Truncated unity functional renormalization group for multiband systems with spin-orbit coupling

Although the functional renormalization group (fRG) is by now a well-established method for investigating correlated electron systems, it is still undergoing significant technical and conceptual improvements. In particular, the motivation to optimally exploit the parallelism of modern computing platforms has recently led to the development of the "truncated-unity" functional renormalization group (TU-fRG). Here, we review this fRG variant, and we provide its extension to multiband systems with spin-orbit coupling. Furthermore, we discuss some aspects of the implementation and outline opportunities and challenges ahead for predicting the ground-state ordering and emergent energy scales for a wide class of quantum materials.Comment: consistent with published version in Frontiers in Physics (2018

Numerical test of the damping time of layer-by-layer growth on stochastic models

We perform Monte Carlo simulations on stochastic models such as the Wolf-Villain (WV) model and the Family model in a modified version to measure mean separation $\ell$ between islands in submonolayer regime and damping time $\tilde t$ of layer-by-layer growth oscillations on one dimension. The stochastic models are modified, allowing diffusion within interval $r$ upon deposited. It is found numerically that the mean separation and the damping time depend on the diffusion interval $r$, leading to that the damping time is related to the mean separation as ${\tilde t} \sim \ell^{4/3}$ for the WV model and ${\tilde t} \sim \ell^2$ for the Family model. The numerical results are in excellent agreement with recent theoretical predictions.Comment: 4 pages, source LaTeX file and 5 PS figure

Truncated-Unity Parquet Equations: Application to the Repulsive Hubbard Model

The parquet equations are a self-consistent set of equations for the effective two-particle vertex of an interacting many-fermion system. The application of these equations to bulk models is, however, demanding due to the complex emergent momentum and frequency structure of the vertex. Here, we show how a channel-decomposition by means of truncated unities, which was developed in the context of the functional renormalization group to efficiently treat the momentum dependence, can be transferred to the parquet equations. This leads to a significantly reduced numerical effort scaling only linearly with the number of discrete momenta. We apply this technique to the half-filled repulsive Hubbard model on the square lattice and present approximate solutions for the channel-projected vertices and the full reducible vertex.Comment: Consistent with published version in Phys. Rev.

Gravitational Waves: Just Plane Symmetry

We present some remarkable properties of the symmetry group for gravitational plane waves. Our main observation is that metrics with plane wave symmetry satisfy every system of generally covariant vacuum field equations except the Einstein equations. The proof uses the homothety admitted by metrics with plane wave symmetry and the scaling behavior of generally covariant field equations. We also discuss a mini-superspace description of spacetimes with plane wave symmetry.Comment: 10 pages, TeX, uses IOP style file

Modulation of Neuronal Signal Transduction Systems by Extracellular ATP

The secretion of ATP by stimulated nerves is well documented. Following repetitive stimulation, extracellular ATP at the synapse can accumulate to levels estimated to be well over 100 Μ M. The present study examined the effects of extracellular ATP in the concentration range of 0.1–1.0 m M on second-messenger-generating systems in cultured neural cells of the clones NG108-15 and NIE-115. Cells in a medium mimicking the physiological extracellular environment were used to measure 45 Ca 2+ uptake, changes in free intracellular Ca 2+ levels by the probes aequorin and Quin-2, de novo generation of cyclic GMP and cyclic AMP from intracellular GTP and ATP pools prelabeled with [ 3 H]guanosine and [ 3 H]adenine, respectively, and phosphoinositide metabolism in cells preloaded with [ 3 H]inositol and assayed in the presence of LiCI. Extracelluar ATP induced a concentration-dependent increase of 45 Ca 2+ uptake by intact cells, which was additive with the uptake induced by K + depolarization. The increased uptake involved elevation of intracellular free Ca 2+ ions, evidenced by measuring aequorin and Quin-2 signals. At the same concentration range (0.1–1.0 m M ), extracellular ATP induced an increase in [ 3 H]cyclic GMP formation, and a decrease in prostaglandin E 1 -stimulated [ 3 H]cyclic AMP generation. In addition, extracellular ATP (1 m M ) caused a large (15-fold) increase in [ 3 H]inositol phosphates accumulation, and this effect was blocked by including La 3+ ions in the assay medium. In parallel experiments, we found in NG 108–15 cells surface protein phosphorylation activity that had an apparent K m for extracellular ATP at the same concentration required to produce half-maximal effects on Ca 2+ uptake. Extracellular ATP at concentrations that can be produced in the synaptic cleft by repetitive stimulation but not during routine transmission can thus initiate a unique chain of events, which may play a role in the induction of long-term adaptive changes in neuronal function.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65952/1/j.1471-4159.1988.tb13263.x.pd

Rigid Singularity Theorem in Globally Hyperbolic Spacetimes

We show the rigid singularity theorem, that is, a globally hyperbolic spacetime satisfying the strong energy condition and containing past trapped sets, either is timelike geodesically incomplete or splits isometrically as space $\times$ time. This result is related to Yau's Lorentzian splitting conjecture.Comment: 3 pages, uses revtex.sty, to appear in Physical Review

Molecular Dynamics Simulation of Semiflexible Polyampholyte Brushes - The Effect of Charged Monomers Sequence

Planar brushes formed by end-grafted semiflexible polyampholyte chains, each chain containing equal number of positively and negatively charged monomers is studied using molecular dynamics simulations. Keeping the length of the chains fixed, dependence of the average brush thickness and equilibrium statistics of the brush conformations on the grafting density and the salt concentration are obtained with various sequences of charged monomers. When similarly charged monomers of the chains are arranged in longer blocks, the average brush thickness is smaller and dependence of brush properties on the grafting density and the salt concentration is stronger. With such long blocks of similarly charged monomers, the anchored chains bond to each other in the vicinity of the grafting surface at low grafting densities and buckle toward the grafting surface at high grafting densities.Comment: 8 pages,7 figure

A Cauchy-Dirac delta function

The Dirac delta function has solid roots in 19th century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac's discovery by over a century, and illuminating the nature of Cauchy's infinitesimals and his infinitesimal definition of delta.Comment: 24 pages, 2 figures; Foundations of Science, 201

Interleukin-8 levels and activity in delayed-healing human thermal wounds

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72020/1/j.1524-475x.2000.00216.x.pd

Nanoscale Observation of Alkane Delayering

Noncontact Atomic Force Microscopy and synchrotron x-ray scattering measurements on dotriacontane (n-C32H66 or C32) films adsorbed on SiO2-coated Si(100) wafers reveal a narrow temperature range near the bulk C32 melting point Tb in which a monolayer phase of C32 molecules oriented perpendicular to surface is stable. This monolayer phase undergoes a delayering transition to a three-dimensional (3D) fluid phase on heating to just above Tb and to a solid 3D phase on cooling below Tb. An equilibrium phase diagram provides a useful framework for interpreting the unusual spreading and receding of the monolayer observed in transitions to and from the respective 3D phases.Comment: 13 pages, 3 figure