175 research outputs found
Tagged particle process in continuum with singular interactions
By using Dirichlet form techniques we construct the dynamics of a tagged
particle in an infinite particle environment of interacting particles for a
large class of interaction potentials. In particular, we can treat interaction
potentials having a singularity at the origin, non-trivial negative part and
infinite range, as e.g., the Lennard-Jones potential.Comment: 27 pages, proof for conservativity added, tightened presentatio
Quantum amplitude estimation with error mitigation for time-evolving probabilistic networks
We present a method to model a discretized time evolution of probabilistic
networks on gate-based quantum computers. We consider networks of nodes, where
each node can be in one of two states: good or failed. In each time step,
probabilities are assigned for each node to fail (switch from good to failed)
or to recover (switch from failed to good). Furthermore, probabilities are
assigned for failing nodes to trigger the failure of other, good nodes. Our
method can evaluate arbitrary network topologies for any number of time steps.
We can therefore model events such as cascaded failure and avalanche effects
which are inherent to financial networks, payment and supply chain networks,
power grids, telecommunication networks and others. Using quantum amplitude
estimation techniques, we are able to estimate the probability of any
configuration for any set of nodes over time. This allows us, for example, to
determine the probability of the first node to be in the good state after the
last time step, without the necessity to track intermediate states. We present
the results of a low-depth quantum amplitude estimation on a simulator with a
realistic noise model. We also present the results for running this example on
the AQT quantum computer system PINE. Finally, we introduce an error model that
allows us to improve the results from the simulator and from the experiments on
the PINE system
The supermembrane revisited
The M2-brane is studied from the perspective of superembeddings. We review
the derivation of the M2-brane dynamics and the supergravity constraints from
the standard superembedding constraint and we discuss explicitly the induced
d=3, N=8 superconformal geometry on the worldvolume. We show that the gauged
supermembrane, for a target space with a U(1) isometry, is the standard
D2-brane in a type IIA supergravity background. In particular, the D2-brane
action, complete with the Dirac-Born-Infeld term, arises from the gauged
Wess-Zumino worldvolume 4-form via the brane action principle. The discussion
is extended to the massive D2-brane considered as a gauged supermembrane in a
massive D=11 superspace background. Type IIA supergeometry is derived using
Kaluza-Klein techniques in superspace.Comment: Latex, 46 pages, clarifying remarks and references adde
Kappa-symmetric Derivative Corrections to D-brane Dynamics
We show how the superembedding formalism can be applied to construct
manifestly kappa-symmetric higher derivative corrections for the D9-brane. We
also show that all correction terms appear at even powers of the fundamental
length scale . We explicitly construct the first potential correction, which
corresponds to the kappa-symmetric version of the , which one
finds from the four-point amplitude of the open superstring.Comment: 20 pages. Minor changes, added reference
Convergence rates in expectation for Tikhonov-type regularization of Inverse Problems with Poisson data
In this paper we study a Tikhonov-type method for ill-posed nonlinear
operator equations \gdag = F(
ag) where \gdag is an integrable,
non-negative function. We assume that data are drawn from a Poisson process
with density t\gdag where may be interpreted as an exposure time. Such
problems occur in many photonic imaging applications including positron
emission tomography, confocal fluorescence microscopy, astronomic observations,
and phase retrieval problems in optics. Our approach uses a
Kullback-Leibler-type data fidelity functional and allows for general convex
penalty terms. We prove convergence rates of the expectation of the
reconstruction error under a variational source condition as both
for an a priori and for a Lepski{\u\i}-type parameter choice rule
Probabilistic Bisimulation: Naturally on Distributions
In contrast to the usual understanding of probabilistic systems as stochastic
processes, recently these systems have also been regarded as transformers of
probabilities. In this paper, we give a natural definition of strong
bisimulation for probabilistic systems corresponding to this view that treats
probability distributions as first-class citizens. Our definition applies in
the same way to discrete systems as well as to systems with uncountable state
and action spaces. Several examples demonstrate that our definition refines the
understanding of behavioural equivalences of probabilistic systems. In
particular, it solves a long-standing open problem concerning the
representation of memoryless continuous time by memory-full continuous time.
Finally, we give algorithms for computing this bisimulation not only for finite
but also for classes of uncountably infinite systems
Supersymmetric Born-Infeld from the D9-brane
Using the superembedding approach, the full supersymmetric effective field
theory of the D9-brane, super Born-Infeld theory, is fixed by the so called
-constraint. The odd-odd components of the theory's super field
strength, , are implied by this constraint. Given , the super Bianchi identities imply the theory's equations of motion.
We calculate up to order 5 in fields, corresponding to order
6 in fields in the Lagrangian.Comment: 15 pages, references adde
Rational F-Theory GUTs without exotics
We construct F-theory GUT models without exotic matter, leading to the MSSM
matter spectrum with potential singlet extensions. The interplay of engineering
explicit geometric setups, absence of four-dimensional anomalies, and realistic
phenomenology of the couplings places severe constraints on the allowed local
models in a given geometry. In constructions based on the spectral cover we
find no model satisfying all these requirements. We then provide a survey of
models with additional U(1) symmetries arising from rational sections of the
elliptic fibration in toric constructions and obtain phenomenologically
appealing models based on SU(5) tops. Furthermore we perform a bottom-up
exploration beyond the toric section constructions discussed in the literature
so far and identify benchmark models passing all our criteria, which can serve
as a guideline for future geometric engineering.Comment: 27 Pages, 1 Figur
Duality Symmetries and G^{+++} Theories
We show that the non-linear realisations of all the very extended algebras
G^{+++}, except the B and C series which we do not consider, contain fields
corresponding to all possible duality symmetries of the on-shell degrees of
freedom of these theories. This result also holds for G_2^{+++} and we argue
that the non-linear realisation of this algebra accounts precisely for the form
fields present in the corresponding supersymmetric theory. We also find a
simple necessary condition for the roots to belong to a G^{+++} algebra.Comment: 35 pages. v2: 2 appendices added, other minor corrections. v3: tables
corrected, other minor changes, one appendix added, refs. added. Version
published in Class. Quant. Gra
The effective action of D6-branes in N=1 type IIA orientifolds
We use a Kaluza-Klein reduction to compute the low-energy effective action
for the massless modes of a spacetime-filling D6-brane wrapped on a special
Lagrangian 3-cycle of a type IIA Calabi-Yau orientifold. The modifications to
the characteristic data of the N=1 bulk orientifold theory in the presence of a
D6-brane are analysed by studying the underlying Type IIA supergravity coupled
to the brane worldvolume in the democratic formulation and performing a
detailed dualisation procedure. The N=1 chiral coordinates are found to be in
agreement with expectations from mirror symmetry. We work out the Kahler
potential for the chiral superfields as well as the gauge kinetic functions for
the bulk and the brane gauge multiplets including the kinetic mixing between
the two. The scalar potential resulting from the dualisation procedure can be
formally interpreted in terms of a superpotential. Finally, the gauging of the
Peccei-Quinn shift symmetries of the complex structure multiplets reproduces
the D-term potential enforcing the calibration condition for special Lagrangian
3-cycles.Comment: 48 pages, v2: typos corrected, references adde
- …