Complete controllability of finite-level quantum systems

Complete controllability is a fundamental issue in the field of control of quantum systems, not least because of its implications for dynamical realizability of the kinematical bounds on the optimization of observables. In this paper we investigate the question of complete controllability for finite-level quantum systems subject to a single control field, for which the interaction is of dipole form. Sufficient criteria for complete controllability of a wide range of finite-level quantum systems are established and the question of limits of complete controllability is addressed. Finally, the results are applied to give a classification of complete controllability for four-level systems.Comment: 14 pages, IoP-LaTe

Orbits of quantum states and geometry of Bloch vectors for NN-level systems

Physical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than two. To shed some light on the complicated structure of the set of quantum states, we consider a stratification with strata given by unitary orbit manifolds, which can be identified with flag manifolds. The results are applied to study the geometry of the coherence vector for n-level quantum systems. It is shown that the unitary orbits can be naturally identified with spheres in R^{n^2-1} only for n=2. In higher dimensions the coherence vector only defines a non-surjective embedding into a closed ball. A detailed analysis of the three-level case is presented. Finally, a refined stratification in terms of symplectic orbits is considered.Comment: 15 pages LaTeX, 3 figures, reformatted, slightly modified version, corrected eq.(3), to appear in J. Physics

Identifying Evidence-Based Educational Practices: Which Research Designs Provide Findings that Can Influence Social Change?

We conducted this conceptual study to determine if the Institute of Education Sciences/National Science Foundation pipeline of evidence guidelines could be applied as a protocol that researchers could follow in establishing evidence of effective instructional practices. To do this, we compared these guidelines, new drug development process, and our own research on major methodological designs and found that they show remarkable consistency in the process by which types of studies intended to answer different research questions build a body of evidence for practice, whether that practice is in the instructional environment or health care environment. However, none of the protocols offers a constellation of studies at each stage that would be essential for movement to the next stage or the indicators of quality for each type of study. The goal of this effort is to develop consensus in the educational research community about a pipeline of evidence protocol that provides educators with confidence that the instructional practices they employ have a high likelihood of success and will enable a positive impact on the student’s learning and, in the broader context, the student’s ability to contribute to society

Relevance of the IES/NSF Protocol to Identification of Evidence-Based Practices

The Institute of Education Sciences (IES) and the National Science Foundation (NSF) issued common guidelines that provide a protocol by which the use of particular methodological designs in a line of research inquiry provides evidence for each successive step in the process of bringing any given instructional intervention into practice. Our purpose was to determine if research on two widely used literacy instruction approaches has been conducted at each methodological stage in the IES/NSF protocol and is relevant to identifying the approach as an evidence-based practice. We applied the IES/NSF pipeline-of-evidence guidelines to assess whether practices touted as having a research base for effectiveness have emerged from an accumulation of empirical evidence and identification of conceptual or theoretical frameworks. In mapping the six steps of the IES/NSF protocol onto the shared book reading and reciprocal teaching studies that had met What Works Clearinghouse evidence standards, we found that only reciprocal teaching involved research at each stage in the protocol and only reciprocal teaching was identified as an evidence-based instructional approach by the What Works Clearinghouse. Our results indicate that the IES/NSF pipeline-of-evidence protocol offers a productive approach to identifying evidence-based practices. The different trajectories of research on reciprocal teaching and shared book reading indicates that research at each stage in the protocol is important to the development of an instructional approach that ultimately demonstrates effectiveness in improving student learning outcomes

IES/NSF Pipeline-of-Evidence Protocol as Explanation for Successes and Failures of Gates Foundation Funded Initiatives

This study was designed to investigate the applicability of the IES/NSF pipeline-of-evidence protocol in ascertaining why two notable educational initiatives spearheaded and financially supported by the Bill and Melinda Gates Foundation achieved or not the goal of improved academic outcomes for K-12 public school students. Our interest was not whether there is a sufficient body of high quality research evidence to support the two initiatives but whether the research considered by the Gates Foundation established the likelihood that the initiatives would be successful and worth the decision to dedicate substantial funding, time, and effort required for each versus the many competing programs seeking sponsorship. We found that in the case of Intensive Partnerships for Effective Teaching, foundational, efficacy, and effectiveness research were absent and the Gates foundation discontinued grant support because the initiative had not achieved the goal of improved high school graduation and college attendance among low-income minority students. In the case of Early College High School, we found empirical evidence was manifest at all but the effectiveness stage of the pipeline and the initiative continued to receive funding. Our findings support the importance of widening the net of methodologies that constitute a framework for elements needed to make predictions of effectiveness for any given intervention before investing in scale-up initiatives and the need for private foundations to be transparent in their decision-making process to enable others to scrutinize the research that informs the design of initiatives

Cyclic di-GMP mediates a histidine kinase/phosphatase switch by noncovalent domain cross-linking

Histidine kinases are key components of regulatory networks in bacteria. Although many of these enzymes are bifunctional, mediating both phosphorylation and dephosphorylation of downstream targets, the molecular details of this central regulatory switch are unclear. We showed recently that the universal second messenger cyclic di-guanosine monophosphate (c-di-GMP) drives Caulobacter crescentus cell cycle progression by forcing the cell cycle kinase CckA from its default kinase into phosphatase mode. We use a combination of structure determination, modeling, and functional analysis to demonstrate that c-di-GMP reciprocally regulates the two antagonistic CckA activities through noncovalent cross-linking of the catalytic domain with the dimerization histidine phosphotransfer (DHp) domain. We demonstrate that both c-di-GMP and ADP (adenosine diphosphate) promote phosphatase activity and propose that c-di-GMP stabilizes the ADP-bound quaternary structure, which allows the receiver domain to access the dimeric DHp stem for dephosphorylation. In silico analyses predict that c-di-GMP control is widespread among bacterial histidine kinases, arguing that it can replace or modulate canonical transmembrane signaling

Optimal Control of One-Qubit Gates

We consider the problem of carrying an initial Bloch vector to a final Bloch vector in a specified amount of time under the action of three control fields (a vector control field). We show that this control problem is solvable and therefore it is possible to optimize the control. We choose the physically motivated criteria of minimum energy spent in the control, minimum magnitude of the rate of change of the control and a combination of both. We find exact analytical solutions.Comment: 5 page

The effect of spatial resolution on optical and near-IR studies of stellar clusters: Implications for the origin of the red excess

Recent ground based near-IR studies of stellar clusters in nearby galaxies have suggested that young clusters remain embedded for 7-10Myr in their progenitor molecular cloud, in conflict with optical based studies which find that clusters are exposed after 1-3Myr. Here, we investigate the role that spatial resolution plays in this apparent conflict. We use a recent catalogue of young ($5000$~\msun) clusters in the nearby spiral galaxy, M83, along with Hubble Space Telescope (HST) imaging in the optical and near-IR, and ground based near-IR imaging, to see how the colours (and hence estimated properties such as age and extinction) are affected by the aperture size employed, in order to simulate studies of differing resolution. We find that the near-IR is heavily affected by the resolution, and when aperture sizes $>40$~pc are used, all young/blue clusters move red-ward in colour space, which results in their appearance as heavily extincted clusters. However, this is due to contamination from nearby sources and nebular emission, and is not an extinction effect. Optical colours are much less affected by resolution. Due to the larger affect of contamination in the near-IR, we find that, in some cases, clusters will appear to show near-IR excess when large ($>20$~pc) apertures are used. Our results explain why few young ($<6$~Myr), low extinction (\av < 1~mag) clusters have been found in recent ground based near-IR studies of cluster populations, while many such clusters have been found in higher resolution HST based studies. Additionally, resolution effects appear to (at least partially) explain the origin of the near-IR excess that has been found in a number of extragalactic YMCs.Comment: 8 pages, 5 figures, accepted for publication in MNRA

Complete controllability of quantum systems

Sufficient conditions for complete controllability of $N$-level quantum systems subject to a single control pulse that addresses multiple allowed transitions concurrently are established. The results are applied in particular to Morse and harmonic-oscillator systems, as well as some systems with degenerate energy levels. Morse and harmonic oscillators serve as models for molecular bonds, and the standard control approach of using a sequence of frequency-selective pulses to address a single transition at a time is either not applicable or only of limited utility for such systems.Comment: 8 pages, expanded and revised versio

Efficient Algorithms for Optimal Control of Quantum Dynamics: The "Krotov'' Method unencumbered

Efficient algorithms for the discovery of optimal control designs for coherent control of quantum processes are of fundamental importance. One important class of algorithms are sequential update algorithms generally attributed to Krotov. Although widely and often successfully used, the associated theory is often involved and leaves many crucial questions unanswered, from the monotonicity and convergence of the algorithm to discretization effects, leading to the introduction of ad-hoc penalty terms and suboptimal update schemes detrimental to the performance of the algorithm. We present a general framework for sequential update algorithms including specific prescriptions for efficient update rules with inexpensive dynamic search length control, taking into account discretization effects and eliminating the need for ad-hoc penalty terms. The latter, while necessary to regularize the problem in the limit of infinite time resolution, i.e., the continuum limit, are shown to be undesirable and unnecessary in the practically relevant case of finite time resolution. Numerical examples show that the ideas underlying many of these results extend even beyond what can be rigorously proved.Comment: 19 pages, many figure