Energy level statistics of electrons in a 2D quasicrystal

A numerical study is made of the spectra of a tight-binding hamiltonian on square approximants of the quasiperiodic octagonal tiling. Tilings may be pure or random, with different degrees of phason disorder considered. The level statistics for the randomized tilings follow the predictions of random matrix theory, while for the perfect tilings a new type of level statistics is found. In this case, the first-, second- level spacing distributions are well described by lognormal laws with power law tails for large spacing. In addition, level spacing properties being related to properties of the density of states, the latter quantity is studied and the multifractal character of the spectral measure is exhibited.Comment: 9 pages including references and figure captions, 6 figures available upon request, LATEX, report-number els

Metal-insulator transition in the Hartree-Fock phase diagram of the fully polarized homogeneous electron gas in two dimensions

We determine numerically the ground state of the two-dimensional, fully polarized electron gas within the Hartree-Fock approximation without imposing any particular symmetries on the solutions. At low electronic densities, the Wigner crystal solution is stable, but for higher densities ($r_s$ less than $\sim 2.7$) we obtain a ground state of different symmetry: the charge density forms a triangular lattice with about 11% more sites than electrons. We prove analytically that this conducting state with broken translational symmetry has lower energy than the uniform Fermi gas state in the high density region giving rise to a metal to insulator transition.Comment: 13 pages, 5 figures, rewrite of 0804.1025 and 0807.077

Water-seeking behavior in worm-infected crickets and reversibility of parasitic manipulation

One of the most fascinating examples of parasite-induced host manipulation is that of hairworms, first, because they induce a spectacular "suicide” water-seeking behavior in their terrestrial insect hosts and, second, because the emergence of the parasite is not lethal per se for the host that can live several months following parasite release. The mechanisms hairworms use to increase the encounter rate between their host and water remain, however, poorly understood. Considering the selective landscape in which nematomorph manipulation has evolved as well as previously obtained proteomics data, we predicted that crickets harboring mature hairworms would display a modified behavioral response to light. Since following parasite emergence in water, the cricket host and parasitic worm do not interact physiologically anymore, we also predicted that the host would recover from the modified behaviors. We examined the effect of hairworm infection on different behavioral responses of the host when stimulated by light to record responses from uninfected, infected, and ex-infected crickets. We showed that hairworm infection fundamentally modifies cricket behavior by inducing directed responses to light, a condition from which they mostly recover once the parasite is released. This study supports the idea that host manipulation by parasites is subtle, complex, and multidimensiona

Generalized quasiperiodic Rauzy tilings

We present a geometrical description of new canonical $d$-dimensional codimension one quasiperiodic tilings based on generalized Fibonacci sequences. These tilings are made up of rhombi in 2d and rhombohedra in 3d as the usual Penrose and icosahedral tilings. Thanks to a natural indexing of the sites according to their local environment, we easily write down, for any approximant, the sites coordinates, the connectivity matrix and we compute the structure factor.Comment: 11 pages, 3 EPS figures, final version with minor change

Non-equilibrium stochastic dynamics of continuous systems and Bogoliubov generating functionals

Combinatorial harmonic analysis techniques are used to develop new functional analysis methods based on Bogoliubov functionals. Concrete applications of the methods are presented, namely, the study of a non-equilibrium stochastic dynamics of continuous systems.Comment: 37 page

Overlapping Unit Cells in 3d Quasicrystal Structure

A 3-dimensional quasiperiodic lattice, with overlapping unit cells and periodic in one direction, is constructed using grid and projection methods pioneered by de Bruijn. Each unit cell consists of 26 points, of which 22 are the vertices of a convex polytope P, and 4 are interior points also shared with other neighboring unit cells. Using Kronecker's theorem the frequencies of all possible types of overlapping are found.Comment: LaTeX2e, 11 pages, 5 figures (8 eps files), uses iopart.class. Final versio

Classification of one-dimensional quasilattices into mutual local-derivability classes

One-dimensional quasilattices are classified into mutual local-derivability (MLD) classes on the basis of geometrical and number-theoretical considerations. Most quasilattices are ternary, and there exist an infinite number of MLD classes. Every MLD class has a finite number of quasilattices with inflation symmetries. We can choose one of them as the representative of the MLD class, and other members are given as decorations of the representative. Several MLD classes of particular importance are listed. The symmetry-preserving decorations rules are investigated extensively.Comment: 42 pages, latex, 5 eps figures, Published in JPS

Shape-Dependent Thermodynamics and Non-Local Hydrodynamics in a Non-Gibbsian Steady-State of a Drift-Diffusion System

Shape-dependent thermodynamics and non-local hydrodynamics are argued to occur in dissipative steady states of driven diffusive systems. These predictions are confirmed by numerical simulations. Unlike power-law correlations, these phenomena cannot be explained by a hypothesis of ``criticality''. Instead, they require the effective Hamiltonian of the system to contain very long-range potentials, making the invariant probability measures formally ``non-Gibbsian''.Comment: 4 pages, Latex Version 2.09, 1 Postscript figur

Comment on "Atomic jumps in quasiperiodic Al72.6_{72.6}Ni10.5_{10.5}Co16.9_{16.9} and related crystalline material"

We disagree with a number of statements by Dolinsek et al. about the specificity of phason dynamics in quasicrystals (QCs).Comment: 2 pages, 0 figures, submitted to Physical Review

Rules for Computing Symmetry, Density and Stoichiometry in a Quasi-Unit-Cell Model of Quasicrystals

The quasi-unit cell picture describes the atomic structure of quasicrystals in terms of a single, repeating cluster which overlaps neighbors according to specific overlap rules. In this paper, we discuss the precise relationship between a general atomic decoration in the quasi-unit cell picture atomic decorations in the Penrose tiling and in related tiling pictures. Using these relations, we obtain a simple, practical method for determining the density, stoichiometry and symmetry of a quasicrystal based on the atomic decoration of the quasi-unit cell taking proper account of the sharing of atoms between clusters.Comment: 14 pages, 8 figure