12,364 research outputs found
Quantum -core conduction on the Bethe lattice
Classical and quantum conduction on a bond-diluted Bethe lattice is
considered. The bond dilution is subject to the constraint that every occupied
bond must have at least neighboring occupied bonds, i.e. -core
diluted. In the classical case, we find the onset of conduction for is
continuous, while for , the onset of conduction is discontinuous with the
geometric random first-order phase transition driving the conduction
transition. In the quantum case, treating each occupied bond as a random
scatterer, we find for that the random first-order phase transition in
the geometry also drives the onset of quantum conduction giving rise to a new
universality class of Anderson localization transitions.Comment: 12 pgs., 6 fig
Level statistics for quantum -core percolation
Quantum -core percolation is the study of quantum transport on -core
percolation clusters where each occupied bond must have at least occupied
neighboring bonds. As the bond occupation probability, , is increased from
zero to unity, the system undergoes a transition from an insulating phase to a
metallic phase. When the lengthscale for the disorder, , is much greater
than the coherence length, , earlier analytical calculations of quantum
conduction on the Bethe lattice demonstrate that for the metal-insulator
transition (MIT) is discontinuous, suggesting a new universality class of
disorder-driven quantum MITs. Here, we numerically compute the level spacing
distribution as a function of bond occupation probability and system size
on a Bethe-like lattice. The level spacing analysis suggests that for ,
, the quantum percolation critical probability, is greater than , the
geometrical percolation critical probability, and the transition is continuous.
In contrast, for , and the transition is discontinuous such that
these numerical findings are consistent with our previous work to reiterate a
new universality class of disorder-driven quantum MITs.Comment: 8 pages, 11 figure
Origin and thermal evolution of Mars
The thermal evolution of Mars is governed by subsolidus mantle convection beneath a thick lithosphere. Models of the interior evolution are developed by parameterizing mantle convective heat transport in terms of mantle viscosity, the superadiabatic temperature rise across the mantle, and mantle heat production. Geological, geophysical, and geochemical observations of the compositon and structure of the interior and of the timing of major events in Martian evolution are used to constrain the model computations. Such evolutionary events include global differentiation, atmospheric outgassing, and the formation of the hemispherical dichotomy and Tharsis. Numerical calculations of fully three-dimensional, spherical convection in a shell the size of the Martian mantle are performed to explore plausible patterns of Martian mantel convection and to relate convective features, such as plumes, to surface features, such as Tharsis. The results from the model calculations are presented
Morphology and evolution of coronae and ovoids on Venus
Coronae and ovoids on Venus were first identified in Venera 15/16 data. They are distinctive and apparently unique to the planet, and may be important indicators of processes operating in the Venusian mantle. Magellan images have provided the first high resolution views of coronae and ovoid morphology. Herein, the general geologic character is described of coronae and ovoids, and some inferences are drawn about their geologic evolution. Coronae are circular to elongate features surrounded by an annulus of deformational features, with a relatively raised or indistinct topographic signature and, commonly, a peripheral trough or moat. Ovoids are circular to elongate features other than coronae with either positive or negative topographic signatures, associated with tectonic deformation and volcanism. The relationship of these two geologic features to each other and to Venusian geology is briefly discussed
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