From Doubled Chern-Simons-Maxwell Lattice Gauge Theory to Extensions of the Toric Code

We regularize compact and non-compact Abelian Chern-Simons-Maxwell theories on a spatial lattice using the Hamiltonian formulation. We consider a doubled theory with gauge fields living on a lattice and its dual lattice. The Hilbert space of the theory is a product of local Hilbert spaces, each associated with a link and the corresponding dual link. The two electric field operators associated with the link-pair do not commute. In the non-compact case with gauge group $\mathbb{R}$, each local Hilbert space is analogous to the one of a charged "particle" moving in the link-pair group space $\mathbb{R}^2$ in a constant "magnetic" background field. In the compact case, the link-pair group space is a torus $U(1)^2$ threaded by $k$ units of quantized "magnetic" flux, with $k$ being the level of the Chern-Simons theory. The holonomies of the torus $U(1)^2$ give rise to two self-adjoint extension parameters, which form two non-dynamical background lattice gauge fields that explicitly break the manifest gauge symmetry from $U(1)$ to $\mathbb{Z}(k)$. The local Hilbert space of a link-pair then decomposes into representations of a magnetic translation group. In the pure Chern-Simons limit of a large "photon" mass, this results in a $\mathbb{Z}(k)$-symmetric variant of Kitaev's toric code, self-adjointly extended by the two non-dynamical background lattice gauge fields. Electric charges on the original lattice and on the dual lattice obey mutually anyonic statistics with the statistics angle $\frac{2 \pi}{k}$. Non-Abelian $U(k)$ Berry gauge fields that arise from the self-adjoint extension parameters may be interesting in the context of quantum information processing.Comment: 38 pages, 4 figure

Extreme morphologies of mantis shrimp larvae

Larvae of stomatopods (mantis shrimps) are generally categorized into four larval types: antizoea, pseudozoea (both representing early larval stages), alima and erichthus (the latter two representing later larval stages). These categories, however, do not reflect the existing morphological diversity of stomatopod larvae, which is largely unstudied. We describe here four previously unknown larval types with extreme morphologies. All specimens were found in the collections of the Zoological Museum, University of Copenhagen and were collected during the Danish Dana Expedition round the world 1928-30. These new larval types all represent erichthus-type larvae, especially differing in their shield morphologies. The shield morphology ranges from almost spherical to rather disc-like, with sometimes extremely elongated spines, but only a general systematic assignment of the larvae was possible. Further investigations of these larvae are crucial to understand their life habits and ecological impact, especially as stomatopod and other crustacean larvae might have a much more important position in the marine ecosystems than their corresponding adults

Bursts and Shocks in a Continuum Shell Model

We study a "burst" event, i. e. the evolution of an initial condition having support only in a finite interval of k-space, in the continuum shell model due to Parisi. We show that the continuum equation without forcing or dissipation can be explicitly written in characteristic form and that the right and left moving parts can be solved exactly. When this is supplemented by the appropriate shock condition it is possible to find the asymptotic form of the burst.Comment: 15 pages, 2 eps figures included, Latex 2e. Contribution to the proceedings of the conference: Disorder and Chaos, in honour of Giovanni Paladin, September 22-24, 1997, in Rom

Exact Periodic Solutions of Shells Models of Turbulence

We derive exact analytical solutions of the GOY shell model of turbulence. In the absence of forcing and viscosity we obtain closed form solutions in terms of Jacobi elliptic functions. With three shells the model is integrable. In the case of many shells, we derive exact recursion relations for the amplitudes of the Jacobi functions relating the different shells and we obtain a Kolmogorov solution in the limit of infinitely many shells. For the special case of six and nine shells, these recursions relations are solved giving specific analytic solutions. Some of these solutions are stable whereas others are unstable. All our predictions are substantiated by numerical simulations of the GOY shell model. From these simulations we also identify cases where the models exhibits transitions to chaotic states lying on strange attractors or ergodic energy surfaces.Comment: 25 pages, 7 figure

Can on-farm bioenergy production make organic farming more sustainable? - A model for energy balance, nitrogen losses, and green house gas emissions in a 1000 ha energy catchment with organic dairy farming and integrated bioenergy production

Can biogas and bioethanol production make organic farming more sustainable? - Results from a model for the fossil energy balance, Nitrogen losses, and greenhouse gas emissions in a 1000 ha energy catchment with organic dairy farming and integrated biogas and bioethanol production. Dalgaard T1, Pugesgaard S1, Jørgensen U1, Olesen JE1, Møller HB1 and Jensen ES2 1) Dept. Agroecology and Environment. Faculty of Agricultural Sciences (DJF), University of Aarhus. DK-8830 Tjele. Denmark. Contact: [email protected] 2) Biosystems Department, Risø DTU, The National Laboratory for Sustainable Energy, The Technical University of Denmark DK-4000 Roskilde, Denmark The vision of organic farming systems, independent of fossil energy resources, with significantly lower nutrient losses, and no net contribution to the greenhouse gas emissions might be fulfilled via the integration of biogas production. This is an important hypothesis investigated in the www.bioconcens.elr.dk/uk/ research project. This poster illustrates preliminary results from a model for the fossil energy balance, Nitrogen losses, and greenhouse gas emissions in a 1000 ha energy catchment with organic dairy farming and integrated biogas production in Denmark. The model will draw on results from previous models (e.g the farmGHG model), and includes a number of organic dairy farm type components, including information on livestock production, housing, manure storage, manure and fodder import/export, crop rotations, yield levels, and soil types. In addition, a biogas plant model component evaluates effects of the inclusion of variable amounts of manures and crop residues from the specified farm types, into the biogas energy production. The model is intended to result in an overall catchment balance for the following three types of indicators: 1) the fossil energy use – i.e. the net fossil energy use minus the bioenergy production, 2) losses of Nitrogen in the form of nitrates, ammonia and nitrous oxide, and 3) the emission of the three main greenhouse gasses from agriculture: carbon dioxide, nitrous oxide and methane, measured in carbon dioxide equivalents. Moreover, these indicator values are specified for each of the farm types included in the model, and for the biogas plant component. Finally, selected model results are discussed in relation to the overall hypothesis of the research project, and it is discussed how the integration of biogas production in organic farming, can help to improve the self-sufficiency in Nitrogen, and thereby reduce the import of nutrients to the organic farming systems

From the SU(2)SU(2) Quantum Link Model on the Honeycomb Lattice to the Quantum Dimer Model on the Kagom\'e Lattice: Phase Transition and Fractionalized Flux Strings

We consider the $(2+1)$-d $SU(2)$ quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the Kagom\'e lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges (which transform non-trivially under the $\mathbb{Z}(2)$ center of the $SU(2)$ gauge group) are confined to each other by fractionalized strings with a delocalized $\mathbb{Z}(2)$ flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the 3-d Ising universality class separates two confining phases; one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.Comment: 16 pages, 20 figures, 2 tables, two more relevant references and one short paragraph are adde

From the SU(2)SU(2) Quantum Link Model on the Honeycomb Lattice to the Quantum Dimer Model on the Kagom\'e Lattice: Phase Transition and Fractionalized Flux Strings

We consider the $(2+1)$-d $SU(2)$ quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the Kagom\'e lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges (which transform non-trivially under the $\mathbb{Z}(2)$ center of the $SU(2)$ gauge group) are confined to each other by fractionalized strings with a delocalized $\mathbb{Z}(2)$ flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the 3-d Ising universality class separates two confining phases; one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.Comment: 16 pages, 20 figures, 2 tables, two more relevant references and one short paragraph are adde

Sources of nitrogen for winter wheat in organic cropping systems

In organic cropping systems, legumes, cover crops, residue incorporation, and manure application are used to maintain soil fertility, but the contributions of these management practices to soil nitrogen (N) supply remain obscure. We examined potential sources of N for winter wheat (Triticum aestivum L.) in four experimental cropping systems established in 1997 on three soil types. Three of the four systems were under organic management. Topsoil N, depth of the A horizon, and cumulated inputs of N since 1997 were determined at plot level. Labile soil N pools (mineral N, potentially mineralizable N [PMN], microbial biomass N [MBN]) were monitored during two growth periods; at one site, biomass C/N ratios were also determined. Soil for labile N analysis was shielded from N inputs during spring application to isolate cumulated system effects. PMN and MBN were correlated across all sites and rotations (r2=0.72). The MBN corresponded to 46-85, 85-145 and 74-172 kg N ha-1 at the three sites and differed significantly between cropping systems, but MBN could not explain differences in wheat grain N yields. Instead, a multiple linear regression model explained 76 and 82% of the variation in grain N yields in organic cropping systems in 2007 and 2008, showing significant effects of, respectively, topsoil N, depth of A horizon, cumulated inputs of N, and N applied to winter wheat in manure. Thus, soil properties, and past and current management all contributed to winter wheat N supply

The string tension in SU(N) gauge theory from a careful analysis of smearing parameters

We report a method to select optimal smearing parameters before production runs and discuss the advantages of this selection for the determination of the string tension.Comment: Contribution to Lat97 poster session, title was 'How to measure the string tension', 3 pages, 5 colour eps figure

Dual strings and magnetohydrodynamics

We investigate whether dual strings could be solutions of the magnetohydrodynamics equations in the limit of infinite conductivity. We find that the induction equation is satisfied, and we discuss the Navier-Stokes equation (without viscosity) with the Lorentz force included. We argue that the dual string equations (with a non-universal maximum velocity) should describe the large scale motion of narrow magnetic flux tubes, because of a large reparametrization (gauge) invariance of the magnetic and electric string fields. It is shown that the energy-momentum tensor for the dual string can be reinterpreted as an energy-momentum tensor for magnetohydrodynamics, provided certain conditions are satisfied. We also give a brief discussion of the case when magnetic monopoles are included, and indicate how this can lead to a non-relativistic "electrohydrodynamics" picture of confinement.Comment: 10 pages. LaTex. A minor correction has been mad