The bisymplectomorphism group of a bounded symmetric domain

An Hermitian bounded symmetric domain in a complex vector space, given in its circled realization, is endowed with two natural symplectic forms: the flat form and the hyperbolic form. In a similar way, the ambient vector space is also endowed with two natural symplectic forms: the Fubini-Study form and the flat form. It has been shown in arXiv:math.DG/0603141 that there exists a diffeomorphism from the domain to the ambient vector space which puts in correspondence the above pair of forms. This phenomenon is called symplectic duality for Hermitian non compact symmetric spaces. In this article, we first give a different and simpler proof of this fact. Then, in order to measure the non uniqueness of this symplectic duality map, we determine the group of bisymplectomorphisms of a bounded symmetric domain, that is, the group of diffeomorphisms which preserve simultaneously the hyperbolic and the flat symplectic form. This group is the direct product of the compact Lie group of linear automorphisms with an infinite-dimensional Abelian group. This result appears as a kind of Schwarz lemma.Comment: 19 pages. Version 2: minor correction

Microdosimetry of diagnostic X-rays: applications of the variance-covariance method.

Microdosimetric measurements in beams of diagnostic X rays (between 30 and 125 kV) have been performed. In these pulsed radiation fields, microdosimetric measurements are possible only by application of the variance-covariance technique. The dose mean lineal energy, yD, is determined for various simulated diameters, at different depths in the absorber, and at different points within the pulse intervals. From the measured temporal dependences one can also obtain values of yD for different X-ray pulse generators. The results demonstrate the potential of the variance-covariance method for a diversity of microdosimetric measurements in radiation protection and in the quality control of radiation beams

Criteria of applicability for autoradiography of tritium

Autoradiography is an effective tool for the imaging of radionuclide distributions in various samples. In sophisticated applications with special preparation and development of sample-emulsion combinations and subsequent grain counts it can be highly quantitative, but it requires carefully controlled conditions and a variety of counter-checks, for example through scintillation spectroscopy. Less refined applications use X-ray films as detectors, and their seeming simplicity tends to invite artefacts and misinterpretations. Particular care needs to be taken, if one deals, or presumes to deal, with the low-energy ß-emitter tritium. Because of the short electron ranges the film must be in intimate contact with the sample, which tends to produce chemographic artefacts; without added spectroscopic measurements it is impossible to discriminate the spurious signals from a blackening of the film due to tritium. Recent statements concerning autoradiographic tritium measurements in tree samples have created considerable public concern and have demonstrated the pitfalls of uncritical use. This paper presents order-of-magnitude criteria for the detection threshold in the autoradiography of tritium; they can serve as an exclusion principle for some of the more extravagant misinterpretations. Dedication to Prof. Wolfgang Jacobi on the occasion of his 65th birthda

Are Expectations Formed by the Anchoring-and-adjustment Heuristic? – An Experimental Investigation

Previous experimental investigations have shown that expectations are not perfectly rational due to bias. Traditional adaptive models, however, in many cases do not perfectly describe the formation of expectations either. This paper makes two contributions to the experimental literature on the formation of expectations: First, we investigate whether subjects who have more information about the economic model than in previous studies also form biased expectations. Second, we argue that in some cases macroeconomic expectations might be formed by the anchoring-and-adjustment heuristic, which is well known in psychology. We find that subjects’ expectations are biased although the design might be more favorable to rational expectations.The anchoring- and-adjustment model of expectations gets some support by our data, but the best model encompasses both the anchoring-and-adjustment model and the traditional adaptive model.Expectations, heuristics, beliefs, mental models, macroeconomic experiment

As if or What? – Expectations and Optimization in a Simple Macroeconomic Environment

In this paper we report the results of a laboratory experiment, in which we observed the behavior of agents in a simple macroeconomic setting. The structure of the economy was only partially known to the players which is a realistic feature of our experiment. We investigate whether subjects manage to approach optimal behavior even if they lack important information. Furthermore, we analyze subjects’ perceptions of the model and whether their behavior is consistent with their perceptions. The full information model predicts changes of employment correctly, but not the level of employment. In the aggregate, subjects have correct perceptions, although individual perceptions are biased.We finally show that deviations from the full information solution are due to optimization failures than than misperceptions.Methodology, macroeconomic experiment, perceptions, optimization, expectations

A slowly rotating perfect fluid body in an ambient vacuum

A global model of a slowly rotating perfect fluid ball in general relativity is presented. To second order in the rotation parameter, the junction surface is an ellipsoidal cylinder. The interior is given by a limiting case of the Wahlquist solution, and the vacuum region is not asymptotically flat. The impossibility of joining an asymptotically flat vacuum region has been shown in a preceding work.Comment: 7 pages, published versio

Entanglement growth in quench dynamics with variable range interactions

Studying entanglement growth in quantum dynamics provides both insight into the underlying microscopic processes and information about the complexity of the quantum states, which is related to the efficiency of simulations on classical computers. Recently, experiments with trapped ions, polar molecules, and Rydberg excitations have provided new opportunities to observe dynamics with long-range interactions. We explore nonequilibrium coherent dynamics after a quantum quench in such systems, identifying qualitatively different behavior as the exponent of algebraically decaying spin-spin interactions in a transverse Ising chain is varied. Computing the build-up of bipartite entanglement as well as mutual information between distant spins, we identify linear growth of entanglement entropy corresponding to propagation of quasiparticles for shorter range interactions, with the maximum rate of growth occurring when the Hamiltonian parameters match those for the quantum phase transition. Counter-intuitively, the growth of bipartite entanglement for long-range interactions is only logarithmic for most regimes, i.e., substantially slower than for shorter range interactions. Experiments with trapped ions allow for the realization of this system with a tunable interaction range, and we show that the different phenomena are robust for finite system sizes and in the presence of noise. These results can act as a direct guide for the generation of large-scale entanglement in such experiments, towards a regime where the entanglement growth can render existing classical simulations inefficient.Comment: 17 pages, 7 figure