Simplified landscapes for optimization of shaken lattice interferometry

Motivated by recent results using shaken optical lattices to perform atom interferometry, we explore splitting of an atom cloud trapped in a phase-modulated ("shaken") optical lattice. Using a simple analytic model we are able to show that we can obtain the simplest case of $\pm2\hbar k_\mathrm{L}$ splitting via single-frequency shaking. This is confirmed both via simulation and experiment. Furthermore, we are able to split with a relative phase $\theta$ between the two split arms of $0$ or $\pi$ depending on our shaking frequency. Addressing higher-order splitting, we determine that $\pm6\hbar k_\mathrm{L}$ splitting is sufficient to be able to accelerate the atoms in counter-propagating lattices. Finally, we show that we can use a genetic algorithm to optimize $\pm4\hbar k_\mathrm{L}$ and $\pm6\hbar k_\mathrm{L}$ splitting to within $\approx0.1\%$ by restricting our optimization to the resonance frequencies corresponding to single- and two-photon transitions between Bloch bands

Open quantum systems approach to atomtronics

We derive a quantum master equation to treat quantum systems interacting with multiple reservoirs. The formalism is used to investigate atomic transport across a variety of lattice configurations. We demonstrate how the behavior of an electronic diode, a field-effect transistor, and a bipolar junction transistor can be realized with neutral, ultracold atoms trapped in optical lattices. An analysis of the current fluctuations is provided for the case of the atomtronic diode. Finally, we show that it is possible to demonstrate AND logic gate behavior in an optical lattice.Comment: 10 pages, 10 figures, 1 tabl

Non-unique factorization of polynomials over residue class rings of the integers

We investigate non-unique factorization of polynomials in Z_{p^n}[x] into irreducibles. As a Noetherian ring whose zero-divisors are contained in the Jacobson radical, Z_{p^n}[x] is atomic. We reduce the question of factoring arbitrary non-zero polynomials into irreducibles to the problem of factoring monic polynomials into monic irreducibles. The multiplicative monoid of monic polynomials of Z_{p^n}[x] is a direct sum of monoids corresponding to irreducible polynomials in Z_p[x], and we show that each of these monoids has infinite elasticity. Moreover, for every positive integer m, there exists in each of these monoids a product of 2 irreducibles that can also be represented as a product of m irreducibles.Comment: 11 page

OPERA superluminal neutrinos and Kinematics in Finsler spacetime

The OPERA collaboration recently reported that muon neutrinos could be superluminal. More recently, Cohen and Glashow pointed that such superluminal neutrinos would be suppressed since they lose their energies rapidly via bremsstrahlung. In this Letter, we propose that Finslerian nature of spacetime could account for the superluminal phenomena of particles. The Finsler spacetime permits the existence of superluminal behavior of particles while the casuality still holds. A new dispersion relation is obtained in a class of Finsler spacetime. It is shown that the superluminal speed is linearly dependent on the energy per unit mass of the particle. We find that such a superluminal speed formula is consistent with data of OPERA, MINOS and Fermilab-1979 neutrino experiments as well as observations on neutrinos from SN1987a.Comment: 10 pages, 2 figures. Viewpoints of Finslerian special relativity on OPERA superluminal neutrino

Multiple Factorizations of Bivariate Linear Partial Differential Operators

We study the case when a bivariate Linear Partial Differential Operator (LPDO) of orders three or four has several different factorizations. We prove that a third-order bivariate LPDO has a first-order left and right factors such that their symbols are co-prime if and only if the operator has a factorization into three factors, the left one of which is exactly the initial left factor and the right one is exactly the initial right factor. We show that the condition that the symbols of the initial left and right factors are co-prime is essential, and that the analogous statement "as it is" is not true for LPDOs of order four. Then we consider completely reducible LPDOs, which are defined as an intersection of principal ideals. Such operators may also be required to have several different factorizations. Considering all possible cases, we ruled out some of them from the consideration due to the first result of the paper. The explicit formulae for the sufficient conditions for the complete reducibility of an LPDO were found also

The Infrared and Radio Fluxes Densities of Galactic HII Regions

We derive infrared and radio flux densities of all ~1000 known Galactic HII regions in the Galactic longitude range 17.5 < l < 65 degree. Our sample comes from the Wide-Field Infrared Survey Explorer (WISE) catalog of Galactic \hii regions \citep{anderson2014}. We compute flux densities at six wavelengths in the infrared (GLIMPSE 8 microns, WISE 12 microns and 22 microns, MIPSGAL 24 microns, and Hi-GAL 70 microns and 160 microns) and two in the radio (MAGPIS 20 cm and VGPS 21 cm). All HII region infrared flux densities are strongly correlated with their ~20 cm flux densities. All HII regions used here, regardless of physical size or Galactocentric radius, have similar infrared to radio flux density ratios and similar infrared colors, although the smallest regions ($r<1\,$pc), have slightly elevated IR to radio ratios. The colors $\log_{10}(F_{24 micron}/F_{12 micron}) \ge 0$ and $\log_{10}(F_{70 micron}/F_{12 micron}) \ge 1.2$, and $\log_{10}(F_{24 micron}/F_{12 micron}) \ge 0$ and $\log_{10}(F_{160 micron}/F_{70 micron}) \le 0.67$ reliably select HII regions, independent of size. The infrared colors of ~22$\%$ of HII regions, spanning a large range of physical sizes, satisfy the IRAS color criteria of \citet{wood1989} for HII regions, after adjusting the criteria to the wavelengths used here. Since these color criteria are commonly thought to select only ultra-compact HII regions, this result indicates that the true ultra-compact HII region population is uncertain. Comparing with a sample of IR color indices from star-forming galaxies, HII regions show higher $\log_{10}(F_{70 micron}/F_{12 micron})$ ratios. We find a weak trend of decreasing infrared to ~20 cm flux density ratios with increasing $R_{gal}$, in agreement with previous extragalactic results, possibly indicating a decreased dust abundance in the outer Galaxy.Comment: 27 pages, 16 figures, 5 table

How Algorithmic Confounding in Recommendation Systems Increases Homogeneity and Decreases Utility

Recommendation systems are ubiquitous and impact many domains; they have the potential to influence product consumption, individuals' perceptions of the world, and life-altering decisions. These systems are often evaluated or trained with data from users already exposed to algorithmic recommendations; this creates a pernicious feedback loop. Using simulations, we demonstrate how using data confounded in this way homogenizes user behavior without increasing utility