Lyapunov spreading of semi-classical wave packets for the Lorentz Gas: theory and applications

We consider the quantum mechanical propagator for a particle moving in a $d$-dimensional Lorentz gas, with fixed, hard sphere scatterers. To evaluate this propagator in the semi-classical region, and for times less than the Ehrenfest time, we express its effect on an initial Gaussian wave packet in terms of quantities analogous to those used to describe the exponential separation of trajectories in the classical version of this system. This result relates the spread of the wave packet to the rate of separation of classical trajectories, characterized by positive Lyapunov exponents. We consider applications of these results, first to illustrate the behavior of the wave-packet auto-correlation functions for wave packets on periodic orbits. The auto-correlation function can be related to the fidelity, or Loschmidt echo, for the special case that the perturbation is a small change in the mass of the particle. An exact expression for the fidelity, appropriate for this perturbation, leads to an analytical result valid over very long time intervals, inversely proportional to the size of the mass perturbation. For such perturbations, we then calculate the long-time echo for semi-classical wave packets on periodic orbits. This paper also corrects an earlier calculation for a quantum echo, included in a previous version of this paper. We explain the reasons for this correction

Crossover from Diffusive to Ballistic Transport in Periodic Quantum Maps

We derive an expression for the mean square displacement of a particle whose motion is governed by a uniform, periodic, quantum multi-baker map. The expression is a function of both time, $t$, and Planck's constant, $\hbar$, and allows a study of both the long time, $t\to\infty$, and semi-classical, $\hbar\to 0$, limits taken in either order. We evaluate the expression using random matrix theory as well as numerically, and observe good agreement between both sets of results. The long time limit shows that particle transport is generically ballistic, for any fixed value of Planck's constant. However, for fixed times, the semi-classical limit leads to diffusion. The mean square displacement for non-zero Planck's constant, and finite time, exhibits a crossover from diffusive to ballistic motion, with crossover time on the order of the inverse of Planck's constant. We argue, that these results are generic for a large class of 1D quantum random walks, similar to the quantum multi-baker, and that a sufficient condition for diffusion in the semi-classical limit is classically chaotic dynamics in each cell. Some connections between our work and the other literature on quantum random walks are discussed. These walks are of some interest in the theory of quantum computation.Comment: Final version to appear in Physica D, Proceedings of the International Workshop and Seminar on Microscopic Chaos and Transport in Many-Particle Systems, Dresden, 2002; corrected a minor error in section 3.1, new section 4.

A spatial data handling system for retrieval of images by unrestricted regions of user interest

The Intelligent Data Management (IDM) project at NASA/Goddard Space Flight Center has prototyped an Intelligent Information Fusion System (IIFS), which automatically ingests metadata from remote sensor observations into a large catalog which is directly queryable by end-users. The greatest challenge in the implementation of this catalog was supporting spatially-driven searches, where the user has a possible complex region of interest and wishes to recover those images that overlap all or simply a part of that region. A spatial data management system is described, which is capable of storing and retrieving records of image data regardless of their source. This system was designed and implemented as part of the IIFS catalog. A new data structure, called a hypercylinder, is central to the design. The hypercylinder is specifically tailored for data distributed over the surface of a sphere, such as satellite observations of the Earth or space. Operations on the hypercylinder are regulated by two expert systems. The first governs the ingest of new metadata records, and maintains the efficiency of the data structure as it grows. The second translates, plans, and executes users' spatial queries, performing incremental optimization as partial query results are returned

Pension systems and reform conceptual framework

The WorldBank's conceptual framework to assess pension systems and reform options evaluates initial conditions and the capacity to improve the enabling environment, and then focuses on how best to work within these to achieve the core objectives of pension systems - protection against the risk of poverty in old age and smoothing consumption from one's work life into retirement. The Bank applies a multi-pillared approach towards pension system modalities to address the needs of target populations including: (i) a non-contributory'zero pillar'extending some level of old-age income security to all of the elderly; (ii) an appropriately sized mandatory'first pillar'with the objective of replacing some portion of lifetime pre-retirement income through contributions linked to earnings; (iii) a funded mandatory defined-contribution'second pillar'that typically provides privately-managed individual savings accounts; (iv) a funded voluntary'third-pillar;'and (v) a non-financial'fourth pillar.'The primary evaluation criteria are the ability of the system to maintain adequacy, affordability, sustainability, equity, predictability, and robustness. The secondary evaluation criteria are the system's capacity to: minimize labor market distortions; contribute to savings mobilization; and contribute to financial market development. Because pension benefits are claims against future economic output, it is essential that over time pension systems contribute to growth and output to support the promised benefits. Going forward, the Bank is focusing on strengthening its support in: (a) establishing a clearer results framework to assess pension systems and reforms; (b) enhancing knowledge management, including research and learning; and (c) improving implementation capacity.Emerging Markets,Debt Markets,Environmental Economics&Policies,Pensions&Retirement Systems,Banks&Banking Reform

Optimal energetic paths for electric cars

A weighted directed graph $G=(V,A,c)$, where $A\subseteq V\times V$ and $c:A\to R$, describes a road network in which an electric car can roam. An arc $uv$ models a road segment connecting the two vertices $u$ and $v$. The cost $c(uv)$ of an arc $uv$ is the amount of energy the car needs to traverse the arc. This amount may be positive, zero or negative. To make the problem realistic, we assume there are no negative cycles. The car has a battery that can store up to $B$ units of energy. It can traverse an arc $uv\in A$ only if it is at $u$ and the charge $b$ in its battery satisfies $b\ge c(uv)$. If it traverses the arc, it reaches $v$ with a charge of $\min(b-c(uv),B)$. Arcs with positive costs deplete the battery, arcs with negative costs charge the battery, but not above its capacity of $B$. Given $s,t\in V$, can the car travel from $s$ to $t$, starting at $s$ with an initial charge $b$, where $0\le b\le B$? If so, what is the maximum charge with which the car can reach $t$? Equivalently, what is the smallest $\delta_{B,b}(s,t)$ such that the car can reach $t$ with a charge of $b-\delta_{B,b}(s,t)$, and which path should the car follow to achieve this? We refer to $\delta_{B,b}(s,t)$ as the energetic cost of traveling from $s$ to $t$. We let $\delta_{B,b}(s,t)=\infty$ if the car cannot travel from $s$ to $t$ starting with an initial charge of $b$. The problem of computing energetic costs is a strict generalization of the standard shortest paths problem. We show that the single-source minimum energetic paths problem can be solved using simple, but subtle, adaptations of the Bellman-Ford and Dijkstra algorithms. To make Dijkstra's algorithm work in the presence of negative arcs, but no negative cycles, we use a variant of the $A^*$ search heuristic. These results are explicit or implicit in some previous papers. We provide a simpler and unified description of these algorithms.Comment: 11 page

Status of the profession

The number of astronomers has grown by about 40 percent over the past decade. The number of astronomers with jobs in industry, or with long-term, non-tenured, jobs has increased dramatically compared with traditional faculty positions. The increase in the number of astronomers and the declining share of the NSF budget going to astronomy has led to extreme difficulties in the NSF grant program and in support of the National Observatories. In 1989, direct NASA support of astronomers through the grants program exceeds that of NSF, although the total of the NSF grants program over decade far exceeds that of NASA. Access to major new telescopes will be important issue for the 1990s. US astronomers, who once had a monopoly on telescopes larger than 3 meters, will, by the year 2000, have access to just half of the world's optical telescope area

Development, Implementation and Outcomes of a Quality Assurance System for the Provision of Continuous Renal Replacement Therapy in the Intensive Care Unit

Critically ill patients with requirement of continuous renal replacement therapy (CRRT) represent a growing intensive care unit (ICU) population. Optimal CRRT delivery demands continuous communication between stakeholders, iterative adjustment of therapy, and quality assurance systems. This Quality Improvement (QI) study reports the development, implementation and outcomes of a quality assurance system to support the provision of CRRT in the ICU. This study was carried out at the University of Kentucky Medical Center between September 2016 and June 2019. We implemented a quality assurance system using a step-wise approach based on the (a) assembly of a multidisciplinary team, (b) standardization of the CRRT protocol, (c) creation of electronic CRRT flowsheets, (d) selection, monitoring and reporting of quality metrics of CRRT deliverables, and (e) enhancement of education. We examined 34-month data comprising 1185 adult patients on CRRT (~ 7420 patient-days of CRRT) and tracked selected QI outcomes/metrics of CRRT delivery. As a result of the QI interventions, we increased the number of multidisciplinary experts in the CRRT team and ensured a continuum of education to health care professionals. We maximized to 100% the use of continuous veno-venous hemodiafiltration and doubled the percentage of patients using regional citrate anticoagulation. The delivered CRRT effluent dose (~ 30 ml/kg/h) and the delivered/prescribed effluent dose ratio (~ 0.89) remained stable within the study period. The average filter life increased from 26 to 31 h (p = 0.020), reducing the mean utilization of filters per patient from 3.56 to 2.67 (p = 0.054) despite similar CRRT duration and mortality rates. The number of CRRT access alarms per treatment day was reduced by 43%. The improvement in filter utilization translated into ~ 20,000 USD gross savings in filter cost per 100-patient receiving CRRT. We satisfactorily developed and implemented a quality assurance system for the provision of CRRT in the ICU that enabled sustainable tracking of CRRT deliverables and reduced filter resource utilization at our institution