On two subgroups of U(n), useful for quantum computing

As two basic building blocks for any quantum circuit, we consider the 1-qubit PHASOR circuit Phi(theta) and the 1-qubit NEGATOR circuit N(theta). Both are roots of the IDENTITY circuit. Indeed: both (NO) and N(0) equal the 2 x 2 unit matrix. Additionally, the NEGATOR is a root of the classical NOT gate. Quantum circuits (acting on w qubits) consisting of controlled PHASORs are represented by matrices from ZU(2(w)); quantum circuits consisting of controlled NEGATORs are represented by matrices from XU(2(w)). Here, ZU(n) and XU(n) are subgroups of the unitary group U(n): the group XU(n) consists of all n x n unitary matrices with all 2n line sums (i.e. all n row sums and all n column sums) equal to 1 and the group ZU(n) consists of all n x n unitary diagonal matrices with first entry equal to 1. Any U(n) matrix can be decomposed into four parts: U = exp(i alpha) Z(1)XZ(2), where both Z(1) and Z(2) are ZU(n) matrices and X is an XU(n) matrix. We give an algorithm to find the decomposition. For n = 2(w) it leads to a four-block synthesis of an arbitrary quantum computer

Global meta-analysis reveals positive effects of biochar on soil microbial diversity

Biochar has gained global attention due to its potential for climate change mitigation and soil quality improvement. Yet, the consequences of biochar additions for soil microbes-the major biotic drivers of soil function-remain unknown across global environmental gradients. We aimed to explore the responses of soil bacterial communities to biochar addition, and further investigate how biochar and soil properties impact these responses. We conducted a global meta-analysis and found that, in general, biochar has a limited impact on the proportion of major bacterial phyla, with only Acidobacteria and Gemmatimonadetes being largely impacted: the relative abundance of Acidobacteria decreased by 14.6%, while that of Gemmatimonadetes increased by 19.8%. Also, the experimental type played a role in shaping the response of microbial community to biochar application. In addition, biochar significantly promoted the diversity of soil bacteria, i.e., genetic richness and diversity. These changes were significantly associated with biochar load, C/N ratio, pyrolysis temperature, biochar pH, as well as soil C/N ratio and pH. We further found that the impacts of biochar on functional diversity, i.e., C substrate richness consumed by soil microbes increased with the biochar load, which might relate to increased genetic richness. Our work suggests that selecting key biochar properties can improve soil quality, microbial function, and climate change mitigation while maintaining the positive impacts of biochar on soil microbial diversity. Further research is needed to link the response of soil microbial composition at the genus level to biochar addition, with microbial functions

Newly plant-derived carbon in the deeper vadose zone of a sandy agricultural soil does not stimulate denitrification

Analysis of stable carbon (C) isotopic signatures ( delta 13 C) in various soil C pools provides useful information on soil C sources, transport, and availability. Understanding the extent of deeper soil (below 40 cm) sequestration and transport of plant derived C is of particular interest as this provides a source for microorganisms to drive biological denitrification (as indicated by denitrification enzyme activity, DEA) and hence mitigate the nitrate leaching to groundwater. Meanwhile, studies on deeper soil C sequestration are rare due to methodological constraints. This study was done in deeper vadose zone (0 -160 cm) of a sandy agricultural soil in a humid and temperature zone after a C 3 -C 4 vegetation change taking advantage of the marked isotopic differences between C 3 and C 4 plants. It took place in a site previously grown with C 3 crops (beet, barley, grass), but where C 4 crops (maize) were grown continuously for the last 20 years. The other site where C 3 crops were continuously grown was used for comparison. Specifically, the delta 13 C signature in top and deeper soil layers was used to distinguish between old C 3 - and newly C 4 -plant derived C in four C pools, i.e., bulk soil C, hot- and cold-water extractable C, and respired CO 2 -C. The delta 13 C signature between C 3 soils and C 3 -C 4 shifted soils was similar for bulk soil C but significantly different for water extractable and respired C pools. Hence, we estimated that the contribution of newly derived C to bulk soil C was negligible, whereas the contributions to the other C pools amounted up to 28.4 % along the soil profile. This emphasizes the importance of simultaneously analysing delta 13 C signature in various soil C pools to accurately assess C vertical transport and distribution. The concentrations of cold-DOC and values of specific ultraviolet visible absorbance of the wavelengths 254 and 280 nm decreased from 50 to 130 cm soil depths, while they increased below these depths. However, this suggested rise in C chemical quality at the deepest soil depths did not cause an increase in soil respiration activity or DEA, which was attributed to the protective effects of iron and aluminium oxides on C decomposition. Upon the application of labile C and N substrates, the deepest soil layers displayed a significantly increased DEA, suggesting the presence of a relatively abundant population of active denitrifying organisms. Overall, this study documents the presence of plantderived C in the deeper vadose zone. Meanwhile, this particular C pool might not be an important substrate to drive deep-soil denitrification due to constraints imposed by the protection by metal oxides

State control can result in good performance for firms

State firms are now hybrid organisations, say Ciprian Stan, David Ahlstrom, Mike W. Peng, Kehan Xu and Garry D. Bruto

A model of flavors

We argue in favor of dynamical mass generation in an SU(2)xU(1) electroweak model with two complex scalar doublets with ordinary masses. The masses of leptons and quarks are generated by ultraviolet-finite non-perturbative solutions of the Schwinger-Dyson equations for full fermion propagators with self-consistently modified scalar boson exchanges. The W and Z boson masses are expressed in terms of spontaneously generated fermion proper self-energies in the form of sum rules. The model predicts two charged and four real neutral heavy scalars.Comment: 5 pages, REVTeX4, 5 feynmp figure

INSTABILITY OF A NIELSEN-OLESEN VORTEX EMBEDDED IN THE ELECTROWEAK THEORY: II. ELECTROWEAK VORTICES AND GAUGE EQUIVALENCE

Vortex configurations in the electroweak gauge theory are investigated. Two gauge-inequivalent solutions of the field equations, the Z and W vortices, have previously been found. They correspond to embeddings of the abelian Nielsen-Olesen vortex solution into a U(1) subgroup of SU(2)xU(1). It is shown here that any electroweak vortex solution can be mapped into a solution of the same energy with a vanishing upper component of the Higgs field. The correspondence is a gauge equivalence for all vortex solutions except those for which the winding numbers of the upper and lower Higgs components add to zero. This class of solutions, which includes the W vortex, instead corresponds to a singular solution in the one-component gauge. The results, combined with numerical investigations, provide an argument against the existence of other vortex solutions in the gauge-Higgs sector of the Standard Model.Comment: 6 pages, plain latex, no figures, submitted to Mod. Phys. Lett. A as "Electroweak Vortices and Gauge Equivalence"

Senior Recital, Binyan Xu, piano

VCU DEPARTMENT OF MUSIC SENIOR RECITAL Binyan Xu, piano Tuesday, November 24 at 4:00 p.m. Sonia Vlahcevic Concert Hall W. E. Singleton Center for the Performing Art