Quantum Belief Propagation

We present an accurate numerical algorithm, called quantum belief propagation (QBP), for simulation of one-dimensional quantum systems at non-zero temperature. The algorithm exploits the fact that quantum effects are short-range in these systems at non-zero temperature, decaying on a length scale inversely proportional to the temperature. We compare to exact results on a spin-1/2 Heisenberg chain. Even a very modest calculation, requiring diagonalizing only 10-by-10 matrices, reproduces the peak susceptibility with a relative error of less than $10^{-5}$, while more elaborate calculations further reduce the error.Comment: 4 pages, 1 figure; revised time estimates due to improved implementation. Typographical corrections to Eq. 7 made; thanks to David Poulin for pointing out the mistak

Disordered Topological Insulators via C∗C^*-Algebras

The theory of almost commuting matrices can be used to quantify topological obstructions to the existence of localized Wannier functions with time-reversal symmetry in systems with time-reversal symmetry and strong spin-orbit coupling. We present a numerical procedure that calculates a Z_2 invariant using these techniques, and apply it to a model of HgTe. This numerical procedure allows us to access sizes significantly larger than procedures based on studying twisted boundary conditions. Our numerical results indicate the existence of a metallic phase in the presence of scattering between up and down spin components, while there is a sharp transition when the system decouples into two copies of the quantum Hall effect. In addition to the Z_2 invariant calculation in the case when up and down components are coupled, we also present a simple method of evaluating the integer invariant in the quantum Hall case where they are decoupled.Comment: Added detail regarding the mapping of almost commuting unitary matrices to almost commuting Hermitian matrices that form an approximate representation of the sphere. 6 pages, 6 figure

Fluctuating thermal environments of shallow-water rocky reefs in the Gulf of California, Mexico.

As part of a broad-scale study of the biogeography of rocky reefs in the Gulf of California, Mexico (GOC), we collected a continuous 1-yr temperature time series at ~5 m water depth at 16 sites spanning 5° of latitude and ~700 km along the western boundary of the basin. Throughout the region, thermal conditions were most variable in summer with fluctuations concentrated at diurnal and semi-diurnal frequencies, likely associated with solar and wind forcing and vertical water column oscillations forced by internal waves. Temperatures in winter were less variable than in summer, and minimum temperatures also differed among sites. Thermal variability integrated across the diurnal and semi-diurnal frequency bands was greatest near the Midriff Islands in the northern GOC and decreased toward the southern sites. Diurnal variability was greater than semi-diurnal variability at 13 of the 16 sites. A statistic-of-extremes analysis indicated shortest return times for cooling events in summer, and reef organisms at many of the sites may experience anomalous 2 to 5 °C cooling events multiple times per month. The significant extent of local temperature variability may play important roles in limiting species occurrences among sites across this biogeographic region

The Effects of Family Background and Religion on Leadership

This study examined the role of family background and religion in predicting leadership skills. Research showed that the impact families and religion have on children and adolescents is significant, influencing children\u27s attributes, habits, and beliefs for their entire lives. The experiment tested university student leaders for a significant effect of family background and religious upbringing on their leadership skills. The subjects were given an informed consent form, a demographics survey, the Santa Clara Religious Faith Questionnaire, and the Student Leadership Practices Inventory. Results are expected to show that a student from a non-divorced, stable family and a religious upbringing will result in higher leadership scores than a student from a divorced and non-religious family

Theory of plasma contactors in ground-based experiments and low Earth orbit

Previous theoretical work on plasma contactors as current collectors has fallen into two categories: collisionless double layer theory (describing space charge limited contactor clouds) and collisional quasineutral theory. Ground based experiments at low current are well explained by double layer theory, but this theory does not scale well to power generation by electrodynamic tethers in space, since very high anode potentials are needed to draw a substantial ambient electron current across the magnetic field in the absence of collisions (or effective collisions due to turbulence). Isotropic quasineutral models of contactor clouds, extending over a region where the effective collision frequency upsilon sub e exceeds the electron cyclotron frequency omega sub ce, have low anode potentials, but would collect very little ambient electron current, much less than the emitted ion current. A new model is presented, for an anisotropic contactor cloud oriented along the magnetic field, with upsilon sub e less than omega sub ce. The electron motion along the magnetic field is nearly collisionless, forming double layers in that direction, while across the magnetic field the electrons diffuse collisionally and the potential profile is determined by quasineutrality. Using a simplified expression for upsilon sub e due to ion acoustic turbulence, an analytic solution has been found for this model, which should be applicable to current collection in space. The anode potential is low and the collected ambient electron current can be several times the emitted ion current

An analytical and experimental evaluation of a Fresnel lens solar concentrator

An analytical and experimental evaluation of line focusing Fresnel lenses with application potential in the 200 to 370 C range was studied. Analytical techniques were formulated to assess the solar transmission and imaging properties of a grooves down lens. Experimentation was based on a 56 cm wide, f/1.0 lens. A Sun tracking heliostat provided a nonmoving solar source. Measured data indicated more spreading at the profile base than analytically predicted, resulting in a peak concentration 18 percent lower than the computed peak of 57. The measured and computed transmittances were 85 and 87 percent, respectively. Preliminary testing with a subsequent lens indicated that modified manufacturing techniques corrected the profile spreading problem and should enable improved analytical experimental correlation

Spaceborne memory organization, an associative data acquisition system, phase II Final report, Apr. - Dec. 1966

Spaceborne memory organization, associative data acquisition system design, and data compression technique