686 research outputs found
Topological Blocking in Quantum Quench Dynamics
We study the non-equilibrium dynamics of quenching through a quantum critical
point in topological systems, focusing on one of their defining features:
ground state degeneracies and associated topological sectors. We present the
notion of 'topological blocking', experienced by the dynamics due to a mismatch
in degeneracies between two phases and we argue that the dynamic evolution of
the quench depends strongly on the topological sector being probed. We
demonstrate this interplay between quench and topology in models stemming from
two extensively studied systems, the transverse Ising chain and the Kitaev
honeycomb model. Through non-local maps of each of these systems, we
effectively study spinless fermionic -wave paired superconductors. Confining
the systems to ring and toroidal geometries, respectively, enables us to
cleanly address degeneracies, subtle issues of fermion occupation and parity,
and mismatches between topological sectors. We show that various features of
the quench, which are related to Kibble-Zurek physics, are sensitive to the
topological sector being probed, in particular, the overlap between the
time-evolved initial ground state and an appropriate low-energy state of the
final Hamiltonian. While most of our study is confined to translationally
invariant systems, where momentum is a convenient quantum number, we briefly
consider the effect of disorder and illustrate how this can influence the
quench in a qualitatively different way depending on the topological sector
considered.Comment: 18 pages, 11 figure
Abelian homotopy Dijkgraaf-Witten theory
We construct a version of Dijkgraaf-Witten theory based on a compact abelian
Lie group within the formalism of Turaev's homotopy quantum field theory. As an
application we show that the 2+1-dimensional theory based on U(1) classifies
lens spaces up to homotopy type.Comment: 23 pages, 1 figur
Regolith production and transport at the Susquehanna Shale Hills Critical Zone Observatory, Part 2: Insights from meteoric 10Be
Regolith-mantled hillslopes are ubiquitous features of most temperate landscapes, and their morphology reflects the climatically, biologically, and tectonically mediated interplay between regolith production and downslope transport. Despite intensive research, few studies have quantified both of these mass fluxes in the same field site. Here we present an analysis of 87 meteoric 10Be measurements from regolith and bedrock within the Susquehanna Shale Hills Critical Zone Observatory (SSHO), in central Pennsylvania. Meteoric 10Be concentrations in bulk regolith samples (n=73) decrease with regolith depth. Comparison of hillslope meteoric 10Be inventories with analyses of rock chip samples (n=14) from a 24 m bedrock core confirms that >80% of the total inventory is retained in the regolith. The systematic downslope increase of meteoric 10Be inventories observed at SSHO is consistent with 10Be accumulation in slowly creeping regolith (∼ 0.2 cm yr-1). Regolith flux inferred from meteoric 10Be varies linearly with topographic gradient (determined from high-resolution light detection and ranging-based topography) along the upper portions of hillslopes at SSHO. However, regolith flux appears to depend on the product of gradient and regolith depth where regolith is thick, near the base of hillslopes. Meteoric 10Be inventories at the north and south ridgetops indicate minimum regolith residence times of 10.5 ± 3.7 and 9.1 ± 2.9 ky, respectively, similar to residence times inferred from U-series isotopes in Ma et al. (2013). The combination of our results with U-series-derived regolith production rates implies that regolith production and erosion rates are similar to within a factor of two on SSHO hillcrests. ©2013. American Geophysical Union. All Rights Reserved
The modular S-matrix as order parameter for topological phase transitions
We study topological phase transitions in discrete gauge theories in two
spatial dimensions induced by the formation of a Bose condensate. We analyse a
general class of euclidean lattice actions for these theories which contain one
coupling constant for each conjugacy class of the gauge group. To probe the
phase structure we use a complete set of open and closed anyonic string
operators. The open strings allow one to determine the particle content of the
condensate, whereas the closed strings enable us to determine the matrix
elements of the modular -matrix, also in the broken phase. From the measured
broken -matrix we may read off the sectors that split or get identified in
the broken phase, as well as the sectors that are confined. In this sense the
modular -matrix can be employed as a matrix valued non-local order parameter
from which the low-energy effective theories that occur in different regions of
parameter space can be fully determined.
To verify our predictions we studied a non-abelian anyon model based on the
quaternion group of order eight by Monte Carlo simulation. We
probe part of the phase diagram for the pure gauge theory and find a variety of
phases with magnetic condensates leading to various forms of (partial)
confinement in complete agreement with the algebraic breaking analysis. Also
the order of various transitions is established.Comment: 37 page
Exploring the challenges and potentialities of the database of religious history for cognitive historiography
This article explores the potential impact and contribution of the Database of Religious History (DRH) project within the field of Cognitive Historiography. The DRH aims to bring together, in a systematic and open-access format, data on religious groups from across the globe and throughout history. By utilizing robust, open-source technologies and best-practice software principles, the DRH constitutes a novel and innovative approach to historical and cultural studies. As a contribution to the scientific study of both religion and history, the DRH offers data amenable to statistical analyses, thus providing tools for assessing diachronic cultural innovation and adaptation, the testing of grand narrative theories of religious change, and for enriching and revitalizing traditional fields such as comparative religions, history of religion(s), and anthropology of religion. In this article we explore the methods employed in collecting and digitizing historical data, identify our unit of analysis, outline the challenges of recruiting historians of various fields, and highlight the DRH’s methodological potential for both Religious Studies and Cognitive Historiography
Product Policy as an Instrument for Water Quality Management.
A main reason for the persistence of current water pollution lies in the diffuse character of many of its sources. For a large part such diffuse pollution is related to the production, use and waste of various kinds of products. For the reduction of this pollution, a product oriented policy strategy, based on interaction with stakeholders could be more successful than the traditional measures of direct regulation that were devised for point source reduction. In this article we identify different types of product policy, and explore the potential benefits and costs for water quality management. The methods that can be used in a product policy approach are illustrated with some examples. Although the specific advantages for water quality management have not been quantified yet, governments increasingly recognise the potential positive effects. In this context, the European Water Framework Directive, in stimulating product policy by enhancing public and stakeholders’ participation, can be considered to be part of a general development towards interactive water management
A theory of topological edges and domain walls
We investigate domain walls between topologically ordered phases in two
spatial dimensions and present a simple but general framework from which their
degrees of freedom can be understood. The approach we present exploits the
results on topological symmetry breaking that we have introduced and presented
elsewhere. After summarizing the method, we work out predictions for the
spectrum of edge excitations and for the transport through edges in some
representative examples. These include domain walls between the Abelian and
non-Abelian topological phases of Kitaev's honeycomb lattice model in a
magnetic field, as well as recently proposed domain walls between spin
polarized and unpolarized non-Abelian fractional quantum Hall states at
different filling fractions.Comment: 4 pages, 1 figure, late
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