Canonical Phase Diagrams of the 1-D Falicov-Kimball Model at T=0

The Falicov-Kimball model of spinless quantum electrons hopping on a 1-dimensional lattice and of immobile classical ions occupying some lattice sites, with only intrasite coupling between those particles, have been studied at zero temperature by means of well-controlled numerical procedures. For selected values of the unique coupling parameter $U$ the restricted phase diagrams (based on all the periodic configurations of localized particles (ions) with period not greater than 16 lattice constants, typically) have been constructed in the grand-canonical ensemble. Then these diagrams have been translated into the canonical ensemble. Compared to the diagrams obtained in other studies our ones contain more details, in particular they give better insight into the way the mixtures of periodic phases are formed. Our study has revealed several families of new characteristic phases like the generalized most homogeneous and the generalized crenel phases, a first example of a structural phase transition and a tendency to build up an additional symmetry -- the hole-particle symmetry with respect to the ions (electrons) only, as $U$ decreases.Comment: 24 pages, 8 figures (not included

Exact results for spatial decay of the one-body density matrix in low-dimensional insulators

We provide a tight-binding model of insulator, for which we derive an exact analytic form of the one-body density matrix and its large-distance asymptotics in dimensions $D=1,2$. The system is built out of a band of single-particle orbitals in a periodic potential. Breaking of the translational symmetry of the system results in two bands, separated by a direct gap whose width is proportional to the unique energy parameter of the model. The form of the decay is a power law times an exponential. We determine the power in the power law and the correlation length in the exponential, versus the lattice direction, the direct-gap width, and the lattice dimension. In particular, the obtained exact formulae imply that in the diagonal direction of the square lattice the inverse correlation length vanishes linearly with the vanishing gap, while in non-diagonal directions, the linear scaling is replaced by the square root one. Independently of direction, for sufficiently large gaps the inverse correlation length grows logarithmically with the gap width.Comment: 4 pages, 2 figure

Features in the diffraction of a scalar plane wave from doubly-periodic Dirichlet and Neumann surfaces

The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichlet or Neumann boundary condition is imposed is studied by means of a rigorous numerical solution of the Rayleigh equation for the amplitudes of the diffracted Bragg beams. From the results of these calculations the diffraction efficiencies of several of the lowest order diffracted beams are calculated as functions of the polar and azimuthal angles of incidence. The angular dependencies of the diffraction efficiencies display features that can be identified as Rayleigh anomalies for both types of surfaces. In the case of a Neumann surface additional features are present that can be attributed to the existence of surface waves on such surfaces. Some of the results obtained through the use of the Rayleigh equation are validated by comparing them with the results of a rigorous Green's function numerical calculation

Difficulty is critical: The importance of social factors in modeling diffusion of green products and practices

Despite the very positive -- as measured by market surveys -- attitude towards eco-innovations and sustainability in general, the actual market penetration of green products and practices generally falls behind the expectations. In this paper we argue that considering \emph{difficulty of engagement}, as used in the Campbell Paradigm, is of critical importance when modeling diffusion of eco-innovations. Such a notion of difficulty possesses three desired properties: (i) parsimony -- it is represented by a single value, (ii) interpretability -- it can be regarded as an estimator of the otherwise complex notion of \emph{behavioral cost}, and (iii) applicability -- it can be easily measured through market surveys. In an extensive simulation and analytical study involving empirically measured difficulty and an agent-based model spanned on different social network structures, we show that innovation adoption may exhibit abrupt changes in market penetration as a result of even small changes in difficulty. The latter may be of particular interest to policy makers who have to make strategic decisions when introducing socially -- but not necessarily individually -- desired products and practices, like dynamic or green electricity tariffs

Numerical response of mammalian carnivores to rodents affects bird reproduction in temperate forests: A case of apparent competition?

Resource pulses such as mast seeding in temperate forests may affect interspecific interactions over multiple trophic levels and link different seed and nonseed consum‐ers directly via predation or indirectly via shared predators. However, the nature and strength of interactions among species remain unknown for most resource pulse–driven ecosystems. We considered five hypotheses concerning the influence of re‐source pulses on the interactions between rodents, predators, and bird reproduction with data from northern Switzerland collected between 2010 and 2015. In high‐ro‐dent‐abundance‐years (HRAYs), wood warbler (Phylloscopus sibilatrix) nest survival was lower than in low‐rodent‐abundance‐years, but rodents were not important nest predators, in contrast to rodent‐hunting predators. The higher proportion of nests predated by rodent‐hunting predators and their increased occurrence in HRAYs sug‐gests a rodent‐mediated aggregative numerical response of rodent‐hunting preda‐tors, which incidentally prey on the wood warbler’s ground nests. There was no evidence that rodent‐hunting predators responded behaviorally by switching prey. Lastly, nest losses caused by nonrodent‐hunting predators were not related to rodent abundance. We show that wood warblers and rodents are linked via shared predators in a manner consistent with apparent competition, where an increase of one species coincides with the decrease of another species mediated by shared predators. Mast seeding frequency and annual seed production appear to have increased over the past century, which may result in more frequent HRAYs and generally higher peaking rodent populations. The associated increase in the magnitude of apparent competi‐tion may thus at least to some extent explain the wood warbler’s decline in much of Western Europe