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Traditionally, population models distinguish individuals on the basis of their current state. Given a distribution, a discrete time model then specifies (precisely in deterministic models, probabilistically in stochastic models) the population distribution at the next time point. The renewal equation alternative concentrates on newborn individuals and the model specifies the production of offspring as a function of age. This has two advantages: (i) as a rule, there are far fewer birth states than individual states in general, so the dimension is often low; (ii) it relates seamlessly to the next-generation matrix and the basic reproduction number. Here we start from the renewal equation for the births and use results of Feller and Thieme to characterise the asymptotic large time behaviour. Next we explicitly elaborate the relationship between the two bookkeeping schemes. This allows us to transfer the characterisation of the large time behaviour to traditional structured-population models.

The class of deterministic 'Daphnia' models treated by Diekmann et al. (J Math Biol 61: 277-318, 2010) has a long history going back to Nisbet and Gurney (Theor Pop Biol 23: 114-135, 1983) and Diekmann et al. (Nieuw Archief voor Wiskunde 4: 82-109, 1984). In this note, we formulate the individual based models (IBM) supposedly underlying those deterministic models. The models treat the interaction between a general size-structured consumer population ('Daphnia') and an unstructured resource ('algae'). The discrete, size and age-structured Daphnia population changes through births and deaths of its individuals and throught their aging and growth. The birth and death rates depend on the sizes of the individuals and on the concentration of the algae. The latter is supposed to be a continuous variable with a deterministic dynamics that depends on the Daphnia population. In this model setting we prove that when the Daphnia population is large, the stochastic differential equation describing the IBM can be approximated by the delay equation featured in (Diekmann et al., l.c.).

We consider a continuous time stochastic individual based model for a population structured only by an inherited vector trait and with logistic interactions. We consider its limit in a context from adaptive dynamics: the population is large, the mutations are rare and we view the process in the timescale of mutations. Using averaging techniques due to Kurtz (1992), we give a new proof of the convergence of the individual based model to the trait substitution sequence of Metz et al. (1992) first worked out by Dieckman and Law (1996) and rigorously proved by Champagnat (2006): rigging the model such that "invasion implies substitution", we obtain in the limit a process that jumps from one population equilibrium to another when mutations occur and invade the population., Comment: 23 pages

Adaptive dynamics so far has been put on a rigorous footing only for clonal inheritance. We extend this to sexually reproducing diploids, although admittedly still under the restriction of an unstructured population with Lotka-Volterra-like dynamics and single locus genetics (as in Kimura's 1965 infinite allele model). We prove under the usual smoothness assumptions, starting from a stochastic birth and death process model, that, when advantageous mutations are rare and mutational steps are not too large, the population behaves on the mutational time scale (the 'long' time scale of the literature on the genetical foundations of ESS theory) as a jump process moving between homozygous states (the trait substitution sequence of the adaptive dynamics literature). Essential technical ingredients are a rigorous estimate for the probability of invasion in a dynamic diploid population, a rigorous, geometric singular perturbation theory based, invasion implies substitution theorem, and the use of the Skorohod $M_1$ topology to arrive at a functional convergence result. In the small mutational steps limit this process in turn gives rise to a differential equation in allele or in phenotype space of a type referred to in the adaptive dynamics literature as 'canonical equation'.

We experimentally investigate the collapse dynamics of dipolar Bose- Einstein condensates of chromium atoms in different harmonic trap geometries, from prolate to oblate. The evolutions of the condensates in the unstable regime are compared to three-dimensional simulations of the Gross-Pitaevskii equation including three-body losses. In order to probe the phase coherence of collapsed condensates, we induce the collapse in several condensates simultaneously and let them interfere.

We report on experiments exploring the physics of dipolar quantum gases using a Chromium Bose-Einstein condensate (BEC). By means of a Feshbach resonance, it is possible to reduce the effects of short range interactions and reach a regime where the physics is governed by the long-range, anisotropic dipole-dipole interaction between the large ($6 \mu_{\rm B}$) magnetic moments of Chromium atoms. Several dramatic effects of the dipolar interaction are observed: the usual inversion of ellipticity of the condensate during time-of flight is inhibited, the stability of the dipolar gas depends strongly on the trap geometry, and the explosion following the collapse of an unstable dipolar condensate displays d-wave like features., Comment: To appear in "ATOMIC PHYSICS 21", proceedings of the XXI International Conference on Atomic Physics (ICAP 2008)

We report on the experimental observation of the dipolar collapse of a quantum gas which sets in when we reduce the contact interaction below some critical value using a Feshbach resonance. Due to the anisotropy of the dipole-dipole interaction, the stability of a dipolar Bose-Einstein condensate depends not only on the strength of the contact interaction, but also on the trapping geometry. We investigate the stability diagram and find good agreement with a universal stability threshold arising from a simple theoretical model. Using a pancake-shaped trap with the dipoles oriented along the short axis of the trap, we are able to tune the scattering length to zero, stabilizing a purely dipolar quantum gas., Comment: 5 pages, 1 table, 3 figures

Many promising schemes for quantum information processing (QIP) rely on few-photon interference effects. In these proposals, the photons are treated as being indistinguishable particles. However, single photon sources are typically subject to variation from device to device. Thus the photons emitted from different sources will not be perfectly identical, and there will be some variation in their frequencies. Here, we analyse the effect of this frequency mismatch on QIP schemes. As examples, we consider the distributed QIP protocol proposed by Barrett and Kok, and Hong-Ou-Mandel interference which lies at the heart of many linear optical schemes for quantum computing. In the distributed QIP protocol, we find that the fidelity of entangled qubit states depends crucially on the time resolution of single photon detectors. In particular, there is no reduction in the fidelity when an ideal detector model is assumed, while reduced fidelities may be encountered when using realistic detectors with a finite response time. We obtain similar results in the case of Hong-Ou-Mandel interference -- with perfect detectors, a modified version of quantum interference is seen, and the visibility of the interference pattern is reduced as the detector time resolution is reduced. Our findings indicate that problems due to frequency mismatch can be overcome, provided sufficiently fast detectors are available., Comment: 14 pages, 8 figures. Comments welcome. v2: Minor changes. v3: Cleaned up 3 formatting errors

We experimentally investigated the decay behavior with time t of resonances near and at exceptional points, where two complex eigenvalues and also the associated eigenfunctions coalesce. The measurements were performed with a dissipative microwave billiard, whose shape depends on two parameters. The t^2-dependence predicted at the exceptional point on the basis of a two-state matrix model could be verified. Outside the exceptional point the predicted Rabi oscillations, also called quantum echoes in this context, were detected. To our knowledge this is the first time that quantum echoes related to exceptional points were observed experimentally., Comment: 10 pages, 3 figures

We report on recent developments in the integration of optical microresonators into atom chips and describe some fabrication and implementation challenges. We also review theoretical proposals for quantum computing with single atoms based on the observation of photons leaking through the cavity mirrors. The use of measurements to generate entanglement can result in simpler, more robust and scalable quantum computing architectures. Indeed, we show that quantum computing with atom-cavity systems is feasible even in the presence of relatively large spontaneous decay rates and finite photon detector efficiencies., Comment: 14 pages, 6 figures

We have analyzed Chandra archival observations of the Antennae galaxies to study the distribution and physical properties of its hot interstellar gas. Eleven distinct diffuse X-ray emission regions are selected according to their underlying interstellar structures and star formation activity. The X-ray spectra of these regions are used to determine their thermal energy contents and cooling timescales. Young star clusters in these regions are also identified and their photometric measurements are compared to evolutionary stellar population synthesis models to assess their masses and ages. The cluster properties are then used to determine the stellar wind and supernova energies injected into the ISM. Comparisons between the thermal energy in the hot ISM and the expected stellar energy input show that young star clusters are sufficient to power the X-ray-emitting gas in some, but not all, active star formation regions. Super-star clusters, with masses >= 1x10^5 M_sol, heat the ISM, but the yield of hot interstellar gas is not directly proportional to the cluster mass. Finally, there exist diffuse X-ray emission regions which do not show active star formation or massive young star clusters. These regions may be powered by field stars or low-mass clusters formed within the last ~100 Myr., Comment: 36 pages, 6 figures, 8 tables, 2 appendices, to appear in the Astrophysical Journal, April 20 issue