Current and charge distributions of the fractional quantum Hall liquids with edges

An effective Chern-Simons theory for the quantum Hall states with edges is studied by treating the edge and bulk properties in a unified fashion. An exact steady-state solution is obtained for a half-plane geometry using the Wiener-Hopf method. For a Hall bar with finite width, it is proved that the charge and current distributions do not have a diverging singularity. It is shown that there exists only a single mode even for the hierarchical states, and the mode is not localized exponentially near the edges. Thus this result differs from the edge picture in which electrons are treated as strictly one dimensional chiral Luttinger liquids.Comment: 21 pages, REV TeX fil

Universal structure of the edge states of the fractional quantum Hall states

We present an effective theory for the bulk fractional quantum Hall states on the Jain sequences on closed surfaces and show that it has a universal form whose structure does not change from fraction to fraction. The structure of this effective theory follows from the condition of global consistency of the flux attachment transformation on closed surfaces. We derive the theory of the edge states on a disk that follows naturally from this globally consistent theory on a torus. We find that, for a fully polarized two-dimensional electron gas, the edge states for all the Jain filling fractions $\nu=p/(2np+1)$ have only one propagating edge field that carries both energy and charge, and two non-propagating edge fields of topological origin that are responsible for the statistics of the excitations. Explicit results are derived for the electron and quasiparticle operators and for their propagators at the edge. We show that these operators create states with the correct charge and statistics. It is found that the tunneling density of states for all the Jain states scales with frequency as $|\omega|^{(1-\nu)/\nu}$.Comment: 10 page

Existence and uniqueness of solutions for systems of fractional differential equations with Riemann–Stieltjes integral boundary condition

In this article, we first establish an existence and uniqueness result for a class of systems of nonlinear operator equations under more general conditions by means of the cone theory and monotone iterative technique. Furthermore, the iterative sequence of the solution and the error estimation of the system are given. Then we use this new result to study the existence and uniqueness of the solution for boundary value problems of systems of fractional differential equations with a Riemann–Stieltjes integral boundary condition in real Banach spaces. The results obtained in this paper are more general than many previous results and complement them

Resonant Tunneling Between Quantum Hall Edge States

Resonant tunneling between fractional quantum Hall edge states is studied in the Luttinger liquid picture. For the Laughlin parent states, the resonance line shape is a universal function whose width scales to zero at zero temperature. Extensive quantum Monte Carlo simulations are presented for $\nu = 1/3$ which confirm this picture and provide a parameter-free prediction for the line shape.Comment: 14 pages , revtex , IUCM93-00

Proactive edge caching in content-centric networks with massive dynamic content requests

Edge computing is a promising infrastructure evolution to reduce traffic loads and support low-latency communications. Furthermore, content-centric networks provide a natural solution to cache contents at edge nodes. However, it is a challenge for edge nodes to handle massive and highly dynamic content requests by users, and if without an efficient content caching strategy, the edge nodes will encounter high traffic load and latency due to increasing retrieval from content providers. This paper formulates a proactive edge caching problem to minimize the content retrieval cost at edge nodes. We exploit the inherent content caching and request aggregation mechanism in the content-centric networks to jointly minimize traffic load and content retrieval delay cost generated by the massive and dynamic content requests. We develop a Q-learning algorithm, which is an online optimal caching strategy, as it is adaptable to dynamic content popularity and content request intensity, and derive the long-term minimization of the content retrieval cost. Simulation results illustrate that the proposed algorithm can achieve a lower content retrieval cost compared with several baseline caching schemes

Edge and Bulk of the Fractional Quantum Hall Liquids

An effective Chern-Simons theory for the Abelian quantum Hall states with edges is proposed to study the edge and bulk properties in a unified fashion. We impose a condition that the currents do not flow outside the sample. With this boundary condition, the action remains gauge invariant and the edge modes are naturally derived. We find that the integer coupling matrix $K$ should satisfy the condition $\sum_I(K^{-1})_{IJ} = \nu/m$ ($\nu$: filling of Landau levels, $m$: the number of gauge fields ) for the quantum Hall liquids. Then the Hall conductance is always quantized irrespective of the detailed dynamics or the randomness at the edge.Comment: 13 pages, REVTEX, one figure appended as a postscript fil

Impurity scattering and transport of fractional Quantum Hall edge state

We study the effects of impurity scattering on the low energy edge state dynamic s for a broad class of quantum Hall fluids at filling factor $\nu =n/(np+1)$, for integer $n$ and even integer $p$. When $p$ is positive all $n$ of the edge modes are expected to move in the same direction, whereas for negative $p$ one mode moves in a direction opposite to the other $n-1$ modes. Using a chiral-Luttinger model to describe the edge channels, we show that for an ideal edge when $p$ is negative, a non-quantized and non-universal Hall conductance is predicted. The non-quantized conductance is associated with an absence of equilibration between the $n$ edge channels. To explain the robust experimental Hall quantization, it is thus necessary to incorporate impurity scattering into the model, to allow for edge equilibration. A perturbative analysis reveals that edge impurity scattering is relevant and will modify the low energy edge dynamics. We describe a non-perturbative solution for the random $n-$channel edge, which reveals the existence of a new disorder-dominated phase, characterized by a stable zero temperature renormalization group fixed point. The phase consists of a single propagating charge mode, which gives a quantized Hall conductance, and $n-1$ neutral modes. The neutral modes all propagate at the same speed, and manifest an exact SU(n) symmetry. At finite temperatures the SU(n) symmetry is broken and the neutral modes decay with a finite rate which varies as $T^2$ at low temperatures. Various experimental predictions and implications which follow from the exact solution are described in detail, focusing on tunneling experiments through point contacts.Comment: 19 pages (two column), 5 post script figures appended, 3.0 REVTE

Quantum Hall Fluids

We review the effective field theory treatment of topological quantum fluids, focussing on the Hall fluids.Comment: 82 pages, TeX, Preprint ITP (This version comes with ALL the MACROS appended at the end of the file)

Evidencia experimental de la abundancia de bacterias del suelo como el principal iniciador del efecto de preparación de la rizosfera

Se piensa que las comunidades microbianas del suelo son responsables del efecto de preparación de la rizósfera (RPE). Sin embargo, desde que las comunidades microbiales están compuestas de diversos componentes, se conoce muy poco acerca de cuál es el componente que tiene el rol principal en dicho efecto. En este estudio, se hicieron crecer soja y algodón en dos lugares a diferentes latitudes con diferentes condiciones de luz y temperatura in situ. Se cuantificó RPE usando un método natural de δC13 y se midió la abundancia, riqueza y composición de las comunidades de hongos y bacterias con métodos moleculares basados en el ADN. Entre todas las variables potenciales, incluyendo los tres índices de comunidades de hongos y bacterias anteriormente mencionados, e índices vegetales y físico-químicos del suelo, se mostró que la abundancia de bacterias explicó una gran proporción de la variación en RPE. Nuestro estudio identificó el mecanismo biológico que subyace este importante proceso ecológico.Soil microbial communities are thougth to be responsible for the rhizosphere priming effect (RPE). However, because soil microbial communities are comprised of diverse components, very little is known about which component plays the critical role. Here, soybean and cottonwood were grown at two latitudinal locations with different temperature and light conditions in-situ. We quantified RPE using a natural 13C method, and measured the abundance, richness and composition of bacteria and fungi communities with DNA-based molecular methods. Among all potential variables, including the three aforementioned indexes of bacteria and fungi communities and soil physiochemical and plant indexes, bacterial abundance was found to explain a large proportion of variation in RPE. Our study identified the biological mechanism underlying this important ecological process.Fil: Ma, Y.P.. Chinese Academy of Sciences. Institute of Applied Ecology; China. Chinese Academy of Agricultural Sciences. Institute of Environment and Sustainable Development in Agriculture. Key Laboratory of Dryland Agriculture;; China. University of Chinese Academy of Science; ChinaFil: Zhang, Z.J.. Chinese Academy of Sciences. Institute of Applied Ecology; China. Chinese Academy of Agricultural Sciences. Institute of Environment and Sustainable Development in Agriculture. Key Laboratory of Dryland Agriculture;; ChinaFil: Su, T.Q.. Chinese Academy of Sciences. Institute of Applied Ecology; ChinaFil: Busso, Carlos Alberto. Universidad Nacional del Sur. Departamento de Agronomía; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Centro de Recursos Naturales Renovables de la Zona Semiárida. Universidad Nacional del Sur. Centro de Recursos Naturales Renovables de la Zona Semiárida; ArgentinaFil: Johnston, E.R.. Georgia Institute of Technology. School of Civil and Environmental Engineering; Estados UnidosFil: Han, X.G.. Chinese Academy of Sciences. Institute of Applied Ecology; China. Chinese Academy of Sciences. Institute of Botany. State Key Laboratory of Vegetation and Environmental Change; ChinaFil: Zhang, X.M.. Chinese Academy of Agricultural Sciences. Institute of Environment and Sustainable Development in Agriculture. Key Laboratory of Dryland Agriculture;; Chin

Wild silkworm cocoon as a natural tough biological composite structure

Silk cocoons are biological composites with intriguing characteristics that have evolved through a long natural selection process. Knowledge of structure-property-function relationship of multilayered composite silk cocoon shells gives insight into the design of next-generation protection materials. The current investigation studied the composite structure and mechanical performance of a wild silkworm cocoon (Chinese tussah silkworm cocoon, Antheraea pernyi) in comparison with the domestic counterpart (Mulberry silkworm cocoon, Bombyx mori). 180º peel and tensile tests were performed on the cocoon walls to understand both their interlaminar and in-plane mechanical properties. The fracture surfaces were investigated under SEM. The wild cocoon showed substantially higher toughness over the domestic cocoon, which explains their unique capability to tackle severe environmental adversaries