Convergence of Quantum Annealing with Real-Time Schrodinger Dynamics

Convergence conditions for quantum annealing are derived for optimization problems represented by the Ising model of a general form. Quantum fluctuations are introduced as a transverse field and/or transverse ferromagnetic interactions, and the time evolution follows the real-time Schrodinger equation. It is shown that the system stays arbitrarily close to the instantaneous ground state, finally reaching the target optimal state, if the strength of quantum fluctuations decreases sufficiently slowly, in particular inversely proportionally to the power of time in the asymptotic region. This is the same condition as the other implementations of quantum annealing, quantum Monte Carlo and Green's function Monte Carlo simulations, in spite of the essential difference in the type of dynamics. The method of analysis is an application of the adiabatic theorem in conjunction with an estimate of a lower bound of the energy gap based on the recently proposed idea of Somma et. al. for the analysis of classical simulated annealing using a classical-quantum correspondence.Comment: 6 pages, minor correction

Convergence theorems for quantum annealing

We prove several theorems to give sufficient conditions for convergence of quantum annealing, which is a protocol to solve generic optimization problems by quantum dynamics. In particular the property of strong ergodicity is proved for the path-integral Monte Carlo implementation of quantum annealing for the transverse Ising model under a power decay of the transverse field. This result is to be compared with the much slower inverse-log decay of temperature in the conventional simulated annealing. Similar results are proved for the Green's function Monte Carlo approach. Optimization problems in continuous space of particle configurations are also discussed.Comment: 19 page

Elemental and Ultrastructural Characteristics of the Egg Capsules of Nautilus Pompilius

Six pearly nautili (Nautilus pompilius) raised in captivity produced nonviable egg capsules which were examined using scanning electron microscopy ( SE M) and energy dispersive x-ray spectrometry (EDS). Macro and microscopic observations revealed two distinct and separate walls encircling the yolk sac. Both walls exhibited a porous appearance in cross-section. Protein analysis demonstrated the proteinaceous nature of nidimental gland secretions and egg capsule walls. EDS analysis of each wall shows the elemental composition to be identical in both, with each wall containing similar proportions of S, CI, Mg, Na, K, and trace amounts of Ca. X-ray mapping of Na and Cl along each wall surface suggests similar construction of both walls. EDS analysis of the nidimental gland secretions of the adult female nautilus have shown a composition similar to that of the egg capsule

Oxygen isotopic composition of nitrate and nitrite produced by nitrifying cocultures and natural marine assemblages

Author Posting. © Association for the Sciences of Limnology and Oceanography, 2012. This article is posted here by permission of Association for the Sciences of Limnology and Oceanography for personal use, not for redistribution. The definitive version was published in Limnology and Oceanography 57 (2012): 1361-1375, doi:10.4319/lo.2012.57.5.1361.The δ18O value of nitrate produced during nitrification (δ18ONO3,nit) was measured in experiments designed to mimic oceanic conditions, involving cocultures of ammonia-oxidizing bacteria or ammonia-oxidizing archaea and nitrite-oxidizing bacteria, as well as natural marine assemblages. The estimates of ranged from −1.5‰ ± 0.1‰ to +1.3‰ ± 1.4‰ at δ18O values of water (H2O) and dissolved oxygen (O2) of 0‰ and 24.2‰ vs. Vienna Standard Mean Ocean Water, respectively. Additions of 18O-enriched H2O allowed us to evaluate the effects of oxygen (O) isotope fractionation and exchange on . Kinetic isotope effects for the incorporation of O atoms were the most important factors for setting overall values relative to the substrates (O2 and H2O). These isotope effects ranged from +10‰ to +22‰ for ammonia oxidation (O2 plus H2O incorporation) and from +1‰ to +27‰ for incorporation of H2O during nitrite oxidation. values were also affected by the amount and duration of nitrite accumulation, which permitted abiotic O atom exchange between nitrite and H2O. Coculture incubations where ammonia oxidation and nitrite oxidation were tightly coupled showed low levels of nitrite accumulation and exchange (3% ± 4%). These experiments had values of −1.5‰ to +0.7‰. Field experiments had greater accumulation of nitrite and a higher amount of exchange (22% to 100%), yielding an average value of +1.9‰ ± 3.0‰. Low levels of biologically catalyzed exchange in coculture experiments may be representative of nitrification in much of the ocean where nitrite accumulation is low. Abiotic oxygen isotope exchange may be important where nitrite does accumulate, such as oceanic primary and secondary nitrite maxima.This research was funded by the National Science Foundation Chemical Oceanography grants 05-26277 and 09- 610998 to K.L.C

Entanglement renormalization of anisotropic XY model

The renormalization group flows of the one-dimensional anisotropic XY model and quantum Ising model under a transverse field are obtained by different multiscale entanglement renormalization ansatz schemes. It is shown that the optimized disentangler removes the short-range entanglement by rotating the system in the parameter space spanned by the anisotropy and the magnetic field. It is understood from the study that the disentangler reduces the entanglement by mapping the system to another one in the same universality class but with smaller short range entanglement. The phase boundary and corresponding critical exponents are calculated using different schemes with different block sizes, look-ahead steps and truncation dimensions. It is shown that larger truncation dimension leads to more accurate results and that using larger block size or look-ahead step improve the overall calculation consistency.Comment: 5 pages, 3 figure

Analytical and experimental studies of impinging liquid jets

Impinging injectors are a common type of injector used in liquid propellant rocket engines and are typically used in engines where both propellants are injected as a liquid, e.g., engines using LOX/hydrocarbon and storable propellant combinations. The present research program is focused on providing the requisite fundamental understanding associated with impinging jet injectors for the development of an advanced a priori combustion stability design analysis capability. To date, a systematic study of the atomization characteristics of impinging liquid jets under cold-flow conditions have been completed. Effects of orifice diameter, impingement angle, pre-impingement length, orifice length-to-diameter ratio, fabrication procedure, jet flow condition and jet velocity under steady and oscillating, and atmospheric- and high-pressure environments have been investigated. Results of these experimental studies have been compared to current models of sheet breakup and drop formation. In addition, the research findings have been scrutinized to provide a fundamental explanation for a proven empirical correlation used in the design of stable impinging injector-based rocket engines

Nitrogen cycling in the secondary nitrite maximum of the eastern tropical North Pacific off Costa Rica

Author Posting. © American Geophysical Union, 2015. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Global Biogeochemical Cycles 29 (2015): 2061–2081, doi:10.1002/2015GB005187.Nitrite is a central intermediate in the marine nitrogen cycle and represents a critical juncture where nitrogen can be reduced to the less bioavailable N2 gas or oxidized to nitrate and retained in a more bioavailable form. We present an analysis of rates of microbial nitrogen transformations in the oxygen deficient zone (ODZ) within the eastern tropical North Pacific Ocean (ETNP). We determined rates using a novel one-dimensional model using the distribution of nitrite and nitrate concentrations, along with their natural abundance nitrogen (N) and oxygen (O) isotope profiles. We predict rate profiles for nitrate reduction, nitrite reduction, and nitrite oxidation throughout the ODZ, as well as the contributions of anammox to nitrite reduction and nitrite oxidation. Nitrate reduction occurs at a maximum rate of 25 nM d−1 at the top of the ODZ, at the same depth as the maximum rate of nitrite reduction, 15 nM d−1. Nitrite oxidation occurs at maximum rates of 10 nM d−1 above the secondary nitrite maximum, but also in the secondary nitrite maximum, within the ODZ. Anammox contributes to nitrite oxidation within the ODZ but cannot account for all of it. Nitrite oxidation within the ODZ that is not through anammox is also supported by microbial gene abundance profiles. Our results suggest the presence of nitrite oxidation within the ETNP ODZ, with implications for the distribution and physiology of marine nitrite-oxidizing bacteria, and for total nitrogen loss in the largest marine ODZ.National Science Foundation. Grant Numbers OCE 05-26277, OCE 09-610998; WHOI Coastal Ocean Institute2016-06-1