242,052 research outputs found
Second-Order Functions and Theorems in ACL2
SOFT ('Second-Order Functions and Theorems') is a tool to mimic second-order
functions and theorems in the first-order logic of ACL2. Second-order functions
are mimicked by first-order functions that reference explicitly designated
uninterpreted functions that mimic function variables. First-order theorems
over these second-order functions mimic second-order theorems universally
quantified over function variables. Instances of second-order functions and
theorems are systematically generated by replacing function variables with
functions. SOFT can be used to carry out program refinement inside ACL2, by
constructing a sequence of increasingly stronger second-order predicates over
one or more target functions: the sequence starts with a predicate that
specifies requirements for the target functions, and ends with a predicate that
provides executable definitions for the target functions.Comment: In Proceedings ACL2 2015, arXiv:1509.0552
Scaling of decoherence and energy flow in interacting quantum spin systems
We address the quantum dynamics of a system composed of a qubit globally
coupled to a many-body system characterized by short-range interactions. We
employ a dynamic finite-size scaling framework to investigate the
out-of-equilibrium dynamics arising from the sudden variation (turning on) of
the interaction between the qubit and the many-body system, in particular when
the latter is in proximity of a quantum first-order or continuous phase
transition. Although the approach is quite general, we consider d-dimensional
quantum Ising spin models in the presence of transverse and longitudinal
fields, as paradigmatic quantum many-body systems. To characterize the
out-of-equilibrium dynamics, we focus on a number of quantum-information
oriented properties of the model. Namely, we concentrate on the decoherence
features of the qubit, the energy interchanges among the qubit and the
many-body system during the out-of-equilibrium dynamics, and the work
distribution associated with the quench. The scaling behaviors predicted by the
dynamic finite-size scaling theory are verified through extensive numerical
computations for the one-dimensional Ising model, which reveal a fast
convergence to the expected asymptotic behavior with increasing the system
size.Comment: 16 pages, 9 figure
Uncertainty and sensitivity analysis of functional risk curves based on Gaussian processes
A functional risk curve gives the probability of an undesirable event as a
function of the value of a critical parameter of a considered physical system.
In several applicative situations, this curve is built using phenomenological
numerical models which simulate complex physical phenomena. To avoid cpu-time
expensive numerical models, we propose to use Gaussian process regression to
build functional risk curves. An algorithm is given to provide confidence
bounds due to this approximation. Two methods of global sensitivity analysis of
the models' random input parameters on the functional risk curve are also
studied. In particular, the PLI sensitivity indices allow to understand the
effect of misjudgment on the input parameters' probability density functions
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