Reflection positivity and invertible topological phases

We implement an extended version of reflection positivity (Wick-rotated unitarity) for invertible topological quantum field theories and compute the abelian group of deformation classes using stable homotopy theory. We apply these field theory considerations to lattice systems, assuming the existence and validity of low energy effective field theory approximations, and thereby produce a general formula for the group of Symmetry Protected Topological (SPT) phases in terms of Thom's bordism spectra; the only input is the dimension and symmetry group. We provide computations for fermionic systems in physically relevant dimensions. Other topics include symmetry in quantum field theories, a relativistic 10-fold way, the homotopy theory of relativistic free fermions, and a topological spin-statistics theorem.Comment: 136 pages, 16 figures; minor changes/corrections in version 2; v3 major revision; v4 minor revision: corrected proof of Lemma 9.55, many small changes throughout; v5 version for publication in Geometry & Topolog

Louisiana Juvenile Justice at the Crossroads

Over the past decade, interest in community-based corrections for juveniles has grown while dissatisfaction with the expense and ineffectiveness of training schools has increased. Since 1985, the National Council on Crime and Delinquency has investigated technologies that would make a shift from juvenile justice systems plagued with over-incarceration to those emphasizing community-based care. The application of a public-safety risk assessment instrument to Louisiana juvenile offenders revealed that substantial numbers of youth could be safely managed in well-run community programs. This risk assessment technology, together with accurate, policy sensitive, population forecasting and an intensive review of existing community programs, can substantially assist administrators in moving toward more effective juvenile correctional systems

A viscoplastic theory applied to copper

A phenomenologically based viscoplastic model is derived for copper. The model is thermodynamically constrained by the condition of material dissipativity. Two internal state variables are considered. The back stress accounts for strain-induced anisotropy, or kinematic hardening. The drag stress accounts for isotropic hardening. Static and dynamic recovery terms are not coupled in either evolutionary equation. The evolution of drag stress depends on static recovery, while the evolution of back stress depends on dynamic recovery. The material constants are determined from isothermal data. Model predictions are compared with experimental data for thermomechanical test conditions. They are in good agreement at the hot end of the loading cycle, but the model overpredicts the stress response at the cold end of the cycle

Pumping conductance, the intrinsic anomalous Hall effect, and statistics of topological invariants

The pumping conductance of a disordered two-dimensional Chern insulator scales with increasing size and fixed disorder strength to sharp plateau transitions at well-defined energies between ordinary and quantum Hall insulators. When the disorder strength is scaled to zero as system size increases, the "metallic" regime of fluctuating Chern numbers can extend over the whole band. A simple argument leads to a sort of weighted equipartition of Chern number over minibands in a finite system with periodic boundary conditions: even though there must be strong fluctuations between disorder realizations, the mean Chern number at a given energy is determined by the {\it clean} Berry curvature distribution expected from the intrinsic anomalous Hall effect formula for metals. This estimate is compared to numerical results using recently developed operator algebra methods, and indeed the dominant variation of average Chern number is explained by the intrinsic anomalous Hall effect. A mathematical appendix provides more precise definitions and a model for the full distribution of Chern numbers.Comment: 12 page