3,590 research outputs found
The Noether-Lefschetz Problem and Gauge-Group-Resolved Landscapes: F-Theory on K3 x K3 as a Test Case
Four-form flux in F-theory compactifications not only stabilizes moduli, but
gives rise to ensembles of string vacua, providing a scientific basis for a
stringy notion of naturalness. Of particular interest in this context is the
ability to keep track of algebraic information (such as the gauge group)
associated with individual vacua while dealing with statistics. In the present
work, we aim to clarify conceptual issues and sharpen methods for this purpose,
using compactification on as a test case. Our first
approach exploits the connection between the stabilization of complex structure
moduli and the Noether-Lefschetz problem. Compactification data for F-theory,
however, involve not only a four-fold (with a given complex structure)
and a flux on it, but also an elliptic fibration morphism , which makes this problem complicated. The heterotic-F-theory duality
indicates that elliptic fibration morphisms should be identified modulo
isomorphism. Based on this principle, we explain how to count F-theory vacua on
while keeping the gauge group information.
Mathematical results reviewed/developed in our companion paper are exploited
heavily. With applications to more general four-folds in mind, we also clarify
how to use Ashok-Denef-Douglas' theory of the distribution of flux vacua in
order to deal with statistics of sub-ensembles tagged by a given set of
algebraic/topological information. As a side remark, we extend the
heterotic/F-theory duality dictionary on flux quanta and elaborate on its
connection to the semistable degeneration of a K3 surface.Comment: 81 pages, 5 figure
The Activation-Relaxation Technique : ART nouveau and kinetic ART
The evolution of many systems is dominated by rare activated events that occur on timescale ranging from nanoseconds to the hour or more. For such systems, simulations must leave aside the full thermal description to focus specifically on mechanisms that generate a configurational change. We present here the activation relaxation technique (ART), an open-ended saddle point search algorithm, and a series of recent improvements to ART nouveau and kinetic ART, an ART-based on-the-fly off-lattice self-learning kinetic Monte Carlo method
Quantum Control Landscapes
Numerous lines of experimental, numerical and analytical evidence indicate
that it is surprisingly easy to locate optimal controls steering quantum
dynamical systems to desired objectives. This has enabled the control of
complex quantum systems despite the expense of solving the Schrodinger equation
in simulations and the complicating effects of environmental decoherence in the
laboratory. Recent work indicates that this simplicity originates in universal
properties of the solution sets to quantum control problems that are
fundamentally different from their classical counterparts. Here, we review
studies that aim to systematically characterize these properties, enabling the
classification of quantum control mechanisms and the design of globally
efficient quantum control algorithms.Comment: 45 pages, 15 figures; International Reviews in Physical Chemistry,
Vol. 26, Iss. 4, pp. 671-735 (2007
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