3,111 research outputs found
Integral representations combining ladders and crossed-ladders
We use the worldline formalism to derive integral representations for three
classes of amplitudes in scalar field theory: (i) the scalar propagator
exchanging N momenta with a scalar background field (ii) the "half-ladder" with
N rungs in x - space (iii) the four-point ladder with N rungs in x - space as
well as in (off-shell) momentum space. In each case we give a compact
expression combining the N! Feynman diagrams contributing to the amplitude. As
our main application, we reconsider the well-known case of two massive scalars
interacting through the exchange of a massless scalar. Applying asymptotic
estimates and a saddle-point approximation to the N-rung ladder plus crossed
ladder diagrams, we derive a semi-analytic approximation formula for the lowest
bound state mass in this model.Comment: 39 pages, 10 pdf figure
Double modelling of the dynamic of activities in rural municipalities.
Land use choices and activity prevalence in a selected territory are determined by individual preferences constrained by the characteristic of the analysed zone: population density, soil properties, urbanization level and other similar factors can drive individuals to make different kind of decisions about their occupations. Different approaches can be used to describe land use change, occupation prevalence and their reciprocal inter-relation. In this paper we describe two different kinds of approaches: an agent based model, centred on individual choices and an aggregated model describing the evolution of activity prevalence in terms of coupled differential equation. We use and we compare the two models to analyse the effect of territorial constraints, like the lack of employment in determined sectors, on the possible activity prevalence scenarios.SBIAgro 2009
Symbolic Algorithms for Language Equivalence and Kleene Algebra with Tests
We first propose algorithms for checking language equivalence of finite
automata over a large alphabet. We use symbolic automata, where the transition
function is compactly represented using a (multi-terminal) binary decision
diagrams (BDD). The key idea consists in computing a bisimulation by exploring
reachable pairs symbolically, so as to avoid redundancies. This idea can be
combined with already existing optimisations, and we show in particular a nice
integration with the disjoint sets forest data-structure from Hopcroft and
Karp's standard algorithm. Then we consider Kleene algebra with tests (KAT), an
algebraic theory that can be used for verification in various domains ranging
from compiler optimisation to network programming analysis. This theory is
decidable by reduction to language equivalence of automata on guarded strings,
a particular kind of automata that have exponentially large alphabets. We
propose several methods allowing to construct symbolic automata out of KAT
expressions, based either on Brzozowski's derivatives or standard automata
constructions. All in all, this results in efficient algorithms for deciding
equivalence of KAT expressions
On the decay law for unstable open systems
We use (nonconservative) dynamical semigroups to investigate the decay law of
a quantum unstable system weakly coupled with a large environment. We find that
the deviations from the classical exponential law are small and can be safely
ignored in any actual experiment.Comment: 12 pages, plain-TeX, to appear in Phys. Lett.
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