25,234 research outputs found
Product and other fine structure in polynomial resolutions of mapping spaces
Let Map_T(K,X) denote the mapping space of continuous based functions between
two based spaces K and X. If K is a fixed finite complex, Greg Arone has
recently given an explicit model for the Goodwillie tower of the functor
sending a space X to the suspension spectrum \Sigma^\infty Map_T(K,X). Applying
a generalized homology theory h_* to this tower yields a spectral sequence, and
this will converge strongly to h_*(Map_T(K,X)) under suitable conditions, e.g.
if h_* is connective and X is at least dim K connected. Even when the
convergence is more problematic, it appears the spectral sequence can still
shed considerable light on h_*(Map_T(K,X)). Similar comments hold when a
cohomology theory is applied. In this paper we study how various important
natural constructions on mapping spaces induce extra structure on the towers.
This leads to useful interesting additional structure in the associated
spectral sequences. For example, the diagonal on Map_T(K,X) induces a
`diagonal' on the associated tower. After applying any cohomology theory with
products h^*, the resulting spectral sequence is then a spectral sequence of
differential graded algebras. The product on the E_\infty -term corresponds to
the cup product in h^*(Map_T(K,X)) in the usual way, and the product on the
E_1-term is described in terms of group theoretic transfers. We use explicit
equivariant S-duality maps to show that, when K is the sphere S^n, our
constructions at the fiber level have descriptions in terms of the
Boardman-Vogt little n-cubes spaces. We are then able to identify, in a
computationally useful way, the Goodwillie tower of the functor from spectra to
spectra sending a spectrum X to \Sigma ^\infty \Omega ^\infty X.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-28.abs.htm
Nonlinear optical response of hole-trion systems in quantum dots in tilted magnetic fields
We discuss, from a theoretical point of view, the four wave mixing
spectroscopy on an ensemble of p-doped quantum dots in a magnetic field
slightly tilted from the in-plane configuration. We describe the system
evolution in the density matrix formalism. In the limit of coherent ultrafast
optical driving, we obtain analytical formulas for the single system dynamics
and for the response of an inhomogeneously broadened ensemble. The results are
compared to the previously studied time-resolved Kerr rotation spectroscopy on
the same system. We show that the Kerr rotation and four wave mixing spectra
yield complementary information on the spin dynamics (precession and damping).Comment: 4 pages, 2 figures, conference NOEKS1
Axial Contributions at the Top Threshold
We calculate the contributions of the axial current to top quark pair
production in e+ e- annihilation at threshold. The QCD dynamics is taken into
account by solving the Lippmann-Schwinger equation for the P wave production
using the QCD potential up to two loops. We demonstrate that the dependence of
the total and differential cross section on the polarization of the e+ and e-
beams allows for an independent extraction of the axial current induced cross
section.Comment: LaTeX, 12 pages, including 5 Postscript figures using eps
Local Approximation Schemes for Ad Hoc and Sensor Networks
We present two local approaches that yield polynomial-time approximation schemes (PTAS) for the Maximum Independent Set and Minimum Dominating Set problem in unit disk graphs. The algorithms run locally in each node and compute a (1+ε)-approximation to the problems at hand for any given ε > 0. The time complexity of both algorithms is O(TMIS + log*! n/εO(1)), where TMIS is the time required to compute a maximal independent set in the graph, and n denotes the number of nodes. We then extend these results to a more general class of graphs in which the maximum number of pair-wise independent nodes in every r-neighborhood is at most polynomial in r. Such graphs of polynomially bounded growth are introduced as a more realistic model for wireless networks and they generalize existing models, such as unit disk graphs or coverage area graphs
Modelling, Estimation and Visualization of Multivariate Dependence for Risk Management
Dependence modelling and estimation is a key issue in the assessment of portfolio risk. When measuring extreme risk in terms of the Value-at-Risk, the multivariate normal model with linear correlation as its natural dependence measure is by no means an ideal model. We suggest a large class of models and a new dependence function which allows us to capture the complete extreme dependence structure of a portfolio. We also present a simple nonparametric estimation procedure. To show our new method at work we apply it to a financial data set of zero coupon swap rates and estimate the extreme dependence in the data
Dependence Estimation and Visualization in Multivariate Extremes with Applications to Financial Data
We investigate extreme dependence in a multivariate setting with special emphasis on financial applications. We introduce a new dependence function which allows us to capture the complete extreme dependence structure and present a nonparametric estimation procedure. The new dependence function is compared with existing measures including the spectral measure and other devices measuring extreme dependence. We also apply our method to a financial data set of zero coupon swap rates and estimate the extreme dependence in the data
Vacuum-Stimulated Raman Scattering based on Adiabatic Passage in a High-Finesse Optical Cavity
We report on the first observation of stimulated Raman scattering from a
Lambda-type three-level atom, where the stimulation is realized by the vacuum
field of a high-finesse optical cavity. The scheme produces one intracavity
photon by means of an adiabatic passage technique based on a counter-intuitive
interaction sequence between pump laser and cavity field. This photon leaves
the cavity through the less-reflecting mirror. The emission rate shows a
characteristic dependence on the cavity and pump detuning, and the observed
spectra have a sub-natural linewidth. The results are in excellent agreement
with numerical simulations.Comment: 4 pages, 5 figure
Kinetic Monte Carlo simulations of oscillatory shape evolution for electromigration-driven islands
The shape evolution of two-dimensional islands under electromigration-driven
periphery diffusion is studied by kinetic Monte Carlo (KMC) simulations and
continuum theory. The energetics of the KMC model is adapted to the Cu(100)
surface, and the continuum model is matched to the KMC model by a suitably
parametrized choice of the orientation-dependent step stiffness and step atom
mobility. At 700 K shape oscillations predicted by continuum theory are
quantitatively verified by the KMC simulations, while at 500 K qualitative
differences between the two modeling approaches are found.Comment: 7 pages, 6 figure
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