Smooth bumps, a Borel theorem and partitions of smooth functions on p.c.f. fractals

We provide two methods for constructing smooth bump functions and for smoothly cutting off smooth functions on fractals, one using a probabilistic approach and sub-Gaussian estimates for the heat operator, and the other using the analytic theory for p.c.f. fractals and a fixed point argument. The heat semigroup (probabilistic) method is applicable to a more general class of metric measure spaces with Laplacian, including certain infinitely ramified fractals, however the cut off technique involves some loss in smoothness. From the analytic approach we establish a Borel theorem for p.c.f. fractals, showing that to any prescribed jet at a junction point there is a smooth function with that jet. As a consequence we prove that on p.c.f. fractals smooth functions may be cut off with no loss of smoothness, and thus can be smoothly decomposed subordinate to an open cover. The latter result provides a replacement for classical partition of unity arguments in the p.c.f. fractal setting.Comment: 26 pages. May differ slightly from published (refereed) versio

Ambiguous Solicitation: Ambiguous Prescription

We conduct a two-phase laboratory experiment, separated by several weeks. In the first phase, we conduct urn games intended to measure ambiguity aversion on a representative population of undergraduate students. In the second phase, we invite the students back with four different solicitation treatments, varying in the ambiguity of information regarding the task and the payout of the laboratory experiment. We find that those who return do not differ from the overall pool with respect to their ambiguity version. However, no solicitation treatment generates a representative sample. The ambiguous task treatment drives away the ambiguity averse disproportionally, and the detailed task treatment draws in the ambiguity averse disproportionally.laboratory experimental methods, experimental economics, laboratory selection effects

Spin-wave chirality and its manifestations in antiferromagnets

As first demonstrated by Tang and Cohen in chiral optics, the asymmetry in the rate of electromagnetic energy absorption between left and right enantiomers is determined by an optical chirality density [1]. Here, we demonstrate that this effect can exist in magnetic spin systems. By constructing a formal analogy with electrodynamics, we show that in antiferromagnets with broken chiral symmetry the asymmetry in local spin-wave energy absorption is proportional to a spin-wave chirality density, which is a direct counterpart of optical zilch. We propose that injection of a pure spin current into an antiferromagnet may serve as a chiral symmetry breaking mechanism, since its effect in the spin-wave approximation can be expressed in terms of additional Lifshitz invariants. We use linear response theory to show that the spin current induces a nonequilibrium spin-wave chirality density.Comment: 6 pages (plus Supplemental Material, 6 pages), 1 figure, published versio

Size-independence of statistics for boundary collisions of random walks and its implications for spin-polarized gases

A bounded random walk exhibits strong correlations between collisions with a boundary. For an one-dimensional walk, we obtain the full statistical distribution of the number of such collisions in a time t. In the large t limit, the fluctuations in the number of collisions are found to be size-independent (independent of the distance between boundaries). This occurs for any inter-boundary distance, including less and greater than the mean-free-path, and means that this boundary effect does not decay with increasing system-size. As an application, we consider spin-polarized gases, such as 3-Helium, in the three-dimensional diffusive regime. The above results mean that the depolarizing effect of rare magnetic-impurities in the container walls is orders of magnitude larger than a Smoluchowski assumption (to neglect correlations) would imply. This could explain why depolarization is so sensitive to the container's treatment with magnetic fields prior to its use.Comment: 5 page manuscript with extra details in appendices (additional 3 pages

Persistence of Tripartite Nonlocality for Non-inertial Observers

We consider the behaviour of bipartite and tripartite non-locality between fermionic entangled states shared by observers, one of whom uniformly accelerates. We find that while fermionic entanglement persists for arbitrarily large acceleration, the Bell/CHSH inequalities cannot be violated for sufficiently large but finite acceleration. However the Svetlichny inequality, which is a measure of genuine tripartite non-locality, can be violated for any finite value of the acceleration.Comment: 4 pages, pdflatex, 2 figure

Cavity Optomechanics of Topological Spin Textures in Magnetic Insulators

Collective dynamics of topological magnetic textures can be thought of as a massive particle moving in a magnetic pinning potential. We demonstrate that inside a cavity resonator this effective mechanical system can feel the electromagnetic radiation pressure from cavity photons through the magneto-optical inverse Faraday and Cotton-Mouton effects. We estimate values for the effective parameters of the optomechanical coupling for two spin textures -- a Bloch domain wall and a chiral magnetic soliton lattice. The soliton lattice has magnetic chirality, so that in circularly polarized light it behaves like a chiral particle with the sign of the optomechanical coupling determined by the helicity of the light and chirality of the lattice. Most interestingly, we find a level attraction regime for the soliton lattice, which is tunable through an applied magnetic field.Comment: 7 pages, 3 figures, published versio

The State of Sustainable Research Software: Results from the Workshop on Sustainable Software for Science: Practice and Experiences (WSSSPE5.1)

This article summarizes motivations, organization, and activities of the Workshop on Sustainable Software for Science: Practice and Experiences (WSSSPE5.1) held in Manchester, UK in September 2017. The WSSSPE series promotes sustainable research software by positively impacting principles and best practices, careers, learning, and credit. This article discusses the Code of Conduct, idea papers, position papers, experience papers, demos, and lightning talks presented during the workshop. The main part of the article discusses the speed-blogging groups that formed during the meeting, along with the outputs of those sessions

Excitation of magnon spin photocurrents in antiferromagnetic insulators

In the circular photogalvanic effect, circularly polarized light can produce a direct electron photocurrent in metals and the direction of the current depends on the polarization. We suggest that an analogous nonlinear effect exists for antiferromagnetic insulators wherein the total spin of light and spin waves is conserved. In consequence, a spin angular momentum is expected to be transfered from photons to magnons so that a circularly polarized electromagnetic field will generate a direct magnon spin current. The direction of the current is determined by the helicity of the light. We show that this resonant effect appears as a second order light-matter interaction. We find also a geometric contribution to the spin photocurrent, which appears for materials with complex lattice structures and Dzyaloshinskii-Moriya interactions.Comment: 10 pages, 2 figures, published versio

A Modified Magnitude System that Produces Well-Behaved Magnitudes, Colors, and Errors Even for Low Signal-to-Noise Ratio Measurements

We describe a modification of the usual definition of astronomical magnitudes, replacing the usual logarithm with an inverse hyperbolic sine function; we call these modified magnitudes `asinh magnitudes'. For objects detected at signal-to-noise ratios of greater than about five, our modified definition is essentially identical to the traditional one; for fainter objects (including those with a formally negative flux) our definition is well behaved, tending to a definite value with finite errors as the flux goes to zero. This new definition is especially useful when considering the colors of faint objects, as the difference of two `asinh' magnitudes measures the usual flux ratio for bright objects, while avoiding the problems caused by dividing two very uncertain values for faint objects. The Sloan Digital Sky Survey (SDSS) data products will use this scheme to express all magnitudes in their catalogs.Comment: 11 pages, including 3 postscript figures. Submitted to A