Effects of Smooth Boundaries on Topological Edge Modes in Optical Lattices

Since the experimental realization of synthetic gauge fields for neutral atoms, the simulation of topologically non-trivial phases of matter with ultracold atoms has become a major focus of cold atom experiments. However, several obvious differences exist between cold atom and solid state systems, for instance the finite size of the atomic cloud and the smooth confining potential. In this article we show that sharp boundaries are not required to realize quantum Hall or quantum spin Hall physics in optical lattices and, on the contrary, that edge states which belong to a smooth confinement exhibit additional interesting properties, such as spatially resolved splitting and merging of bulk bands and the emergence of robust auxiliary states in bulk gaps to preserve the topological quantum numbers. In addition, we numerically validate that these states are robust against disorder. Finally, we analyze possible detection methods, with a focus on Bragg spectroscopy, to demonstrate that the edge states can be detected and that Bragg spectroscopy can reveal how topological edge states are connected to the different bulk bands.Comment: 12 pages, 10 figures, updated figures and minor text correction

tt-sails and sparse hereditary classes of unbounded tree-width

It has long been known that the following basic objects are obstructions to bounded tree-width: for arbitrarily large $t$, $(1)$ the complete graph $K_t$, $(2)$ the complete bipartite graph $K_{t,t}$, $(3)$ a subdivision of the $(t \times t)$-wall and $(4)$ the line graph of a subdivision of the $(t \times t)$-wall. We now add a further \emph{boundary object} to this list, a subdivision of a \emph{$t$-sail}. These results have been obtained by studying sparse hereditary \emph{path-star} graph classes, each of which consists of the finite induced subgraphs of a single infinite graph whose edges can be decomposed into a path (or forest of paths) with a forest of stars, characterised by an infinite word over a possibly infinite alphabet. We show that a path-star class whose infinite graph has an unbounded number of stars, each of which connects an unbounded number of times to the path, has unbounded tree-width. In addition, we show that such a class is not a subclass of circle graphs, a hereditary class whose unavoidable induced subgraphs with large treewidth were identified by Hickingbotham, Illingworth, Mohar and Wood \cite{hickingbotham:treewidth_circlegraphs:}. We identify a collection of \emph{nested} words with a recursive structure that exhibit interesting characteristics when used to define a path-star graph class. These graph classes do not contain any of the four basic obstructions but instead contain graphs that have large tree-width if and only if they contain arbitrarily large subdivisions of a $t$-sail. Furthermore, like classes of bounded degree or classes excluding a fixed minor, these sparse graph classes do not contain a minimal class of unbounded tree-width

MEETING PRIVATE GRADES AND STANDARDS IN TRANSITION AGRICULTURE: EXPERIENCES FROM THE ARMENIAN DAIRY INDUSTRY

One of the main trends emerging from the agroindustrialization process is the rise of 'grades and standards' (G&S) in food products. G&S were initially developed by the public sector to reduce transaction costs and ensure product quality and safety but have become a strategic instrument of competition in differentiated product markets (Reardon et al, 2001). Firms are using grades and standards to protect and develop brands in the international marketplace and in some cases to fill in for missing public standards. While producers in developed countries have the resources to meet these requirements, in developing countries these changes have tended to exclude small firms and farmers from participating in market growth, because of the implied investment requirements (Reardon et al, 2001). This is leading to already disadvantaged farmers in these countries being forced to produce basic subsistence food crops and become further excluded from the opportunity to join the global food industry. While past research has evaluated the effects and trends of G&S (Reardon, et al, 2001; Farina & Reardon, 2000; Reardon & Farina, 2002) the organizational structure to enable small farmers to meet these requirements has largely been overlooked. In this paper we use a theoretical contract enforcement framework to argue that private enforcement capital developed through the facilitation of an external aid agency can be an effective means for creating credible and sustainable relationships capable of meeting G&S. We draw upon theory from Cocks and Gow (2002), Oliver and Gow (2002) and Gow et al. (2000) to argue that in situations characterized by high discount rates and low reputation or trust levels (such as transition agriculture) that the use of a third party external enforcement agent can be used to provide the necessary linkage between the parties to facilitate transactions. Through the facilitation role of the external agency, private enforcement capital is developed between the firm and the farmers, opening the path for a sustainable mutually beneficial relationship. Empirical evidence is provided by the case of the United States Department of Agriculture Marketing Assistance Project (USDA MAP) in Armenia and its role in establishing farmer owned milk marketing cooperatives. By acting as an external facilitator in the initial establishment and ongoing development of milk supply cooperatives the USDA MAP has provided a solution to the dual market failure problems of reliable supply of the consistent quality of milk required by processors while enabling farmers access to markets and ensuring timely payment and therefore enabling farmers and firms to credibly contract for the collective marketing of their milk. Through the establishment of a unique and flexibly designed combination of leadership development, training in governance, financial management, dairy management, and quality improvement programs, the USDA MAP has assisted the groups in expanding the self enforcing range in such a manner that the cooperative should be capable of sustaining long term credible exchange relationships once the external agency withdraws. This is important as aid programs have often failed at ensuring sustainability once external management and financial support is removed. Data for this paper was collected through a series of semi-structured interview with USDA MAP staff, dairy processing firm managers, cooperative managers, and cooperative presidents during the fall of 2002, and over a two week period in March, 2003.Livestock Production/Industries,

MEETING PRIVATE GRADES AND STANDARDS IN TRANSITION AGRICULTURE: EXPERIENCES FROM THE ARMENIAN DAIRY INDUSTRY

Livestock Production/Industries,

Generalised balance equations for charged particle transport via localised and delocalised states: Mobility, generalised Einstein relations and fractional transport

A generalised phase-space kinetic Boltzmann equation for highly non-equilibrium charged particle transport via localised and delocalised states is used to develop continuity, momentum and energy balance equations, accounting explicitly for scattering, trapping/detrapping and recombination loss processes. Analytic expressions detail the effect of these microscopic processes on the mobility and diffusivity. Generalised Einstein relations (GER) are developed that enable the anisotropic nature of diffusion to be determined in terms of the measured field-dependence of the mobility. Interesting phenomena such as negative differential conductivity and recombination heating/cooling are shown to arise from recombination loss processes and the localised and delocalised nature of transport. Fractional transport emerges naturally within this framework through the appropriate choice of divergent mean waiting time distributions for localised states, and fractional generalisations of the GER and mobility are presented. Signature impacts on time-of-flight current transients of recombination loss processes via both localised and delocalised states are presented.Comment: 21 pages, 4 figure

Photoassociation spectra and the validity of the dipole approximation for weakly bound dimers

Photoassociation (PA) of ultracold metastable helium to the 2s2p manifold is theoretically investigated using a non-perturbative close-coupled treatment in which the laser coupling is evaluated without assuming the dipole approximation. The results are compared with our previous study [Cocks and Whittingham, Phys. Rev. A 80, 023417 (2009)] that makes use of the dipole approximation. The approximation is found to strongly affect the PA spectra because the photoassociated levels are weakly bound, and a similar impact is predicted to occur in other systems of a weakly bound nature. The inclusion or not of the approximation does not affect the resonance positions or widths, however significant differences are observed in the background of the spectra and the maximum laser intensity at which resonances are discernable. Couplings not satisfying the dipole selection rule |J-1| <= J' <= |J+1| do not lead to observable resonances.Comment: 5 pages, 2 figures; Minor textual revision

Third-order transport coefficients for localised and delocalised charged-particle transport

We derive third order transport coefficients of skewness for a phase-space kinetic model that considers the processes of scattering collisions, trapping, detrapping and recombination losses. The resulting expression for the skewness tensor provides an extension to Fick's law which is in turn applied to yield a corresponding generalised advection-diffusion-skewness equation. A physical interpretation of trap-induced skewness is presented and used to describe an observed negative skewness due to traps. A relationship between skewness, diffusion, mobility and temperature is formed by analogy with Einstein's relation. Fractional transport is explored and its effects on the flux transport coefficients are also outlined.Comment: 11 pages, 3 figure

Time-Reversal-Invariant Hofstadter-Hubbard Model with Ultracold Fermions

We consider the time-reversal-invariant Hofstadter-Hubbard model which can be realized in cold atom experiments. In these experiments, an additional staggered potential and an artificial Rashba--type spin-orbit coupling are available. Without interactions, the system exhibits various phases such as topological and normal insulator, metal as well as semi--metal phases with two or even more Dirac cones. Using a combination of real-space dynamical mean-field theory and analytical techniques, we discuss the effect of on-site interactions and determine the corresponding phase diagram. In particular, we investigate the semi--metal to antiferromagnetic insulator transition and the stability of different topological insulator phases in the presence of strong interactions. We compute spectral functions which allow us to study the edge states of the strongly correlated topological phases.Comment: 4+ pages, 4 figures; includes Supplemental Material (5 pages). Published versio