Quantum Chaos, Delocalization, and Entanglement in Disordered Heisenberg Models

We investigate disordered one- and two-dimensional Heisenberg spin lattices across a transition from integrability to quantum chaos from both a statistical many-body and a quantum-information perspective. Special emphasis is devoted to quantitatively exploring the interplay between eigenvector statistics, delocalization, and entanglement in the presence of nontrivial symmetries. The implications of basis dependence of state delocalization indicators (such as the number of principal components) is addressed, and a measure of {\em relative delocalization} is proposed in order to robustly characterize the onset of chaos in the presence of disorder. Both standard multipartite and {\em generalized entanglement} are investigated in a wide parameter regime by using a family of spin- and fermion- purity measures, their dependence on delocalization and on energy spectrum statistics being examined. A distinctive {\em correlation between entanglement, delocalization, and integrability} is uncovered, which may be generic to systems described by the two-body random ensemble and may point to a new diagnostic tool for quantum chaos. Analytical estimates for typical entanglement of random pure states restricted to a proper subspace of the full Hilbert space are also established and compared with random matrix theory predictions.Comment: 17 pages, 10 figures, revised versio

Parameters of Pseudorandom Quantum Circuits

Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudorandom circuits, with the goal of identifying relevant tradeoffs and optimizing convergence. The parameters we explore include the choice of single- and two-qubit gates, the topology of the underlying physical qubit architecture, the probabilistic application of two-qubit gates, as well as circuit size, initialization, and the effect of control constraints. Building on the equivalence between pseudorandom circuits and approximate t-designs, a Markov matrix approach is employed to analyze asymptotic convergence properties of pseudorandom second-order moments to a 2-design. Quantitative results on the convergence rate as a function of the circuit size are presented for qubit topologies with a sufficient degree of symmetry. Our results may be useful towards optimizing the efficiency of random state and operator generation

Quantum Pseudorandomness from Cluster-State Quantum Computation

We show how to efficiently generate pseudorandom states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudorandom algorithms in the cluster-state picture, we identify a strategy for optimizing pseudorandom circuits by properly choosing single-qubit rotations. A Markov chain analysis provides the tool for analyzing convergence rates to the Haar measure and finding the optimal single-qubit gate distribution. Our results may be viewed as an alternative construction of approximate unitary 2-designs

Fate and Transport of Low-Ph Hazardous Materials After Deep Well Disposal.

The ultimate fate and chemical kinetics of low-pH hazardous wastes after deep well injection were studied. Two experimental approaches were taken. Chemical kinetics of reactions involving acids and typical formation clays was studied using a batch reaction scheme. The effects of reactions involving flowing acidic waste streams and disposal formations were characterized using sand packs of length one foot, four feet, and twenty feet. A numerical ground water flow simulator was used to model the interactions of flowing acidic wastes with linear sand packs and with a hypothetical waste disposal system. Reaction rate coefficients and activation energies were determined for reactions of hydrochloric acid, nitric acid, and sulfuric acid with sodium montmorillonite, kaolinite, and illite. Reactions were studied at temperature of fifty degrees Celsius (122 degrees Fahrenheit) and seventy degrees Celsius (158 degrees Fahrenheit). Values of rate coefficients and activation energies agree reasonably well with those obtained by a previous investigator using a different experimental approach. Sand pack experimentation provided evidence of the neutralizing effect on acid of typical formation clays. Sand packs containing typical proportions of sodium montmorillonite, illite, and kaolinite were found to have a neutralizing effect on hydrochloric acid, nitric acid, and sulfuric acid. Actual formation material from a waste disposal well in St. Bernard Parish, Louisiana (the Kaiser well), was found to neutralize hydrochloric acid. The Kaiser well material was the most effective at neutralizing acid, and kaolinite was the least effective at neutralizing acid. The ground water flow simulator SUTRA was used to simulate flow of acidic fluids through sand packs containing Kaiser well material. Simulated results of one foot, four foot, and twenty foot sand pack runs agree reasonably well with experimental results. SUTRA was used to model a hypothetical but realistic low-pH waste disposal system in which wastes were injected for periods of time up to twenty years

Sonification Mapping Configurations: Pairings Of Real-Time Exhibits And Sound

Presented at the 19th International Conference on Auditory Display (ICAD2013) on July 6-9, 2013 in Lodz, Poland.Visitors to aquariums typically rely on their vision to interact with live exhibits that convey rich descriptive and aesthetic visual information. However, some visitors may prefer or need to have an alternative interpretation of the exhibitÕs visual scene to improve their experience. Musical sonification has been explored as an interpretive strategy for this purpose and related work provides some guidance for sonification design, yet more empirical work on developing and validating the music-to-visual scene mappings needs to be completed. This paper discusses work to validate mappings that were developed through an investigation of musician performances for two specific live animal exhibits at the Georgia Aquarium. In this proposed study, participants will provide feedback on musical mapping examples which will help inform design of a real-time sonification system for aquarium exhibits. Here, we describe our motivation, methods, and expected contributions

Review of best management practices for aquatic vegetation control in stormwater ponds, wetlands, and lakes

Auckland Council (AC) is responsible for the development and operation of a stormwater network across the region to avert risks to citizens and the environment. Within this stormwater network, aquatic vegetation (including plants, unicellular and filamentous algae) can have both a positive and negative role in stormwater management and water quality treatment. The situations where management is needed to control aquatic vegetation are not always clear, and an inability to identify effective, feasible and economical control options may constrain management initiatives. AC (Infrastructure and Technical Services, Stormwater) commissioned this technical report to provide information for decision- making on aquatic vegetation management with in stormwater systems that are likely to experience vegetation-related issues. Information was collated from a comprehensive literature review, augmented by knowledge held by the authors. This review identified a wide range of management practices that could be potentially employed. It also demonstrated complexities and uncertainties relating to these options that makes the identification of a best management practice difficult. Hence, the focus of this report was to enable users to screen for potential options, and use reference material provided on each option to confirm the best practice to employ for each situation. The report identifies factors to define whether there is an aquatic vegetation problem (Section 3.0), and emphasises the need for agreed management goals for control (e.g. reduction, mitigation, containment, eradication). Resources to screen which management option(s) to employ are provided (Section 4.0), relating to the target aquatic vegetation, likely applicability of options to the system being managed, indicative cost, and ease of implementation. Initial screening allows users to shortlist potential control options for further reference (Section 5.0). Thirty-five control options are described (Section 5.0) in sufficient detail to consider applicability to individual sites and species. These options are grouped under categories of biological, chemical or physical control. Biological control options involve the use of organisms to predate, infect or control vegetation growth (e.g. classical biological control) or manipulate conditions to control algal growth (e.g. pest fish removal, microbial products). Chemical control options involve the use of pesticides and chemicals (e.g. glyphosate, diquat), or the use of flocculants and nutrient inactivation products that are used to reduce nutrient loading, thereby decreasing algal growth. Physical control options involve removing vegetation or algal biomass (e.g. mechanical or manual harvesting), or setting up barriers to their growth (e.g. shading, bottom lining, sediment capping). Preventative management options are usually the most cost effective, and these are also briefly described (Section 6.0). For example, the use of hygiene or quarantine protocols can reduce weed introductions or spread. Catchment- based practices to reduce sediment and nutrient sources to stormwater are likely to assist in the avoidance of algal and possibly aquatic plant problems. Nutrient removal may be a co-benefit where harvesting of submerged weed biomass is undertaken in stormwater systems. It should also be considered that removal of substantial amounts of submerged vegetation may result in a sudden and difficult-to-reverse s witch to a turbid, phytoplankton dominated state. Another possible solution is the conversion of systems that experience aquatic vegetation issues, to systems that are less likely to experience issues. The focus of this report is on systems that receive significant stormwater inputs, i.e. constructed bodies, including ponds, amenity lakes, wetlands, and highly-modified receiving bodies. However, some information will have application to other natural water bodies

Quantum pseudo-randomness from cluster-state quantum computation

We show how to efficiently generate pseudo-random states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudo-random algorithms in the cluster-state picture, we identify a strategy for optimizing pseudo-random circuits by properly choosing single-qubit rotations. A Markov chain analysis provides the tool for analyzing convergence rates to the Haar measure and finding the optimal single-qubit gate distribution. Our results may be viewed as an alternative construction of approximate unitary 2-designs.Comment: 4 pages, 4 figures, version appearing in Phys. Rev.

Parameters of Pseudo-Random Quantum Circuits

Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudo-random circuits, with the goal of identifying relevant trade-offs and optimizing convergence. The parameters we explore include the choice of single- and two-qubit gates, the topology of the underlying physical qubit architecture, the probabilistic application of two-qubit gates, as well as circuit size, initialization, and the effect of control constraints. Building on the equivalence between pseudo-random circuits and approximate $t$-designs, a Markov matrix approach is employed to analyze asymptotic convergence properties of pseudo-random second-order moments to a 2-design. Quantitative results on the convergence rate as a function of the circuit size are presented for qubit topologies with a sufficient degree of symmetry. Our results may be theoretically and practically useful to optimize the efficiency of random state and operator generation.Comment: 17 pages, 14 figures, 2 Appendice