Retrieval of interatomic separations of molecules from laser-induced high-order harmonic spectra

We illustrate an iterative method for retrieving the internuclear separations of N$_2$, O$_2$ and CO$_2$ molecules using the high-order harmonics generated from these molecules by intense infrared laser pulses. We show that accurate results can be retrieved with a small set of harmonics and with one or few alignment angles of the molecules. For linear molecules the internuclear separations can also be retrieved from harmonics generated using isotropically distributed molecules. By extracting the transition dipole moment from the high-order harmonic spectra, we further demonstrated that it is preferable to retrieve the interatomic separation iteratively by fitting the extracted dipole moment. Our results show that time-resolved chemical imaging of molecules using infrared laser pulses with femtosecond temporal resolutions is possible.Comment: 14 pages, 9 figure

Theoretical analysis of dynamic chemical imaging with lasers using high-order harmonic generation

We report theoretical investigations of the tomographic procedure suggested by Itatani {\it et al.} [Nature, {\bf 432} 867 (2004)] for reconstructing highest occupied molecular orbitals (HOMO) using high-order harmonic generation (HHG). Using the limited range of harmonics from the plateau region, we found that under the most favorable assumptions, it is still very difficult to obtain accurate HOMO wavefunction, but the symmetry of the HOMO and the internuclear separation between the atoms can be accurately extracted, especially when lasers of longer wavelengths are used to generate the HHG. We also considered the possible removal or relaxation of the approximations used in the tomographic method in actual applications. We suggest that for chemical imaging, in the future it is better to use an iterative method to locate the positions of atoms in the molecule such that the resulting HHG best fits the macroscopic HHG data, rather than by the tomographic method.Comment: 13 pages, 14 figure

General equilibrium in asset markets with or without short-selling

Equilibrium Theory;Assets

Arbitrage and Equilibrium in Economies with Externalities.

We introduce consumption externalities into a general equilibrium model with arbitrary consumption sets. To treat the problem of existence of equilibrium, a condition of no unbounded arbitrage, extending the condition of Page (1987) and Page and Wooders (1993, 1996) is defined. It is proven that this condition is sufficient for the existence of an equilibrium and both necessary and sufficient for compactness of the set of rational allocations.CONSUMPTION ; EXTERNALITIES ; ARBITRAGE

Low-temperature dynamics of the Curie-Weiss Model: Periodic orbits, multiple histories, and loss of Gibbsianness

We consider the Curie-Weiss model at a given initial temperature in vanishing external field evolving under a Glauber spin-flip dynamics corresponding to a possibly different temperature. We study the limiting conditional probabilities and their continuity properties and discuss their set of points of discontinuity (bad points). We provide a complete analysis of the transition between Gibbsian and non-Gibbsian behavior as a function of time, extending earlier work for the case of independent spin-flip dynamics. For initial temperature bigger than one we prove that the time-evolved measure stays Gibbs forever, for any (possibly low) temperature of the dynamics. In the regime of heating to low-temperatures from even lower temperatures, when the initial temperature is smaller than the temperature of the dynamics, and smaller than 1, we prove that the time-evolved measure is Gibbs initially and becomes non-Gibbs after a sharp transition time. We find this regime is further divided into a region where only symmetric bad configurations exist, and a region where this symmetry is broken. In the regime of further cooling from low-temperatures there is always symmetry-breaking in the set of bad configurations. These bad configurations are created by a new mechanism which is related to the occurrence of periodic orbits for the vector field which describes the dynamics of Euler-Lagrange equations for the path large deviation functional for the order parameter. To our knowledge this is the first example of the rigorous study of non-Gibbsian phenomena related to cooling, albeit in a mean-field setup.Comment: 31 pages, 24 figure

Development and selection of operational management strategies to achieve policy objectives

Since the reform of the EU Common Fisheries Policy in 2002, effort has been devoted to addressing the governance, scientific, social and economic issues required to introduce an ecosystem approach to fisheries management (EAFM) in Europe. Fisheries management needs to support the three pillars of sustainability (ecological, social and economic) and Fisheries Ecosystem Plans (FEPs) have been developed as a tool to assist managers considering the ecological, social and economic implications of their decision. Building upon previous studies (e.g. the FP5-funded European Fisheries Ecosystem Plan project), the core concept of the Making the European Fisheries Ecosystem Plan Operational (MEFEPO) project is to deliver operational frameworks (FEPs) for three regional seas. The project focus is on how best to make current institutional frameworks responsive to an EAFM at regional and pan-European levels in accordance with the principles of good governance. The regional seas selected for the project are the North Sea (NS), North Western Waters (NWW) and South Western Waters (SWW) RAC regions. The aim of this work package (WP5) was to develop operational objectives to achieve the ecological objectives identified for the 3 regional seas in WP2. This report describes the development and implementation of a transparent and formal process that should lead to identification of the “best” operational management strategies for an EAFM, based on sound scientific information and stakeholder involvement (e.g. regional industry groups, citizen groups, managers and other interest groups)

Absence of Dobrushin states for 2d2d long-range Ising models

We consider the two-dimensional Ising model with long-range pair interactions of the form $J_{xy}\sim|x-y|^{-\alpha}$ with $\alpha>2$, mostly when $J_{xy} \geq 0$. We show that Dobrushin states (i.e. extremal non-translation-invariant Gibbs states selected by mixed $\pm$-boundary conditions) do not exist. We discuss possible extensions of this result in the direction of the Aizenman-Higuchi theorem, or concerning fluctuations of interfaces. We also mention the existence of rigid interfaces in two long-range anisotropic contexts.Comment: revised versio

Gibbs-non-Gibbs transitions via large deviations: computable examples

We give new and explicitly computable examples of Gibbs-non-Gibbs transitions of mean-field type, using the large deviation approach introduced in [4]. These examples include Brownian motion with small variance and related diffusion processes, such as the Ornstein-Uhlenbeck process, as well as birth and death processes. We show for a large class of initial measures and diffusive dynamics both short-time conservation of Gibbsianness and dynamical Gibbs-non-Gibbs transitions

Entropic repulsion and lack of the gg-measure property for Dyson models

We consider Dyson models, Ising models with slow polynomial decay, at low temperature and show that its Gibbs measures deep in the phase transition region are not $g$-measures. The main ingredient in the proof is the occurrence of an entropic repulsion effect, which follows from the mesoscopic stability of a (single-point) interface for these long-range models in the phase transition region.Comment: 22 pages, 4 figure

Variational description of Gibbs-non-Gibbs dynamical transitions for the Curie-Weiss model

We perform a detailed study of Gibbs-non-Gibbs transitions for the Curie-Weiss model subject to independent spin-flip dynamics ("infinite-temperature" dynamics). We show that, in this setup, the program outlined in van Enter, Fern\'andez, den Hollander and Redig can be fully completed, namely that Gibbs-non-Gibbs transitions are equivalent to bifurcations in the set of global minima of the large-deviation rate function for the trajectories of the magnetization conditioned on their endpoint. As a consequence, we show that the time-evolved model is non-Gibbs if and only if this set is not a singleton for some value of the final magnetization. A detailed description of the possible scenarios of bifurcation is given, leading to a full characterization of passages from Gibbs to non-Gibbs -and vice versa- with sharp transition times (under the dynamics Gibbsianness can be lost and can be recovered). Our analysis expands the work of Ermolaev and Kulske who considered zero magnetic field and finite-temperature spin-flip dynamics. We consider both zero and non-zero magnetic field but restricted to infinite-temperature spin-flip dynamics. Our results reveal an interesting dependence on the interaction parameters, including the presence of forbidden regions for the optimal trajectories and the possible occurrence of overshoots and undershoots in the optimal trajectories. The numerical plots provided are obtained with the help of MATHEMATICA.Comment: Key words and phrases: Curie-Weiss model, spin-flip dynamics, Gibbs vs. non-Gibbs, dynamical transition, large deviations, action integral, bifurcation of rate functio