1,013 research outputs found
Dessins, their delta-matroids and partial duals
Given a map on a connected and closed orientable surface, the
delta-matroid of is a combinatorial object associated to which captures some topological information of the embedding. We explore how
delta-matroids associated to dessins d'enfants behave under the action of the
absolute Galois group. Twists of delta-matroids are considered as well; they
correspond to the recently introduced operation of partial duality of maps.
Furthermore, we prove that every map has a partial dual defined over its field
of moduli. A relationship between dessins, partial duals and tropical curves
arising from the cartography groups of dessins is observed as well.Comment: 34 pages, 20 figures. Accepted for publication in the SIGMAP14
Conference Proceeding
Generalized Dualities and Supergroups
Using a recently developed formulation of double field theory in superspace,
the graviton, -field, gravitini, dilatini, and Ramond-Ramond bispinor are
encoded in a single generalized supervielbein. Duality transformations are
encoded as orthosymplectic transformations, extending the bosonic
duality group, and these act on all constituents of the supervielbein in an
easily computable way. We first review conventional non-abelian T-duality in
the Green-Schwarz superstring and describe the dual geometries in the language
of double superspace. Since dualities are related to super-Killing vectors,
this includes as special cases both abelian and non-abelian fermionic
T-duality.
We then extend this approach to include Poisson-Lie T-duality and its
generalizations, including the generalized coset construction recently
discussed in arXiv:1912.11036. As an application, we construct the
supergeometries associated with the integrable and
deformations of the superstring. The deformation parameters
and are identified with the possible one-parameter embeddings
of the supergravity frame within the doubled supergeometry. In this framework,
the Ramond-Ramond bispinors are directly computable purely from the algebraic
data of the supergroup.Comment: 85 pages; v2: references added, additional comments in introduction
and conclusio
Consistent Truncations and Dualities
Recent progress in generalised geometry and extended field theories suggests
a deep connection between consistent truncations and dualities, which is not
immediately obvious. A prime example is generalised Scherk-Schwarz reductions
in double field theory, which have been shown to be in one-to-one
correspondence with Poisson-Lie T-duality. Here we demonstrate that this
relation is only the tip of the iceberg. Currently, the most general known
classes of T-dualities (excluding mirror symmetry) are based on dressing
cosets. But as we discuss, they can be further extended to the even larger
class of generalised cosets. We prove that the latter give rise to consistent
truncations for which the ansatz can be constructed systematically. Hence, we
pave the way for many new examples of T-dualities and consistent truncations.
The arising structures result in covariant tensors with more than two
derivatives and we argue how they might be key to understand generalised
T-dualities and consistent truncations beyond the leading two derivative level.Comment: 43 page
Picturing and modeling catchments by representative hillslopes
This study explores the suitability of a single hillslope as a parsimonious representation of a catchment in a physically based model. We test this hypothesis by picturing two distinctly different catchments in perceptual models and translating these pictures into parametric setups of 2-D physically based hillslope models. The model parametrizations are based on a comprehensive field data set, expert knowledge and process-based reasoning. Evaluation against streamflow data highlights that both models predicted the annual pattern of streamflow generation as well as the hydrographs acceptably. However, a look beyond performance measures revealed deficiencies in streamflow simulations during the summer season and during individual rainfall–runoff events as well as a mismatch between observed and simulated soil water dynamics. Some of these shortcomings can be related to our perception of the systems and to the chosen hydrological model, while others point to limitations of the representative hillslope concept itself. Nevertheless, our results confirm that representative hillslope models are a suitable tool to assess the importance of different data sources as well as to challenge our perception of the dominant hydrological processes we want to represent therein. Consequently, these models are a promising step forward in the search for the optimal representation of catchments in physically based models
Partitioning of on-demand electron pairs
We demonstrate the high fidelity splitting of electron pairs emitted on
demand from a dynamic quantum dot by an electronic beam splitter. The fidelity
of pair splitting is inferred from the coincidence of arrival in two detector
paths probed by a measurement of the partitioning noise. The emission
characteristic of the on-demand electron source is tunable from electrons being
partitioned equally and independently to electron pairs being split with a
fidelity of 90%. For low beam splitter transmittance we further find evidence
of pair bunching violating statistical expectations for independent fermions
The quiet Sun average Doppler shift of coronal lines up to 2 MK
The average Doppler shift shown by spectral lines formed from the
chromosphere to the corona reveals important information on the mass and energy
balance of the solar atmosphere, providing an important observational
constraint to any models of the solar corona. Previous spectroscopic
observations of vacuum ultra-violet (VUV) lines have revealed a persistent
average wavelength shift of lines formed at temperatures up to 1 MK. At higher
temperatures, the behaviour is still essentially unknown. Here we analyse
combined SUMER/SoHO and EIS/Hinode observations of the quiet Sun around disk
centre to determine, for the first time, the average Doppler shift of several
spectral lines formed between 1 and 2 MK, where the largest part of the quiet
coronal emission is formed. The measurements are based on a novel technique
applied to EIS spectra to measure the difference in Doppler shift between lines
formed at different temperatures. Simultaneous wavelength-calibrated SUMER
spectra allow establishing the absolute value at the reference temperature of 1
MK. The average line shifts at 1 MK < T < 1.8 MK are modestly, but clearly
bluer than those observed at 1 MK. By accepting an average blue shift of about
(-1.8+/-0.6) km/s at 1 MK (as provided by SUMER measurements), this translates
into a maximum Doppler shift of (-4.4+/-2.2) km/s around 1.8 MK. The measured
value appears to decrease to about (-1.3+/-2.6) km/s at the Fe XV formation
temperature of 2.1 MK. The measured average Doppler shift between 0.01 and 2.1
MK, for which we provide a parametrisation, appears to be qualitatively and
roughly quantitatively consistent with what foreseen by 3-D coronal models
where heating is produced by dissipation of currents induced by photospheric
motions and by reconnection with emerging magnetic flux.Comment: 9 pages, 10 figures. Astronomy and Astrophysics (in press
It is Hobbes, not Rousseau:an experiment on voting and redistribution
We perform an experiment which provides a laboratory replica of some
important features of the welfare state. In the experiment, all individuals in a group
decide whether to make a costly effort, which produces a random (independent) outcome
for each one of them. The group members then vote on whether to redistribute
the resulting and commonly known total sum of earnings equally amongst themselves.
This game has two equilibria, if played once. In one of them, all players make
effort and there is little redistribution. In the other one, there is no effort and nothingWe thank Iris Bohnet, Tim Cason, David Cooper, John Duffy, Maia Guell, John Van Huyck and Robin Mason for helpful conversations and encouragement. The comments of the Editor and two referees helped improve the paper. We gratefully acknowledge the financial support from Spain’s Ministry of Science and Innovation under grants CONSOLIDER INGENIO 2010 CSD2006-0016 (all authors), ECO2009-10531 (Cabrales), ECO2008-01768 (Nagel) and the Comunidad de Madrid under grant Excelecon (Cabrales), the Generalitat de Catalunya and the CREA program (Nagel), and project SEJ2007-64340 of Spain’s Ministerio de Educación y Ciencia (Rodríguez Mora).Publicad
A road to reality with topological superconductors
Topological states of matter are a source of low-energy quasiparticles, bound
to a defect or propagating along the surface. In a superconductor these are
Majorana fermions, described by a real rather than a complex wave function. The
absence of complex phase factors promises protection against decoherence in
quantum computations based on topological superconductivity. This is a tutorial
style introduction written for a Nature Physics focus issue on topological
matter.Comment: pre-copy-editing, author-produced version of the published paper: 4
pages, 2 figure
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