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 R, each local Hilbert space is analogous to the one of a charged “particle” moving in the link-pair group space R2 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 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 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 . 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.

A Dynamical Tool to Study the Cultural Context of Conflict Escalation

The present article describes research in progress which is developing a simple, replicable methodology aimed at identifying the regularities and specificity of human behavior in conflict escalation and de-escalation prooesses. These research efforts will ultimately be used to study conflict dynamics across cultures. The experimental data collected through this methodology, together with case studies and aggregated, time-series macro data are key for identifying relevant parameters, systems' properties, and micromechanisms defining the behavior of naturally occurring conflict escalation and de-escalation dynamics. This, in turn, is critical for the development of realistic, empirically supported computational models. The article outlines the theoretical assumptions of Dynamical Systems Theory with regard to conflict dynamics, with an emphasis on the process of conflict escalation and de-escalation. Next, work on a methodology for empirical study of escalation processes from a DST perspective is outlined. Specifically, the development of a progressive scenario methodology designed to map escalation sequences, together with anexample of a preliminary study based on the proposed researcb paradigm, is presented. Implications of the approach for the study of culture are discussed.

Comparison of different lattice definitions of the topological charge

We present a comparison of different definitions of the topological charge on the lattice, using a small-volume ensemble with 2 flavours of dynamical twisted mass fermions. The investigated definitions are: index of the overlap Dirac operator, spectral projectors, spectral flow of the HermitianWilson- Dirac operator and field theoretic with different kinds of smoothing of gauge fields (HYP and APE smearings, gradient flow, cooling). We also show some results on the topological susceptibility.

Magnetic properties of Cenozoic MORB and Cretaceous MORB from DSDP and ODP holes

The fact that the natural remanent magnetization (NRM) intensity of mid-oceanic-ridge basalt (MORB) samples shows systematic variations as a function of age has long been recognized: maximum as well as average intensities are generally high for very young samples, falling off rather rapidly to less than half the recent values in samples between 10 and 30 Ma, whereupon they slowly rise in the early Tertiary and Cretaceous to values that approach those of the very young samples. NRM intensities measured in this study follow the same trends as those observed in previous publications. In this study, we take a statistical approach and examine whether this pattern can be explained by variations in one or more of all previously proposed mechanisms: chemical composition of the magnetic minerals, abundance of these magnetization carriers, vectorial superposition of parallel or antiparallel components of magnetization, magnetic grain or domain size patterns, low-temperature oxidation to titanomaghemite, or geomagnetic field behavior. We find that the samples do not show any compositional, petrological, rock-magnetic, or paleomagnetic patterns that can explain the trends. Geomagnetic field intensity is the only effect that cannot be directly tested on the same samples, but it shows a similar pattern as our measured NRM intensities. We therefore conclude that the geomagnetic field strength was, on-average, significantly greater during the Cretaceous than during the Oligocene and Miocene.

Molecular properties of gases of ODP Leg 204 sites

The recognition of finely disseminated gas hydrate in deep marine sediments heavily depends on various indirect techniques because this mineral quickly decomposes upon recovery from in situ pressure and temperature conditions. Here, we discuss molecular properties of closely spaced gas voids (formed as a result of core recovery) and gas hydrates from an area of relatively low gas flux at the flanks of the southern Hydrate Ridge offshore Oregon (ODP Sites 1244, 1245 and 1247). Within the gas hydrate occurrence zone (GHOZ), the concentration of ethane (C2) and propane (C3) in adjacent gas voids shows large variability. Sampled gas hydrates are enriched in C2 relative to void gases but do not contain C3. We suggest that the observed variations in the composition of void gases is a result of molecular fractionation during crystallization of structure I gas hydrate that contains C2 but excludes C3 from its crystal lattice. This hypothesis is used to identify discrete intervals of finely disseminated gas hydrate in cored sediments. Variations in gas composition help better constrain gas hydrate distribution near the top of the GHOZ along with variations in pore water chemistry and core temperature. Sediments near the base of the gas hydrate stability zone are relatively enriched in C2+ hydrocarbon gases. Complex and poorly understood geological and geochemical processes in these deeper sediments make the identification of gas hydrate based on molecular properties of void gases more ambiguous. The proposed technique appears to be a useful tool to better understand the distribution of gas hydrate in marine sediments and ultimately the role of gas hydrate in the global carbon cycle.

High quality InAlN single layers lattice-matched to GaN grown by molecular beam epitaxy

We report on properties of high quality ~60 nm thick InAlN layers nearly in-plane lattice-matched to GaN, grown on c-plane GaN-on-sapphire templates by plasma-assisted molecular beam epitaxy. Excellent crystalline quality and low surface roughness are confirmed by X-ray diffraction, transmission electron microscopy, and atomic force microscopy. High annular dark field observations reveal a periodic in-plane indium content variation (8 nm period), whereas optical measurements evidence certain residual absorption below the band-gap. The indium fluctuation is estimated to be +/- 1.2% around the nominal 17% indium content via plasmon energy oscillations assessed by electron energy loss spectroscopy with sub-nanometric spatial resolution.

Investigation on the structural and magnetic properties of sputtered TbFe2/Fe3Ga heterostructures

We have analyzed the structural and magnetic properties of as-grown and annealed [TbFe2/Fe3Ga]n heterostructures grown by sputtering. Evidence of the bcc structure in the Fe3Ga layers has been found. The diffraction peak related to this structure shifts to high angles with the annealing temperature. Also, we have observed a change in the microstructure of the Tb-Fe layers when the thickness layer is reduced in the as-grown heterostructures. Moreover, the Tb content is lower than 33% of the TbFe2 Laves phase and it depends on the layer thickness. The thermal treatments promote the increase of the Tb content, but only in the heterostructures with thick layers. The strong lattice mismatch between the Tb-Fe and Fe-Ga layers seems to prevent a complete Tb diffusion upon the annealing process. Thus, the crystallization of the TbFe2 Laves phase is inhibited in the heterostructures with thin layers, although our experimental results indicate the presence of potential magnetostrictive TbFeGa alloys

Structural properties of InAlN single layers nearly latice-matched to GaN grown by plasma assisted molecular beal epitaxy

The high lattice mismatch between III-nitride binaries (InN, GaN and AlN) remains a key problem to grow high quality III-nitride heterostructures. Recent interest has been focused on the growth of high-quality InAlN layers, with approximately 18% of indium incorporation, in-plane lattice-matched (LM) to GaN. While a lot of work has been done by metal-organic vapour phase epitaxy (MOVPE) by Carlin and co-workers, its growth by molecular beam epitaxy (MBE) is still in infancy

Optical and structural properties of InAlN/GaN Bragg reflectors examined by transmission electron microscopy and electron energy loss spectroscopy

Molecular beam epitaxy growth of ten-period lattice-matched InAlN/GaN distributed Bragg reflectors (DBRs) with peak reflectivity centered around 400nm is reported including optical and transmission electron microscopy (TEM) measurements [1]. Good periodicity heterostructures with crack-free surfaces were confirmed, but, also a significant residual optical absorption below the bandgap was measured. The TEM characterization ascribes the origin of this problem to polymorfism and planar defects in the GaN layers and to the existence of an In-rich layer at the InAlN/GaN interfaces. In this work, several TEM based techniques have been combined.

Optoelectronic Properties of InAlN/GaN Distributed Bragg Reflector Heterostructure Examined by Valence

High-resolution monochromated electron energy loss spectroscopy (EELS) at subnanometric spatial resolution and <200 meV energy resolution has been used to assess the valence band properties of a distributed Bragg reflector multilayer heterostructure composed of InAlN lattice matched to GaN. This work thoroughly presents the collection of methods and computational tools put together for this task. Among these are zero-loss-peak subtraction and nonlinear fitting tools, and theoretical modeling of the electron scattering distribution. EELS analysis allows retrieval of a great amount of information: indium concentration in the InAlN layers is monitored through the local plasmon energy position and calculated using a bowing parameter version of Vegard Law. Also a dielectric characterization of the InAlN and GaN layers has been performed through Kramers-Kronig analysis of the Valence-EELS data, allowing band gap energy to be measured and an insight on the polytypism of the GaN layers.

Analytical properties of horizontal visibility graphs in the Feigenbaum scenario

Time series are proficiently converted into graphs via the horizontal visibility (HV) algorithm, which prompts interest in its capability for capturing the nature of different classes of series in a network context. We have recently shown [B. Luque et al., PLoS ONE 6, 9 (2011)] that dynamical systems can be studied from a novel perspective via the use of this method. Specifically, the period-doubling and band-splitting attractor cascades that characterize unimodal maps transform into families of graphs that turn out to be independent of map nonlinearity or other particulars. Here, we provide an in depth description of the HV treatment of the Feigenbaum scenario, together with analytical derivations that relate to the degree distributions, mean distances, clustering coefficients, etc., associated to the bifurcation cascades and their accumulation points. We describe how the resultant families of graphs can be framed into a renormalization group scheme in which fixed-point graphs reveal their scaling properties. These fixed points are then re-derived from an entropy optimization process defined for the graph sets, confirming a suggested connection between renormalization group and entropy optimization. Finally, we provide analytical and numerical results for the graph entropy and show that it emulates the Lyapunov exponent of the map independently of its sign.