1,071 research outputs found
Extensions and block decompositions for finite-dimensional representations of equivariant map algebras
Suppose a finite group acts on a scheme and a finite-dimensional Lie
algebra . The associated equivariant map algebra is the Lie
algebra of equivariant regular maps from to . The irreducible
finite-dimensional representations of these algebras were classified in
previous work with P. Senesi, where it was shown that they are all tensor
products of evaluation representations and one-dimensional representations. In
the current paper, we describe the extensions between irreducible
finite-dimensional representations of an equivariant map algebra in the case
that is an affine scheme of finite type and is reductive.
This allows us to also describe explicitly the blocks of the category of
finite-dimensional representations in terms of spectral characters, whose
definition we extend to this general setting. Applying our results to the case
of generalized current algebras (the case where the group acting is trivial),
we recover known results but with very different proofs. For (twisted) loop
algebras, we recover known results on block decompositions (again with very
different proofs) and new explicit formulas for extensions. Finally,
specializing our results to the case of (twisted) multiloop algebras and
generalized Onsager algebras yields previously unknown results on both
extensions and block decompositions.Comment: 41 pages; v2: minor corrections, formatting changed to match
published versio
Optical control of internal electric fields in band-gap graded InGaN nanowires
InGaN nanowires are suitable building blocks for many future optoelectronic
devices. We show that a linear grading of the indium content along the nanowire
axis from GaN to InN introduces an internal electric field evoking a
photocurrent. Consistent with quantitative band structure simulations we
observe a sign change in the measured photocurrent as a function of photon
flux. This negative differential photocurrent opens the path to a new type of
nanowire-based photodetector. We demonstrate that the photocurrent response of
the nanowires is as fast as 1.5 ps
The Complex Langevin method: When can it be trusted?
We analyze to what extent the complex Langevin method, which is in principle
capable of solving the so-called sign problems, can be considered as reliable.
We give a formal derivation of the correctness and then point out various
mathematical loopholes. The detailed study of some simple examples leads to
practical suggestions about the application of the method.Comment: 14 pages, including several eps figures and tables; clarification and
minor corrections added, to appear in PR
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
Gauge theories are fundamental to our understanding of interactions between
the elementary constituents of matter as mediated by gauge bosons. However,
computing the real-time dynamics in gauge theories is a notorious challenge for
classical computational methods. In the spirit of Feynman's vision of a quantum
simulator, this has recently stimulated theoretical effort to devise schemes
for simulating such theories on engineered quantum-mechanical devices, with the
difficulty that gauge invariance and the associated local conservation laws
(Gauss laws) need to be implemented. Here we report the first experimental
demonstration of a digital quantum simulation of a lattice gauge theory, by
realising 1+1-dimensional quantum electrodynamics (Schwinger model) on a
few-qubit trapped-ion quantum computer. We are interested in the real-time
evolution of the Schwinger mechanism, describing the instability of the bare
vacuum due to quantum fluctuations, which manifests itself in the spontaneous
creation of electron-positron pairs. To make efficient use of our quantum
resources, we map the original problem to a spin model by eliminating the gauge
fields in favour of exotic long-range interactions, which have a direct and
efficient implementation on an ion trap architecture. We explore the Schwinger
mechanism of particle-antiparticle generation by monitoring the mass production
and the vacuum persistence amplitude. Moreover, we track the real-time
evolution of entanglement in the system, which illustrates how particle
creation and entanglement generation are directly related. Our work represents
a first step towards quantum simulating high-energy theories with atomic
physics experiments, the long-term vision being the extension to real-time
quantum simulations of non-Abelian lattice gauge theories
PopBERT. Detecting populism and its host ideologies in the German Bundestag
The rise of populism concerns many political scientists and practitioners,
yet the detection of its underlying language remains fragmentary. This paper
aims to provide a reliable, valid, and scalable approach to measure populist
stances. For that purpose, we created an annotated dataset based on
parliamentary speeches of the German Bundestag (2013 to 2021). Following the
ideational definition of populism, we label moralizing references to the
virtuous people or the corrupt elite as core dimensions of populist language.
To identify, in addition, how the thin ideology of populism is thickened, we
annotate how populist statements are attached to left-wing or right-wing host
ideologies. We then train a transformer-based model (PopBERT) as a multilabel
classifier to detect and quantify each dimension. A battery of validation
checks reveals that the model has a strong predictive accuracy, provides high
qualitative face validity, matches party rankings of expert surveys, and
detects out-of-sample text snippets correctly. PopBERT enables dynamic analyses
of how German-speaking politicians and parties use populist language as a
strategic device. Furthermore, the annotator-level data may also be applied in
cross-domain applications or to develop related classifiers
A Model for QCD at High Density and Large Quark Mass
We study the high density region of QCD within an effective model obtained in
the frame of the hopping parameter expansion and choosing Polyakov type of
loops as the main dynamical variables representing the fermionic matter. To get
a first idea of the phase structure, the model is analyzed in strong coupling
expansion and using a mean field approximation. In numerical simulations, the
model still shows the so-called sign problem, a difficulty peculiar to non-zero
chemical potential, but it permits the development of algorithms which ensure a
good overlap of the Monte Carlo ensemble with the true one. We review the main
features of the model and present calculations concerning the dependence of
various observables on the chemical potential and on the temperature, in
particular of the charge density and the diquark susceptibility, which may be
used to characterize the various phases expected at high baryonic density. We
obtain in this way information about the phase structure of the model and the
corresponding phase transitions and cross over regions, which can be considered
as hints for the behaviour of non-zero density QCD.Comment: 21 pages, 29 figure
Electrically and Magnetically Charged States and Particles in the 2+1-Dimensional Z_N-Higgs Gauge Model
Electrically as well as magnetically charged states are constructed in the
2+1-dimensional Euclidean Z_N-Higgs lattice gauge model, the former following
ideas of Fredenhagen and Marcu and the latter using duality transformations on
the algebra of observables. The existence of electrically and of magnetically
charged particles is also established. With this work we prepare the ground for
the constructive study of anyonic statistics of multiparticle scattering states
of electrically and magnetically charged particles in this model (work in
progress).Comment: 57 pages, Sfb 288 Preprint No. 109. To appear in Commun. Math. Phys.
About the file: This is a uuencoded, "gzip-ed" postscript file. It is about
300kB large. The original ps file is about 700kB large. All figures are
included. The LaTeX sources ou even hard copies can be required to the
authors at [email protected] or Freie Universitaet Berlin.
Institut fuer Theoretische Physik. Arnimallee 14. Berlin 14195 German
Universality Class of Models
We point out that existing numerical data on the correlation length and
magnetic susceptibility suggest that the two dimensional model with
standard action has critical exponent , which is inconsistent with
asymptotic freedom. This value of is also different from the one of the
Wess-Zumino-Novikov-Witten model that is supposed to correspond to the
model at .Comment: 8 pages, with 3 figures included, postscript. An error concerning the
errors has been correcte
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