Statistics and Nos\'e formalism for Ehrenfest dynamics

Quantum dynamics (i.e., the Schr\"odinger equation) and classical dynamics (i.e., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. In this paper we first show that the hybrid quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for Ehrenfest dynamics. Then, the existence of a well defined Poisson bracket allows to arrive to a Liouville equation for a statistical ensemble of Ehrenfest systems. The study of a generic toy model shows that the evolution produced by Ehrenfest dynamics is ergodic and therefore the only constants of motion are functions of the Hamiltonian. The emergence of the canonical ensemble characterized by the Boltzmann distribution follows after an appropriate application of the principle of equal a priori probabilities to this case. Once we know the canonical distribution of a Ehrenfest system, it is straightforward to extend the formalism of Nos\'e (invented to do constant temperature Molecular Dynamics by a non-stochastic method) to our Ehrenfest formalism. This work also provides the basis for extending stochastic methods to Ehrenfest dynamics.Comment: 28 pages, 1 figure. Published version. arXiv admin note: substantial text overlap with arXiv:1010.149

Using step width to compare locomotor biomechanics between extinct, non-avian theropod dinosaurs and modern obligate bipeds

How extinct, non-avian theropod dinosaurs locomoted is a subject of considerable interest, as is the manner in which it evolved on the line leading to birds. Fossil footprints provide the most direct evidence for answering these questions. In this study, step width—the mediolateral (transverse) distance between successive footfalls—was investigated with respect to speed (stride length) in non-avian theropod trackways of Late Triassic age. Comparable kinematic data were also collected for humans and 11 species of ground-dwelling birds. Permutation tests of the slope on a plot of step width against stride length showed that step width decreased continuously with increasing speed in the extinct theropods (p < 0.001), as well as the five tallest bird species studied (p < 0.01). Humans, by contrast, showed an abrupt decrease in step width at the walk–run transition. In the modern bipeds, these patterns reflect the use of either a discontinuous locomotor repertoire, characterized by distinct gaits (humans), or a continuous locomotor repertoire, where walking smoothly transitions into running (birds). The non-avian theropods are consequently inferred to have had a continuous locomotor repertoire, possibly including grounded running. Thus, features that characterize avian terrestrial locomotion had begun to evolve early in theropod history

Fast and simple assessment of surface contamination in operations involving nanomaterials

The deposition of airborne nanosized matter onto surfaces could pose a potential risk in occupational and environmental scenarios. The incorporation of fluorescent labels, namely fluorescein isotiocyanate (FITC) or tris-1, 3-phenanthroline ruthenium (II) chloride (Ru(phen)3Cl2), into spherical 80-nm silica nanoparticles allowed the detection after the illumination with LED light of suitable wavelength (365 or 405 nm respectively). Monodisperse nanoparticle aerosols from fluorescently labeled nanoparticles were produced under safe conditions using powder generators and the deposition was tested into different surfaces and filtering media. The contamination of gloves and work surfaces that was demonstrated by sampling and SEM analysis becomes immediately clear under laser or LED illumination. Furthermore, nanoparticle aerosols of about 105 nanoparticles/cm3 were alternatively fed through a glass pipe and personal protective masks to identify the presence of trapped nanoparticles under 405 nm or 365 nm LED light. This testing procedure allowed a fast and reliable estimation of the contamination of surfaces with nanosized matter, with a limit of detection based on the fluorescence emission of the accumulated solid nanoparticles of 40 ng of Ru(phen)3@SiO2 of silica per mg of non-fluorescent matter

Reduction Procedures in Classical and Quantum Mechanics

We present, in a pedagogical style, many instances of reduction procedures appearing in a variety of physical situations, both classical and quantum. We concentrate on the essential aspects of any reduction procedure, both in the algebraic and geometrical setting, elucidating the analogies and the differences between the classical and the quantum situations.Comment: AMS-LaTeX, 35 pages. Expanded version of the Invited review talk delivered by G. Marmo at XXIst International Workshop On Differential Geometric Methods In Theoretical Mechanics, Madrid (Spain), 2006. To appear in Int. J. Geom. Methods in Modern Physic

SSDSS IV MaNGA - Properties of AGN host galaxies

We present here the characterization of the main properties of a sample of 98 AGN host galaxies, both type-II and type-I, in comparison with those of about 2700 non-active galaxies observed by the MaNGA survey. We found that AGN hosts are morphologically early-type or early-spirals. For a given morphology AGN hosts are, in average, more massive, more compact, more central peaked and rather pressurethan rotational-supported systems. We confirm previous results indicating that AGN hosts are located in the intermediate/transition region between star-forming and non-star-forming galaxies (i.e., the so-called green valley), both in the ColorMagnitude and the star formation main sequence diagrams. Taking into account their relative distribution in terms of the stellar metallicity and oxygen gas abundance and a rough estimation of their molecular gas content, we consider that these galaxies are in the process of halting/quenching the star formation, in an actual transition between both groups. The analysis of the radial distributions of the starformation rate, specific star-formation rate, and molecular gas density shows that the quenching happens from inside-out involving both a decrease of the efficiency of the star formation and a deficit of molecular gas. All the intermediate data-products used to derive the results of our analysis are distributed in a database including the spatial distribution and average properties of the stellar populations and ionized gas, published as a Sloan Digital Sky Survey Value Added Catalog being part of the 14th Data Release: http://www.sdss.org/dr14/manga/manga-data/manga-pipe3d-value-added-catalog/Comment: 48 pages, 14 figures, in press in RMxA

The dicey dinner dilemma : asymmetry in predator-prey risk-taking, a broadly-applicable alternative to the life-dinner principle

RKH is grateful to both the University of St Andrews and the Perry Foundation for funding.Forty years ago, the ‘life‐dinner principle’ was proposed as an example of an asymmetry that may lead prey species to experience stronger selection than their predators, thus accounting for the high frequency with which prey escape alive from interaction with a predator. This principle remains an influential concept in the scientific literature, despite several works suggesting that the concept relies on many under‐appreciated assumptions and does not apply as generally as was initially proposed. Here, we present a novel model describing a very different asymmetry to that proposed in the life‐dinner principle, but one that could apply broadly. We argue that asymmetries between the relative costs and benefits to predators and prey of selecting a risky behaviour during an extended predator–prey encounter could lead to an enhanced likelihood of escape for the prey. Any resulting advantage to prey depends upon there being a behaviour or choice that introduces some inherent danger to both predator and prey if they adopt it, but which if the prey adopts the predator must match in order to have a chance of successful predation. We suggest that the circumstances indicated by our model could apply broadly across diverse taxa, including both risky spatial or behavioural choices.PostprintPeer reviewe

Towards a definition of quantum integrability

We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to the quantum framework would not work because all infinite dimensional Hilbert spaces are unitarily isomorphic and, as a consequence, it would not be easy to define degrees of freedom. We argue that a geometrical formulation of quantum mechanics might provide a way out.Comment: 37 pages, AmsLatex, 1 figur

Geometrization of Quantum Mechanics

We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified geometrical description for the different pictures of Quantum Mechanics. This construction provides an alternative to the usual GNS construction for pure states.Comment: 16 pages. To appear in Theor. Math. Phys. Some typos corrected. Definition 2 in page 5 rewritte

Phase Transitions in Operational Risk

In this paper we explore the functional correlation approach to operational risk. We consider networks with heterogeneous a-priori conditional and unconditional failure probability. In the limit of sparse connectivity, self-consistent expressions for the dynamical evolution of order parameters are obtained. Under equilibrium conditions, expressions for the stationary states are also obtained. The consequences of the analytical theory developed are analyzed using phase diagrams. We find co-existence of operational and non-operational phases, much as in liquid-gas systems. Such systems are susceptible to discontinuous phase transitions from the operational to non-operational phase via catastrophic breakdown. We find this feature to be robust against variation of the microscopic modelling assumptions.Comment: 13 pages, 7 figures. Accepted in Physical Review