19,743 research outputs found
Quasi-phase-matching of high-order-harmonic generation using multimode polarization beating
The generalization of quasi-phase-matching using polarization beating and of
multimode quasi-phase-matching (MMQPM) for the generation of high-order
harmonics is explored, and a method for achieving polarization beating is
proposed. If two (and in principle more) modes of a waveguide are excited,
modulation of the intensity, phase, and/or polarization of the guided radiation
will be achieved. By appropriately matching the period of this modulation to
the coherence length, quasi-phase-matching of high-order-harmonic radiation
generated by the guided wave can occur. We show that it is possible to achieve
efficiencies with multimode quasi-phase-matching greater than the ideal square
wave modulation. We present a Fourier treatment of QPM and use this to show
that phase modulation, rather than amplitude modulation, plays the dominant
role in the case of MMQPM. The experimental parameters and optimal conditions
for this scheme are explored
The \Phi^4 quantum field in a scale invariant random metric
We discuss a D-dimensional Euclidean scalar field interacting with a scale
invariant quantized metric. We assume that the metric depends on d-dimensional
coordinates where d<D. We show that the interacting quantum fields have more
regular short distance behaviour than the free fields. A model of a Gaussian
metric is discussed in detail. In particular, in the \Phi^4 theory in four
dimensions we obtain explicit lower and upper bounds for each term of the
perturbation series. It turns out that there is no coupling constant
renormalization in the \Phi^4 model in four dimensions. We show that in a
particular range of the scale dimension there are models in D=4 without any
divergencies
Markov quantum fields on a manifold
We study scalar quantum field theory on a compact manifold. The free theory
is defined in terms of functional integrals. For positive mass it is shown to
have the Markov property in the sense of Nelson. This property is used to
establish a reflection positivity result when the manifold has a reflection
symmetry. In dimension d=2 we use the Markov property to establish a sewing
operation for manifolds with boundary circles. Also in d=2 the Markov property
is proved for interacting fields.Comment: 14 pages, 1 figure, Late
Differential equation approximations of stochastic network processes: an operator semigroup approach
The rigorous linking of exact stochastic models to mean-field approximations
is studied. Starting from the differential equation point of view the
stochastic model is identified by its Kolmogorov equations, which is a system
of linear ODEs that depends on the state space size () and can be written as
. Our results rely on the convergence of the transition
matrices to an operator . This convergence also implies that the
solutions converge to the solution of . The limiting ODE
can be easily used to derive simpler mean-field-type models such that the
moments of the stochastic process will converge uniformly to the solution of
appropriately chosen mean-field equations. A bi-product of this method is the
proof that the rate of convergence is . In addition, it turns
out that the proof holds for cases that are slightly more general than the
usual density dependent one. Moreover, for Markov chains where the transition
rates satisfy some sign conditions, a new approach for proving convergence to
the mean-field limit is proposed. The starting point in this case is the
derivation of a countable system of ordinary differential equations for all the
moments. This is followed by the proof of a perturbation theorem for this
infinite system, which in turn leads to an estimate for the difference between
the moments and the corresponding quantities derived from the solution of the
mean-field ODE
Learning from openness : the dynamics of breadth in external innovation linkages
We explore how openness in terms of external linkages generates learning effects, which enable firms to generate more innovation outputs from any given breadth of external linkages. Openness to external knowledge sources, whether through search activity or linkages to external partners in new product development, involves a process of interaction and information processing. Such activities are likely to be subject to a learning process, as firms learn which knowledge sources and collaborative linkages are most useful to their particular needs, and which partnerships are most effective in delivering innovation performance. Using panel data from Irish manufacturing plants, we find evidence of such learning effects: establishments with substantial experience of external collaborations in previous periods derive more innovation output from openness in the current period
Solving topological defects via fusion
Integrable defects in two-dimensional integrable models are purely
transmitting thus topological. By fusing them to integrable boundaries new
integrable boundary conditions can be generated, and, from the comparison of
the two solved boundary theories, explicit solutions of defect models can be
extracted. This idea is used to determine the transmission factors and defect
energies of topological defects in sinh-Gordon and Lee-Yang models. The
transmission factors are checked in Lagrangian perturbation theory in the
sinh-Gordon case, while the defect energies are checked against defect
thermodynamic Bethe ansatz equations derived to describe the ground-state
energy of diagonal defect systems on a cylinder. Defect bootstrap equations are
also analyzed and are closed by determining the spectrum of defect bound-states
in the Lee-Yang model.Comment: LaTeX, 24 pages, 34 eps figure
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