Transforming Power Relationships: Leadership, Risk, and Hope. IHS Political Science Series No. 135, May 2013

Chronic communal conflicts resemble the prisoner’s dilemma. Both communities prefer peace to war. But neither trusts the other, viewing the other’s gain as its own loss, so potentially shared interests often go unrealized. Achieving positive-sum outcomes from apparently zero-sum struggles requires a kind of riskembracing leadership. To succeed leaders must: a) see power relations as potentially positive-sum; b) strengthen negotiating adversaries instead of weakening them; and c) demonstrate hope for a positive future and take great personal risks to achieve it. Such leadership is exemplified by Nelson Mandela and F.W. de Klerk in the South African democratic transition. To illuminate the strategic dilemmas Mandela and de Klerk faced, we examine the work of Robert Axelrod, Thomas Schelling, and Josep Colomer, who highlight important dimensions of the problem but underplay the role of risk-embracing leadership. Finally we discuss leadership successes and failures in the Northern Ireland settlement and the Israeli-Palestinian conflict

Monte Carlo Evaluation of Non-Abelian Statistics

We develop a general framework to (numerically) study adiabatic braiding of quasiholes in fractional quantum Hall systems. Specifically, we investigate the Moore-Read (MR) state at $\nu=1/2$ filling factor, a known candidate for non-Abelian statistics, which appears to actually occur in nature. The non-Abelian statistics of MR quasiholes is demonstrated explicitly for the first time, confirming the results predicted by conformal field theories.Comment: 4 pages, 4 figure

Capacity loss of non-aqueous Li-Air battery due to insoluble product formation: Approximate solution and experimental validation

In this paper, we present a study of Lithium (Li)-air battery capacity by accounting for the voltage loss associated with the electrode passivation and transport resistance caused by insoluble product formation. Two regimes are defined, in which approximate formulas are developed to explicitly evaluate the battery capacity, along with extensive validation against experimental data of various cathode properties and materials from our and several other groups. The dependence of battery capacity on the surface coverage factor, tortuosity, and Damköhler numbers (Da) is explicitly expressed and discussed. The formulas provide a guideline for experimentalists and practitioners in air cathode design, analysis, and control

Exponents and bounds for uniform spanning trees in d dimensions

Uniform spanning trees are a statistical model obtained by taking the set of all spanning trees on a given graph (such as a portion of a cubic lattice in d dimensions), with equal probability for each distinct tree. Some properties of such trees can be obtained in terms of the Laplacian matrix on the graph, by using Grassmann integrals. We use this to obtain exact exponents that bound those for the power-law decay of the probability that k distinct branches of the tree pass close to each of two distinct points, as the size of the lattice tends to infinity.Comment: 5 pages. v2: references added. v3: closed form results can be extended slightly (thanks to C. Tanguy). v4: revisions, and a figure adde

Fractional Chern Insulators in Bands with Zero Berry Curvature

Even if a noninteracting system has zero Berry curvature everywhere in the Brillouin zone, it is possible to introduce interactions that stabilise a fractional Chern insulator. These interactions necessarily break time-reversal symmetry (either spontaneously or explicitly) and have the effect of altering the underlying band structure. We outline a number of ways in which this may be achieved, and show how similar interactions may also be used to create a (time-reversal symmetric) fractional topological insulator. While our approach is rigorous in the limit of long range interactions, we show numerically that even for short range interactions a fractional Chern insulator can be stabilised in a band with zero Berry curvature.Comment: 7 pages, 2 figures; Published versio

The traveling salesman problem, conformal invariance, and dense polymers

We propose that the statistics of the optimal tour in the planar random Euclidean traveling salesman problem is conformally invariant on large scales. This is exhibited in power-law behavior of the probabilities for the tour to zigzag repeatedly between two regions, and in subleading corrections to the length of the tour. The universality class should be the same as for dense polymers and minimal spanning trees. The conjectures for the length of the tour on a cylinder are tested numerically.Comment: 4 pages. v2: small revisions, improved argument about dimensions d>2. v3: Final version, with a correction to the form of the tour length in a domain, and a new referenc

Non-Abelian quantized Hall states of electrons at filling factors 12/5 and 13/5 in the first excited Landau level

We present results of extensive numerical calculations on the ground state of electrons in the first excited (n=1) Landau level with Coulomb interactions, and including non-zero thickness effects, for filling factors 12/5 and 13/5 in the torus geometry. In a region that includes these experimentally-relevant values, we find that the energy spectrum and the overlaps with the trial states support the previous hypothesis that the system is in the non-Abelian k = 3 liquid phase we introduced in a previous paper.Comment: 5 pages (Revtex4), 7 figure

The periodic sl(2|1) alternating spin chain and its continuum limit as a bulk Logarithmic Conformal Field Theory at c=0

The periodic sl(2|1) alternating spin chain encodes (some of) the properties of hulls of percolation clusters, and is described in the continuum limit by a logarithmic conformal field theory (LCFT) at central charge c=0. This theory corresponds to the strong coupling regime of a sigma model on the complex projective superspace $\mathbb{CP}^{1|1} = \mathrm{U}(2|1) / (\mathrm{U}(1) \times \mathrm{U}(1|1))$, and the spectrum of critical exponents can be obtained exactly. In this paper we push the analysis further, and determine the main representation theoretic (logarithmic) features of this continuum limit by extending to the periodic case the approach of [N. Read and H. Saleur, Nucl. Phys. B 777 316 (2007)]. We first focus on determining the representation theory of the finite size spin chain with respect to the algebra of local energy densities provided by a representation of the affine Temperley-Lieb algebra at fugacity one. We then analyze how these algebraic properties carry over to the continuum limit to deduce the structure of the space of states as a representation over the product of left and right Virasoro algebras. Our main result is the full structure of the vacuum module of the theory, which exhibits Jordan cells of arbitrary rank for the Hamiltonian.Comment: 69pp, 8 fig