11,761 research outputs found
Bottom-quark associated Higgs-boson production: reconciling the four- and five-flavour scheme approach
The main arguments in the discussion of the proper treatment of the total
inclusive cross section for bottom-quark associated Higgs-boson production are
briefly reviewed. A simple and pragmatic formula for the combination of the
so-called four- and five-flavour schemes is suggested, including the treatment
of the respective theory error estimates. The numerical effects of this
matching formula are discussed.Comment: 8 pages, 4 figure
Learning Optimal Control of Synchronization in Networks of Coupled Oscillators using Genetic Programming-based Symbolic Regression
Networks of coupled dynamical systems provide a powerful way to model systems
with enormously complex dynamics, such as the human brain. Control of
synchronization in such networked systems has far reaching applications in many
domains, including engineering and medicine. In this paper, we formulate the
synchronization control in dynamical systems as an optimization problem and
present a multi-objective genetic programming-based approach to infer optimal
control functions that drive the system from a synchronized to a
non-synchronized state and vice-versa. The genetic programming-based controller
allows learning optimal control functions in an interpretable symbolic form.
The effectiveness of the proposed approach is demonstrated in controlling
synchronization in coupled oscillator systems linked in networks of increasing
order complexity, ranging from a simple coupled oscillator system to a
hierarchical network of coupled oscillators. The results show that the proposed
method can learn highly-effective and interpretable control functions for such
systems.Comment: Submitted to nonlinear dynamic
Optimal Control for Open Quantum Systems: Qubits and Quantum Gates
This article provides a review of recent developments in the formulation and
execution of optimal control strategies for the dynamics of quantum systems. A
brief introduction to the concept of optimal control, the dynamics of of open
quantum systems, and quantum information processing is followed by a
presentation of recent developments regarding the two main tasks in this
context: state-specific and state-independent optimal control. For the former,
we present an extension of conventional theory (Pontryagin's principle) to
quantum systems which undergo a non-Markovian time-evolution. Owing to its
importance for the realization of quantum information processing, the main body
of the review, however, is devoted to state-independent optimal control. Here,
we address three different approaches: an approach which treats dissipative
effects from the environment in lowest-order perturbation theory, a general
method based on the time--evolution superoperator concept, as well as one based
on the Kraus representation of the time-evolution superoperator. Applications
which illustrate these new methods focus on single and double qubits (quantum
gates) whereby the environment is modeled either within the Lindblad equation
or a bath of bosons (spin-boson model). While these approaches are widely
applicable, we shall focus our attention to solid-state based physical
realizations, such as semiconductor- and superconductor-based systems. While an
attempt is made to reference relevant and representative work throughout the
community, the exposition will focus mainly on work which has emerged from our
own group.Comment: 27 pages, 18 figure
Superdiffusion, large-scale synchronization and topological defects
We study an ensemble of random walkers carrying internal noisy phase
oscillators which are synchronized among the walkers by local interactions. Due
to individual mobility, the interaction partners of every walker change
randomly, hereby introducing an additional, independent source of fluctuations,
thus constituting the intrinsic nonequilibrium nature of the temporal dynamics.
We employ this paradigmatic model system to discuss how the emergence of order
is affected by motion of individual entities. In particular, we consider both,
normal diffusive motion and superdiffusion. A non-Hamiltonian field theory
including multiplicative noise terms is derived which describes the
nonequilibrium dynamics at the macroscale. This theory reveals a
defect-mediated transition from incoherence to quasi long-range order for
normal diffusion of oscillators in two dimensions, implying a power-law
dependence of all synchronization properties on system size. In contrast,
superdiffusive transport suppresses the emergence of topological defects,
thereby inducing a continuous synchronization transition to long-range order in
two dimensions. These results are consistent with particle-based simulations.Comment: 7 pages, 5 figures, submitted to Phys. Rev.
Phase Diagram of Bosons in Two-Color Superlattices from Experimental Parameters
We study the zero-temperature phase diagram of a gas of bosonic 87-Rb atoms
in two-color superlattice potentials starting directly from the experimental
parameters, such as wavelengths and intensities of the two lasers generating
the superlattice. In a first step, we map the experimental setup to a
Bose-Hubbard Hamiltonian with site-dependent parameters through explicit
band-structure calculations. In the second step, we solve the many-body problem
using the density-matrix renormalization group (DMRG) approach and compute
observables such as energy gap, condensate fraction, maximum number
fluctuations and visibility of interference fringes. We study the phase diagram
as function of the laser intensities s_2 and s_1 as control parameters and show
that all relevant quantum phases, i.e. superfluid, Mott-insulator, and quasi
Bose-glass phase, and the transitions between them can be investigated through
a variation of these intensities alone.Comment: 4 pages, 3 figure
Nonlinear optics with full three-dimensional illumination
We investigate the nonlinear optical process of third-harmonic generation in
the thus far unexplored regime of focusing the pump light from a full solid
angle, where the nonlinear process is dominantly driven by a standing
dipole-wave. We elucidate the influence of the focal volume and the pump
intensity on the number of frequency-tripled photons by varying the solid angle
from which the pump light is focused, finding good agreement between the
experiments and numerical calculations. As a consequence of focusing the pump
light to volumes much smaller than a wavelength cubed the Gouy phase does not
limit the yield of frequency-converted photons. This is in stark contrast to
the paraxial regime. We believe that our findings are generic to many other
nonlinear optical processes when the pump light is focused from a full solid
angle.Comment: 6 pages main text + 4 pages appendix, modified abstract and
introduction + some other minor change
Stock options as incentive contracts and dividend policy
Executive Stock Option Programs (SOPs) have become the dominant compensation instrument for top-management in recent years. The incentive effects of an SOP both with respect to corporate investment and financing decisions critically depend on the design of the SOP. A specific problem in designing SOPs concerns dividend protection. Usually, SOPs are not dividend protected, i.e. any dividend payout decreases the value of a manager’s options. Empirical evidence shows that this results in a significant decrease in the level of corporate dividends and, at the same time, into an increase in share repurchases. Yet, few suggestions have been made on how to account for dividends in SOPs. This paper applies arguments from principal-agent-theory and from the theory of finance to analyze different forms of dividend protection, and to address the relevance of dividend protection in SOPs. Finally, the paper relates the theoretical analysis to empirical work on the link between share repurchases and SOPs
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