiment indicates the formation of progressively larger coherent fragments, consistent with a fragmented BEC, or Bose glass.Comment: 16 pages, 8 figure

Designing disorder

This is the author accepted manuscript. The final version is available from Springer Nature via the DOI in this recordMetasurfaces can in principle provide a versatile platform for optical functionalities, but in practice designing and fabricating them to specifications can be difficult. Now, the realization of metasurfaces with engineered disorder allows for versatile optical components that combine the best features of periodic and random systems