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ESA's mission Euclid, while undertaking its final integration stage, is fully qualified. Euclid will perform an extragalactic survey ($0

In this paper, we seek optimal solutions for a transfer from a parking orbit around the Moon to a halo orbit around $L_2$ of the Earth-Moon system, by applying a single maneuver and exploiting the stable invariant manifold of the hyperbolic parking solution at arrival. For that, we propose an optimization problem considering as variables both the orbital characteristics of a parking solution around the Moon, (namely, its Keplerian elements) and the characteristics of a transfer trajectory guided by the stable manifold of the arrival Halo orbit. The problem is solved by a nonlinear programming method (NLP), aiming to minimize the cost of $\Delta V$ to perform a single maneuver transfer, within the framework of the Earth-Moon system of the circular restricted three-body problem. Results with low $\Delta V$ and suitable time of flight show the feasibility of this kind of transfer for a Cubesat.

In this article we introduce an entropy-based, scale-dependent centrality that is evaluated as the Shannon entropy of the distribution at time t of a continuous-time random walk. It ranks nodes as a function of the time t, which acts as a parameter and defines the scale of the network. It is able capture well-known centralities such as degree, eigenvector and closeness depending on the range of t. We compare it with the broad class of total $f$-communicability centralities, of which both Katz centrality and total communicability are particular cases., Comment: 10 pages, 10 figures

The mechanism behind the high throughput rate in K$^{+}$ channels is still an open problem. Recent simulations have shown that the passage of potassium through the K$^{+}$ channel core, the so-called selectivity filter (SF), is water-free against models where the strength of Coulomb repulsion freezes ions conduction. It has been suggested that quantum coherent hopping might be relevant in mediating ion conduction. Within the quantum approach and the hypothesis of desolvated ions along the pathway, we start with a number of particles in a source to see how they go across the SF modeled by a linear chain of sites to be collected in a drain. As a main result we show that there is a threshold SF occupancy is three ions on average, which is in agreement with recent classical model simulations., Comment: 11 pages, 4 figures

One of the defining representations of women from medieval times is in the role of peace-weaver, that is, a woman was expected to 'weave' peace between warring men. The underlying assumption in scholarship on this topic is that female mediation lessens male violence. This stance can however be questioned since it may be the result of gender-based peace and diplomacy models that relegate women's roles to that of conduits between men. By analyzing the concept of communicability and relevance of certain nodes in complex networks we show how our sources afford women more complex and nuanced social roles. As a case study we consider a historical narrative, namely Bede's "Ecclesiastical History of the English People", which is a history of Britain from the first to eighth centuries AD and was immensely popular all over Europe in the Middle Ages., Comment: 14 pages, 5 figures, 2 tables

Assuming that the selectivity filter of KcsA potassium ion channel may exhibit quantum coherence, we extend a previous model by Vaziri and Plenio (2010) to take into account Coulomb repulsion between potassium ions. We show that typical ion transit timescales are determined by this interaction, which imposes optimal input/output parameter ranges. Also, as observed in other examples of quantum tunneling in biological systems, addition of moderate noise helps coherent ion transport., Comment: 12 pages, 10 figures

We numerically show fractal Weyl law behavior in an open Hamiltonian system that is described by a smooth potential and which supports numerous above-barrier resonances. This behavior holds even relatively far away from the classical limit. The complex resonance wave functions are found to be localized on the fractal classical repeller., Comment: 4 pages, 3 figures. to appear in Phys Rev E

We demonstrate the existence of superscarring in the LiNC=LiCN isomerization reaction described by a realistic potential interaction in the range of readily attainable experimental energies. This phenomenon arises as the effect of two periodic orbits appearing "out of the blue"in a saddle--node bifurcation taking place in the dynamics of the system. Potential practical consequences of this superlocalization in the corresponding wave functions are also considered., Comment: 6 pages, 5 figures. to appear in EPL

We study fluctuations of the Wigner time delay for open (scattering) systems which exhibit mixed dynamics in the classical limit. It is shown that in the semiclassical limit the time delay fluctuations have a distribution that differs markedly from those which describe fully chaotic (or strongly disordered) systems: their moments have a power law dependence on a semiclassical parameter, with exponents that are rational fractions. These exponents are obtained from bifurcating periodic orbits trapped in the system. They are universal in situations where sufficiently long orbits contribute. We illustrate the influence of bifurcations on the time delay numerically using an open quantum map., Comment: 9 pages, 3 figures, contribution to QMC2006

We study the resonance (or Gamow) eigenstates of open chaotic systems in the semiclassical limit, distinguishing between left and right eigenstates of the non-unitary quantum propagator, and also between short-lived and long-lived states. The long-lived left (right) eigenstates are shown to concentrate as $\hbar\to 0$ on the forward (backward) trapped set of the classical dynamics. The limit of a sequence of eigenstates $\{\psi(\hbar)\}_{\hbar\to 0}$ is found to exhibit a remarkably rich structure in phase space that depends on the corresponding limiting decay rate. These results are illustrated for the open baker map, for which the probability density in position space is observed to have self-similarity properties., Comment: 4 pages, 4 figures; some minor corrections, some changes in presentation

We investigate phase coherent ballistic transport through antidot lattices in the generic case where the classical phase space has both regular and chaotic components. It is shown that the conductivity fluctuations have a non-Gaussian distribution, and that their moments have a power-law dependence on a semiclassical parameter, with fractional exponents. These exponents are obtained from bifurcating periodic orbits in the semiclassical approximation. They are universal in situations where sufficiently long orbits contribute., Comment: 7 pages

We argue here for a more conceptual or qualitative approach in the introductory teaching of Quantum Physics which is built on the basis of epistemological and ontological discussions and as such is a valuable tool mainly in the initial and continued formation of school teachers. We illustrate our point with the analysis of undulatory and corpuscular phenomena of a single photon in a virtual Mach-Zehnder Interferometer - an experimental setup similar to double slits device but simpler - using key ideas of the most known interpretations of quantum formalism, including the many worlds interpretation., Comment: 5 pages, 2 figures. Submitted to American Journal of Physics

The stability of photon trajectories in models of the Universe that have constant spatial curvature is determined by the sign of the curvature: they are exponentially unstable if the curvature is negative and stable if it is positive or zero. We demonstrate that random fluctuations in the curvature provide an additional stabilizing mechanism. This mechanism is analogous to the one responsible for stabilizing the stochastic Kapitsa pendulum. When the mean curvature is negative it is capable of stabilizing the photon trajectories; when the mean curvature is zero or positive it determines the characteristic frequency with which neighbouring trajectories oscillate about each other. In constant negative curvature models of the Universe that have compact topology, exponential instability implies chaos (e.g. mixing) in the photon dynamics. We discuss some consequences of stochastic stabilization in this context., Comment: 4 pages, 3 postscript figures in color which are also appropriate for black and white printers; v2 emphasizes relevance to flat as well as negatively curved cosmologies; to appear in J. Phys. A

It was recently shown (Keating & Prado, {\it Proc. R. Soc. Lond. A} {\bf 457}, 1855-1872 (2001)) that, in the semiclassical limit, the scarring of quantum eigenfunctions by classical periodic orbits in chaotic systems may be dramatically enhanced when the orbits in question undergo bifurcation. Specifically, a bifurcating orbit gives rise to a scar with an amplitude that scales as $\hbar^{\alpha}$ and a width that scales as $\hbar^{\omega}$, where $\alpha$ and $\omega$ are bifurcation-dependent scar exponents whose values are typically smaller than those ($\alpha=\omega=1/2$) associated with isolated and unstable periodic orbits. We here analyze the influence of bifurcations on the autocorrelation function of quantum eigenstates, averaged with respect to energy. It is shown that the length-scale of the correlations around a bifurcating orbit scales semiclassically as $\hbar^{1-\alpha}$, where $\alpha$ is the corresponding scar amplitude exponent. This imprint of bifurcations on quantum autocorrelations is illustrated by numerical computations for a family of perturbed cat maps., Comment: 25 pages, 11 postscript figures. Some of the pictures are included in low resolution only. For a version with pictures in high resolution see http://www.physik.uni-ulm.de/theo/qc/

We extend the semiclassical theory of scarring of quantum eigenfunctions psi_{n}(q) by classical periodic orbits to include situations where these orbits undergo generic bifurcations. It is shown that |psi_{n}(q)|^{2}, averaged locally with respect to position q and the energy spectrum E_{n}, has structure around bifurcating periodic orbits with an amplitude and length-scale whose hbar-dependence is determined by the bifurcation in question. Specifically, the amplitude scales as hbar^{alpha} and the length-scale as hbar^{w}, and values of the scar exponents, alpha and w, are computed for a variety of generic bifurcations. In each case, the scars are semiclassically wider than those associated with isolated and unstable periodic orbits; moreover, their amplitude is at least as large, and in most cases larger. In this sense, bifurcations may be said to give rise to superscars. The competition between the contributions from different bifurcations to determine the moments of the averaged eigenfunction amplitude is analysed. We argue that there is a resulting universal hbar-scaling in the semiclassical asymptotics of these moments for irregular states in systems with a mixed phase-space dynamics. Finally, a number of these predictions are illustrated by numerical computations for a family of perturbed cat maps., Comment: 24 pages, 6 Postscript figures, corrected some typos