Systematic study of finite-size effects in quantum Monte Carlo calculations of real metallic systems

We present a systematic and comprehensive study of finite-size effects in diffusion quantum Monte Carlo calculations of metals. Several previously introduced schemes for correcting finite-size errors are compared for accuracy and efficiency, and practical improvements are introduced. In particular, we test a simple but efficient method of finite-size correction based on an accurate combination of twist averaging and density functional theory. Our diffusion quantum Monte Carlo results for lithium and aluminum, as examples of metallic systems, demonstrate excellent agreement between all of the approaches considered

Three results on representations of Mackey Lie algebras

I. Penkov and V. Serganova have recently introduced, for any non-degenerate pairing $W\otimes V\to\mathbb C$ of vector spaces, the Lie algebra $\mathfrak{gl}^M=\mathfrak{gl}^M(V,W)$ consisting of endomorphisms of $V$ whose duals preserve $W\subseteq V^*$. In their work, the category $\mathbb{T}_{\mathfrak{gl}^M}$ of $\mathfrak{gl}^M$-modules which are finite length subquotients of the tensor algebra $T(W\otimes V)$ is singled out and studied. In this note we solve three problems posed by these authors concerning the categories $\mathbb{T}_{\mathfrak{gl}^M}$. Denoting by $\mathbb{T}_{V\otimes W}$ the category with the same objects as $\mathbb{T}_{\mathfrak{gl}^M}$ but regarded as $V\otimes W$-modules, we first show that when $W$ and $V$ are paired by dual bases, the functor $\mathbb{T}_{\mathfrak{gl}^M}\to \mathbb{T}_{V\otimes W}$ taking a module to its largest weight submodule with respect to a sufficiently nice Cartan subalgebra of $V\otimes W$ is a tensor equivalence. Secondly, we prove that when $W$ and $V$ are countable-dimensional, the objects of $\mathbb{T}_{\mathrm{End}(V)}$ have finite length as $\mathfrak{gl}^M$-modules. Finally, under the same hypotheses, we compute the socle filtration of a simple object in $\mathbb{T}_{\mathrm{End}(V)}$ as a $\mathfrak{gl}^M$-module.Comment: 9 page

Astrometry.net: Blind astrometric calibration of arbitrary astronomical images

We have built a reliable and robust system that takes as input an astronomical image, and returns as output the pointing, scale, and orientation of that image (the astrometric calibration or WCS information). The system requires no first guess, and works with the information in the image pixels alone; that is, the problem is a generalization of the "lost in space" problem in which nothing--not even the image scale--is known. After robust source detection is performed in the input image, asterisms (sets of four or five stars) are geometrically hashed and compared to pre-indexed hashes to generate hypotheses about the astrometric calibration. A hypothesis is only accepted as true if it passes a Bayesian decision theory test against a background hypothesis. With indices built from the USNO-B Catalog and designed for uniformity of coverage and redundancy, the success rate is 99.9% for contemporary near-ultraviolet and visual imaging survey data, with no false positives. The failure rate is consistent with the incompleteness of the USNO-B Catalog; augmentation with indices built from the 2MASS Catalog brings the completeness to 100% with no false positives. We are using this system to generate consistent and standards-compliant meta-data for digital and digitized imaging from plate repositories, automated observatories, individual scientific investigators, and hobbyists. This is the first step in a program of making it possible to trust calibration meta-data for astronomical data of arbitrary provenance.Comment: submitted to A

Using Classical Probability To Guarantee Properties of Infinite Quantum Sequences

We consider the product of infinitely many copies of a spin-$1\over 2$ system. We construct projection operators on the corresponding nonseparable Hilbert space which measure whether the outcome of an infinite sequence of $\sigma^x$ measurements has any specified property. In many cases, product states are eigenstates of the projections, and therefore the result of measuring the property is determined. Thus we obtain a nonprobabilistic quantum analogue to the law of large numbers, the randomness property, and all other familiar almost-sure theorems of classical probability.Comment: 7 pages in LaTe

Underlying event sensitive observables in Drell-Yan production using GENEVA

We present an extension of the GENEVA Monte Carlo framework to include multiple parton interactions (MPI) provided by PYTHIA8. This allows us to obtain predictions for underlying-event sensitive measurements in Drell-Yan production, in conjunction with GENEVA's fully-differential NNLO calculation, NNLL' resummation for the 0-jet resolution variable (beam thrust), and NLL resummation for the 1-jet resolution variable. We describe the interface with the parton shower algorithm and MPI model of PYTHIA8, which preserves both the precision of partonic N-jet cross sections in GENEVA as well as the shower accuracy and good description of soft hadronic physics of PYTHIA8. We present results for several underlying-event sensitive observables and compare to data from ATLAS and CMS as well as to standalone PYTHIA8 predictions. This includes a comparison with the recent ATLAS measurement of the beam thrust spectrum, which provides a potential avenue to fully disentangle the physical effects from the primary hard interaction, primary soft radiation, multiple parton interactions, and nonperturbative hadronization.Comment: 23 pages, 11 figures. v3: version accepted by EPJ