Structural changes in quasi-one-dimensional many-electron systems: From linear to zigzag and beyond

Many-electron systems confined to a quasi-one-dimensional geometry by a cylindrical distribution of positive charge have been investigated by density functional computations in the unrestricted local spin density approximation. Our investigations have been focused on the low-density regime, in which electrons are localized. The results reveal a wide variety of different charge and spin configurations, including linear and zig-zag chains, single-and double-strand helices, and twisted chains of dimers. The spin-spin coupling turns from weakly antiferromagnetic at relatively high density, to weakly ferromagnetic at the lowest densities considered in our computations. The stability of linear chains of localized charge has been investigated by analyzing the radial dependence of the self-consistent potential and by computing the dispersion relation of low-energy harmonic excitations.

The response of small mammals to natural and human-altered edges associated with Afromontane forests of South Africa

An increase in edge area reduces the effective size of habitat fragments and thus the area available for habitat-interior specialists. However, it is unclear how edge effects compare at different ecotones in the same system. We investigated the response of a small mammal community associated with Afromontane forests to edge effects at three different habitat transitions: natural forest to grassland (natural edge, structurally different vegetation types), natural forest to mature plantation (human-altered edge, structurally similar vegetation types) and natural forest to harvested plantation (human-altered edge, structurally different vegetation types). We predicted that edge effects should be less severe at natural ecotones and at similarly structured contiguous vegetation types than human-altered ecotones and differently structured contiguous vegetation types, respectively. We found that forest species seemed to avoid all habitat edges in our study area. Surprisingly, natural edges supported a less diverse small mammal community than human-altered forest edges. However, edge effects were observed deeper into native forests surrounded by mature alien plantations (and more so at harvested plantations) than into native forests surrounded by native grasslands. The net effect of mature plantations was therefore to reduce the functional size of the natural forest by creating a larger edge. We suggest that when plantations are established a buffer zone of natural vegetation be left between natural forests and newly established plantations to mitigate the negative effects of plantation forestry.

Spontaneous nucleation of structural defects in inhomogeneous ion chains

Structural defects in ion crystals can be formed during a linear quench of the transverse trapping frequency across the mechanical instability from a linear chain to a zigzag structure. The density of defects after the sweep can be conveniently described by the Kibble-Zurek mechanism (KZM). In particular, the number of kinks in the zigzag ordering can be derived from a time-dependent Ginzburg-Landau equation for the order parameter, here the zigzag transverse size, under the assumption that the ions are continuously laser cooled. In a linear Paul trap, the transition becomes inhomogeneous, since the charge density is larger in the center and more rarefied at the edges. During the linear quench, the mechanical instability is first crossed in the center of the chain, and a front, at which the mechanical instability is crossed during the quench, is identified that propagates along the chain from the center to the edges. If the velocity of this front is smaller than the sound velocity, the dynamics become adiabatic even in the thermodynamic limit and no defect is produced. Otherwise, the nucleation of kinks is reduced with respect to the case in which the charges are homogeneously distributed, leading to a new scaling of the density of kinks with the quenching rate. The analytical predictions are verified numerically by integrating the Langevin equations of motion of the ions, in the presence of a time-dependent transverse confinement. We argue that the non-equilibrium dynamics of an ion chain in a Paul trap constitutes an ideal scenario to test the inhomogeneous extension of the KZM, which lacks experimental evidence to date.

Ground state of low-dimensional dipolar gases: Linear and zigzag chains

We study the ground-state phase diagram of ultracold dipolar gases in highly anisotropic traps. Starting from a one-dimensional geometry, by ramping down the transverse confinement along one direction, the gas reaches various planar distributions of dipoles. At large linear densities, when the dipolar gas exhibits a crystal-like phase, critical values of the transverse frequency exist below which the configuration exhibits transverse patterns. These critical values are found by means of a classical theory, and are in full agreement with classical Monte Carlo simulations. The study of the quantum system is performed numerically with Monte Carlo techniques and shows that the quantum fluctuations smoothen the transition and make it completely disappear in a gas phase. These predictions could be experimentally tested and would allow one to reveal the effect of zero-point motion on self-organized mesoscopic structures of matter waves, such as the transverse pattern of the zigzag chain.

Full characterization of the quantum linear-zigzag transition in atomic chains

A string of repulsively interacting particles exhibits a phase transition to a zigzag structure, by reducing the transverse trap potential or the interparticle distance. Based on the emergent symmetry Z2 it has been argued that this instability is a quantum phase transition, which can be mapped to an Ising model in transverse field. An extensive Density Matrix Renormalization Group analysis is performed, resulting in an high-precision evaluation of the critical exponents and of the central charge of the system, confirming that the quantum linear-zigzag transition belongs to the critical Ising model universality class. Quantum corrections to the classical phase diagram are computed, and the range of experimental parameters where quantum effects play a role is provided. These results show that structural instabilities of one-dimensional interacting atomic arrays can simulate quantum critical phenomena typical of ferromagnetic systems.

Building pH Sensors into Paper-based Small-molecular Logic Sys-tems for Very Simple Detection of Edges of Objects

Genetically-engineered bacteria and reactive DNA networks detect edges of objects, as done in our retinas and as also found within computer vision. We now demonstrate that simple molecular logic systems (a combination of a pH sensor, a photo acid generator and a pH buffer spread on paper) without any organization can achieve this relatively complex computational goal with good-fidelity. This causes a jump in the complexity achievable by molecular logic-based computation and extends its applicability. The molecular species involved in light dose-driven 'off-on-off' fluorescence is diverted in the ‘on’ state by proton diffusion from irradiated to unirradiated regions where it escapes a strong quencher, thus visualizing the edge of a mask.

Identifying the trend of reactivity for sp2 materials: an electron delocalization model from first principles calculations

The reactivity of sp² carbon materials is studied using the adsorption and dissociation of O₂ on graphene and graphene oxide as model systems. The reactions on the basal plane, zigzag and armchair edges of graphene and graphene oxide with different oxygen-containing groups are calculated using first principles calculations. Two Brønsted-Evans- Polanyi relationships are identified and an electron delocalization model is suggested to understand the general trend of reactivity for sp² carbon materials.

Building the what and where systems: multi-scale lines, edges and keypoints

Computer vision for realtime applications requires tremendous computational power because all images must be processed from the first to the last pixel. Ac tive vision by probing specific objects on the basis of already acquired context may lead to a significant reduction of processing. This idea is based on a few concepts from our visual cortex (Rensink, Visual Cogn. 7, 17-42, 2000): (1) our physical surround can be seen as memory, i.e. there is no need to construct detailed and complete maps, (2) the bandwidth of the what and where systems is limited, i.e. only one object can be probed at any time, and (3) bottom-up, low-level feature extraction is complemented by top-down hypothesis testing, i.e. there is a rapid convergence of activities in dendritic/axonal connections.