Regolith production and transport at the Susquehanna Shale Hills Critical Zone Observatory, Part 2: Insights from meteoric 10Be

Regolith-mantled hillslopes are ubiquitous features of most temperate landscapes, and their morphology reflects the climatically, biologically, and tectonically mediated interplay between regolith production and downslope transport. Despite intensive research, few studies have quantified both of these mass fluxes in the same field site. Here we present an analysis of 87 meteoric 10Be measurements from regolith and bedrock within the Susquehanna Shale Hills Critical Zone Observatory (SSHO), in central Pennsylvania. Meteoric 10Be concentrations in bulk regolith samples (n=73) decrease with regolith depth. Comparison of hillslope meteoric 10Be inventories with analyses of rock chip samples (n=14) from a 24 m bedrock core confirms that >80% of the total inventory is retained in the regolith. The systematic downslope increase of meteoric 10Be inventories observed at SSHO is consistent with 10Be accumulation in slowly creeping regolith (∼ 0.2 cm yr-1). Regolith flux inferred from meteoric 10Be varies linearly with topographic gradient (determined from high-resolution light detection and ranging-based topography) along the upper portions of hillslopes at SSHO. However, regolith flux appears to depend on the product of gradient and regolith depth where regolith is thick, near the base of hillslopes. Meteoric 10Be inventories at the north and south ridgetops indicate minimum regolith residence times of 10.5 ± 3.7 and 9.1 ± 2.9 ky, respectively, similar to residence times inferred from U-series isotopes in Ma et al. (2013). The combination of our results with U-series-derived regolith production rates implies that regolith production and erosion rates are similar to within a factor of two on SSHO hillcrests. ©2013. American Geophysical Union. All Rights Reserved

Clebsch-Gordan and 6j-coefficients for rank two quantum groups

We calculate (q-deformed) Clebsch-Gordan and 6j-coefficients for rank two quantum groups. We explain in detail how such calculations are done, which should allow the reader to perform similar calculations in other cases. Moreover, we tabulate the q-Clebsch-Gordan and 6j-coefficients explicitly, as well as some other topological data associated with theories corresponding to rank-two quantum groups. Finally, we collect some useful properties of the fusion rules of particular conformal field theories.Comment: 43 pages. v2: minor changes and added references. For mathematica notebooks containing the various q-CG and 6j symbols, see http://arxiv.org/src/1004.5456/an

Dynamics and level statistics of interacting fermions in the lowest Landau level

We consider the unitary dynamics of interacting fermions in the lowest Landau level, on spherical and toroidal geometries. The dynamics are driven by the interaction Hamiltonian which, viewed in the basis of single-particle Landau orbitals, contains correlated pair hopping terms in addition to static repulsion. This setting and this type of Hamiltonian has a significant history in numerical studies of fractional quantum Hall (FQH) physics, but the many-body quantum dynamics generated by such correlated hopping has not been explored in detail. We focus on initial states containing all the fermions in one block of orbitals. We characterize in detail how the fermionic liquid spreads out starting from such a state. We identify and explain differences with regular (single-particle) hopping Hamiltonians. Such differences are seen, e.g. in the entanglement dynamics, in that some initial block states are frozen or near-frozen, and in density gradients persisting in long-time equilibrated states. Examining the level spacing statistics, we show that the most common Hamiltonians used in FQH physics are not integrable, and explain that GOE statistics (level statistics corresponding to the Gaussian orthogonal ensemble) can appear in many cases despite the lack of time-reversal symmetry

Composite Fermion Wavefunctions Derived by Conformal Field Theory

The Jain theory of hierarchical Hall states is reconsidered in the light of recent analyses that have found exact relations between projected Jain wavefunctions and conformal field theory correlators. We show that the underlying conformal theory is precisely given by the W-infinity minimal models introduced earlier. This theory involves a reduction of the multicomponent Abelian theory that is similar to the projection to the lowest Landau level in the Jain approach. The projection yields quasihole excitations obeying non-Abelian fractional statistics. The analysis closely parallels the bosonic conformal theory description of the Pfaffian and Read-Rezayi states.Comment: 4 pages, 1 figur

Non-locality of non-Abelian anyons

Topological systems, such as fractional quantum Hall liquids, promise to successfully combat environmental decoherence while performing quantum computation. These highly correlated systems can support non-Abelian anyonic quasiparticles that can encode exotic entangled states. To reveal the non-local character of these encoded states we demonstrate the violation of suitable Bell inequalities. We provide an explicit recipe for the preparation, manipulation and measurement of the desired correlations for a large class of topological models. This proposal gives an operational measure of non-locality for anyonic states and it opens up the possibility to violate the Bell inequalities in quantum Hall liquids or spin lattices.Comment: 7 pages, 3 figure

Quasiparticles and excitons for the Pfaffian quantum Hall state

We propose trial wave functions for quasiparticle and exciton excitations of the Moore-Read Pfaffian fractional quantum Hall states, both for bosons and for fermions, and study these numerically. Our construction of trial wave functions employs a picture of the bosonic Moore-Read state as a symmetrized double layer composite fermion state. We obtain the number of independent angular momentum multiplets of quasiparticle and exciton trial states for systems of up to 20 electrons. We find that the counting for quasielectrons at large angular momentum on the sphere matches that expected from the CFT which describes the Moore-Read state's boundary theory. In particular, the counting for quasielectrons is the same as for quasiholes, in accordance with the idea that the CFT describing both sides of the FQH plateau should be the same. We also show that our trial wave functions have good overlaps with exact wave functions obtained using various interactions, including second Landau level Coulomb interactions and the 3-body delta interaction for which the Pfaffian states and their quasiholes are exact ground states. We discuss how these results relate to recent work by Sreejith et al. on a similar set of trial wave functions for excitations over the Pfaffian state as well as to earlier work by Hansson et al., which has produced trial wave functions for quasiparticles based on conformal field theory methods and by Bernevig and Haldane, which produced trial wave functions based on clustering properties and `squeezing'.Comment: 22 pages, 18 figure

Paired and clustered quantum Hall states

We briefly summarize properties of quantum Hall states with a pairing or clustering property. Their study employs a fundamental connection with parafermionic Conformal Field Theories. We report on closed form expressions for the many-body wave functions and on multiplicities of the fundamental quasi-hole excitations.Comment: 13 pages, Contribution to the proceedings of the NATO Advanced Research Workshop "Statistical Field Theories" Como (Italy), June 18-23 200