Quantum Transport through Hierarchical Structures

The transport of quantum electrons through hierarchical lattices is of interest because such lattices have some properties of both regular lattices and random systems. We calculate the electron transmission as a function of energy in the tight binding approximation for two related Hanoi networks. HN3 is a Hanoi network with every site having three bonds. HN5 has additional bonds added to HN3 to make the average number of bonds per site equal to five. We present a renormalization group approach to solve the matrix equation involved in this quantum transport calculation. We observe band gaps in HN3, while no such band gaps are observed in linear networks or in HN5.Comment: 15 pages, RevTex, 10 figures, for related work, see http://www.physics.emory.edu/faculty/boettcher

Anomalous Defects and Their Quantized Transverse Conductivities

Using a description of defects in solids in terms of three-dimensional gravity, we study the propagation of electrons in the background of disclinations and screw dislocations. We study the situations where there are bound states that are effectively localized on the defect and hence can be described in terms of an effective 1+1 dimensional field theory for the low energy excitations. In the case of screw dislocations, we find that these excitations are chiral and can be described by an effective field theory of chiral fermions. Fermions of both chirality occur even for a given direction of the magnetic field. The ``net'' chirality of the system however is not always the same for a given direction of the magnetic field, but changes from one sign of the chirality through zero to the other sign as the Fermi momentum or the magnitude of the magnetic flux is varied. On coupling to an external electromagnetic field, the latter becomes anomalous, and predicts novel conduction properties for these materials.Comment: New material added. ReVTeX , 31 pgs., 4 figs.(uses epsf

Far Field Deposition Of Scoured Regolith Resulting From Lunar Landings

As a lunar lander approaches a dusty surface, the plume from the descent engine impinges on the ground, entraining loose regolith into a high velocity dust spray. Without the inhibition of a background atmosphere, the entrained regolith can travel many kilometers from the landing site. In this work, we simulate the flow field from the throat of the descent engine nozzle to where the dust grains impact the surface many kilometers away. The near field is either continuum or marginally rarefied and is simulated via a loosely coupled hybrid DSMC - Navier Stokes (DPLR) solver. Regions of two-phase and polydisperse granular flows are solved via DSMC. The far field deposition is obtained by using a staged calculation, where the first stages are in the near field where the flow is quasi-steady and the outer stages are unsteady. A realistic landing trajectory is approximated by a set of discrete hovering altitudes which range from 20m to 3m. The dust and gas motions are fully coupled using an interaction model that conserves mass, momentum, and energy statistically and inelastic collisions between dust particles are also accounted for. Simulations of a 4 engine configuration are also examined, and the erosion rates as well as near field particle fluxes are discussed.Astronom

Formal geometric quantisation for proper actions

Published online: 23 April 2015We define formal geometric quantisation for proper Hamiltonian actions by possibly noncompact groups on possibly noncompact, prequantised symplectic manifolds, generalising work of Weitsman and Paradan. We study the functorial properties of this version of formal geometric quantisation, and relate it to a recent result by the authors via a version of the shifting trick. For (pre)symplectic manifolds of a certain form, quantisation commutes with reduction, in the sense that formal quantisation equals a more direct version of quantisation.Peter Hochs, Varghese Matha

Transition to the ultimate regime in two-dimensional Rayleigh-B\'enard convection

The possible transition to the so-called ultimate regime, wherein both the bulk and the boundary layers are turbulent, has been an outstanding issue in thermal convection, since the seminal work by Kraichnan [Phys. Fluids 5, 1374 (1962)]. Yet, when this transition takes place and how the local flow induces it is not fully understood. Here, by performing two-dimensional simulations of Rayleigh-B\'enard turbulence covering six decades in Rayleigh number Ra up to $10^{14}$ for Prandtl number Pr $=1$, for the first time in numerical simulations we find the transition to the ultimate regime, namely at $\textrm{Ra}^*=10^{13}$. We reveal how the emission of thermal plumes enhances the global heat transport, leading to a steeper increase of the Nusselt number than the classical Malkus scaling $\textrm{Nu} \sim \textrm{Ra}^{1/3}$ [Proc. R. Soc. London A 225, 196 (1954)]. Beyond the transition, the mean velocity profiles are logarithmic throughout, indicating turbulent boundary layers. In contrast, the temperature profiles are only locally logarithmic, namely within the regions where plumes are emitted, and where the local Nusselt number has an effective scaling $\textrm{Nu} \sim \textrm{Ra}^{0.38}$, corresponding to the effective scaling in the ultimate regime.Comment: 6 pages, 4figure

The index of projective families of elliptic operators: the decomposable case

An index theory for projective families of elliptic pseudodifferential operators is developed under two conditions. First, that the twisting, i.e. Dixmier-Douady, class is in H2(X; Z)[H1(X; Z) H3(X; Z) and secondly that the 2-class part is trivialized on the total space of the fibration. One of the features of this special case is that the corresponding Azumaya bundle can be refined to a bundle of smoothing operators. The topological and the analytic index of a projective family of elliptic operators associated with the smooth Azumaya bundle both take values in twisted K-theory of the parameterizing space and the main result is the equality of these two notions of index. The twisted Chern character of the index class is then computed by a variant of Chern-Weil theory.V. Mathai, R.B. Melrose and I.M. Singe

Evolution of electromagnetic and Dirac perturbations around a black hole in Horava gravity

The evolution of electromagnetic and Dirac perturbations in the spacetime geometry of Kehagias-Sfetsos(KS) black hole in the deformed Horava-Lifshitz(HL) gravity is investigated and the associated quasinormal modes are evaluated using time domain integration and WKB methods. We find a considerable deviation in the nature of field evolution in HL theory from that in the Schwarzschild spacetime and QNMs region extends over a longer time in HL theory before the power-law tail decay begins. The dependence of the field evolution on the HL parameter $\alpha$ are studied. In the time domain picture we find that the length of QNM region increases with $\alpha$. But the late time decay of field follows the same power-law tail behavior as in the case of Schwarzschild black hole.Comment: The article was fully rewritten, references added, to appear in MPL