Semiclassical evolution of dissipative Markovian systems

A semiclassical approximation for an evolving density operator, driven by a `closed` Hamiltonian operator and `open` Markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the Hamiltonian operator is a quadratic function and the Lindblad operators are linear functions of positions and momenta. Initially, the semiclassical formulae for the case of Hermitian Lindblad operators are reinterpreted in terms of a (real) double phase space, generated by an appropriate classical double Hamiltonian. An extra `open` term is added to the double Hamiltonian by the non-Hermitian part of the Lindblad operators in the general case of dissipative Markovian evolution. The particular case of generic Hamiltonian operators, but linear dissipative Lindblad operators, is studied in more detail. A Liouville-type equivariance still holds for the corresponding classical evolution in double phase space, but the centre subspace, which supports the Wigner function, is compressed, along with expansion of its conjugate subspace, which supports the chord function. Decoherence narrows the relevant region of double phase space to the neighbourhood of a caustic for both the Wigner function and the chord function. This difficulty is avoided by a propagator in a mixed representation, so that a further `small-chord` approximation leads to a simple generalization of the quadratic theory for evolving Wigner functions.

Modelling the secular evolution of migrating planet pairs

The subject of this paper is the secular behaviour of a pair of planets evolving under dissipative forces. In particular, we investigate the case when dissipative forces affect the planetary semimajor axes and the planets move inwards/outwards the central star, in a process known as planet migration. To perform this investigation, we introduce fundamental concepts of conservative and dissipative dynamics of the three-body problem. Based on these concepts, we develop a qualitative model of the secular evolution of the migrating planetary pair. Our approach is based on the analysis of the energy and the orbital angular momentum exchange between the two-planet system and an external medium; thus no specific kind of dissipative forces is invoked. We show that, under the assumption that dissipation is weak and slow, the evolutionary routes of the migrating planets are traced by the Mode I and Mode II stationary solutions of the conservative secular problem. The ultimate convergence and the evolution of the system along one of these secular modes of motion are determined uniquely by the condition that the dissipation rate is sufficiently smaller than the proper secular frequency of the system. We show that it is possible to reassemble the starting configurations and the migration history of the systems on the basis of their final states and consequently to constrain the parameters of the physical processes involved.

PLANETARY NEBULAE AND THE CHEMICAL EVOLUTION OF THE MAGELLANIC CLOUDS

The determination of accurate chemical abundances of planetary nebulae (PN) in different galaxies allows us to obtain important constraints on chemical evolution models for these systems. We have a long-term program to derive abundances in the galaxies of the Local Group, particularly the Large and Small Magellanic Clouds. In this work, we present our new results on these objects and discuss their implications in view of recent abundance determinations in the literature. In particular, we obtain distance-independent correlations involving He, N, O, Ne, S, and Ar, and compare the results with data from our own Galaxy and other galaxies in the Local Group. As a result of our observational program, we have a large database of PN in the Galaxy and the Magellanic Clouds, so that we can obtain reliable constraints on the nucleosynthesis processes in the progenitor stars in galaxies of different metallicities.

MODELING THE EVOLUTION OF COMPLEX NETWORKS THROUGH THE PATH-STAR TRANSFORMATION AND OPTIMAL MULTIVARIATE METHODS

The topology of real-world complex networks, such as in transportation and communication, is always changing with time. Such changes can arise not only as a natural consequence of their growth, but also due to major modi. cations in their intrinsic organization. For instance, the network of transportation routes between cities and towns ( hence locations) of a given country undergo a major change with the progressive implementation of commercial air transportation. While the locations could be originally interconnected through highways ( paths, giving rise to geographical networks), transportation between those sites progressively shifted or was complemented by air transportation, with scale free characteristics. In the present work we introduce the path-star transformation ( in its uniform and preferential versions) as a means to model such network transformations where paths give rise to stars of connectivity. It is also shown, through optimal multivariate statistical methods (i.e. canonical projections and maximum likelihood classification) that while the US highways network adheres closely to a geographical network model, its path-star transformation yields a network whose topological properties closely resembles those of the respective airport transportation network.

Dynamical self-stabilization of the Mott insulator: Time evolution of the density and entanglement entropy of out-of-equilibrium cold fermion gases

The time evolution of the out-of-equilibrium Mott insulator is investigated numerically through calculations of space-time-resolved density and entropy profiles resulting from the release of a gas of ultracold fermionic atoms from an optical trap. For adiabatic, moderate and sudden switching-off of the trapping potential, the out-of-equilibrium dynamics of the Mott insulator is found to differ profoundly from that of the band insulator and the metallic phase, displaying a self-induced stability that is robust within a wide range of densities, system sizes and interaction strengths. The connection between the entanglement entropy and changes of phase, known for equilibrium situations, is found to extend to the out-of-equilibrium regime. Finally, the relation between the system`s long time behavior and the thermalization limit is analyzed. Copyright (C) EPLA, 2011

Evolution of a rift basin dominated by subaerial deposits: The Guaritas Rift, Early Cambrian, Southern Brazil

Most existing models for the evolution of rift basins predict the development of deep-water depositional systems during the stage of greatest tectonic subsidence, when accommodation generation potentially outpaces sedimentation. Despite this, some rift basins do not present deep-water systems, instead being dominated by subaerial deposits. This paper focuses on one of these particular rift basins, the Cambrian Guaritas Rift, Southern Brazil, characterized by more than 1500 m of alluvial and aeolian strata deposited in a 50-km-wide basin. The deposits of the Guaritas Rift can be ascribed to four depositional systems: basin-border alluvial fans, bedload-dominated ephemeral rivers, mixed-load ephemeral rivers and aeolian dune fields. These four systems are in part coeval and in part succeed each other, forming three stages of basin evolution: (i) Rift Initiation to Early Rift Climax stage, (ii) Mid to Late Rift Climax stage, and (iii) Early Post-Rift stage. The first stage comprises most of the Guaritas Group and is characterized by homogeneous bed-load-dominated river deposits, which do not clearly record the evolution of subsidence rates. The onset of sedimentation of finer-grained deposits occurred as a consequence of a reactivation event that changed the outline of the basin and the distribution of the nearby highlands. This strongly suggests that the capture of the main river system to another depression decreased the sediment supply to the basin. The study of the Guaritas Rift indicates that rift basins in which the sediment supply exceeds the accommodation generation occur as a consequence of moderate subsidence combined with the capture of a major river system to the basin during the initial stages of basin evolution. In these basins, changes in the average discharge of the river system or tectonic modification of the drainage network may be the major control on the stratigraphic architecture. (c) 2009 Published by Elsevier B.V.

Tectono-sedimentary evolution of the Neoproterozoic BIF-bearing Jacadigo Group, SW-Brazil

The Jacadigo Group contains one of the largest sedimentary iron and associated manganese deposits of the Neoproterozoic. Despite its great relevance, no detailed sedimentological study concerning the unit has been carried out to date. Here we present detailed sedimentological data and interpretation on depositional systems, system tracts, external controls on basin evolution, basin configuration and regional tectonic setting of the Jacadigo Basin. Six depositional systems were recognized: (I) an alluvial fan system; (II) a siliciclastic lacustrine system; (III) a fan-delta system; (IV) a bedload-dominated river system; (V) an iron formation-dominated lacustrine or marine gulf system; and (VI) a rimmed carbonate platform system. The interpreted depositional systems are related to three tectonic system tracts. The first four depositional systems are mainly made of continental siliciclastics and refer to the rift initiation to early rift climax stage; the lake/gulf system corresponds to the mid to late rift climax stage and the carbonate platform represents the immediate to late post rift stage (Bocaina Formation deposits of the Ediacaran fossil-bearing Corumba Group). The spatial distribution of the depositional systems and associated paleocurrent patterns indicate a WNW-ESE orientation of the master fault zone related to the formation of the Jacadigo Basin. Thus, the iron formations of the Jacadigo Group were deposited in a starved waterbody related to maximum fault displacement and accommodation rates in a restricted continental rift basin. The Fe-Si-Mn source was probably related to hydrothermal plume activity that reached the basin through the fault system during maximum fault displacement phases. Our results also suggest a restricted tectono-sedimentary setting for the type section of the Puga Formation. The Jacadigo Group and the Puga Formation, usually interpreted as glacial deposits, are readdressed here as basin margin gravitational deposits with no necessary relation to glacial processes. (C) 2011 Elsevier B.V. All rights reserved.