Stabilizing Open Quantum Systems by Markovian Reservoir Engineering

We study open quantum systems whose evolution is governed by a master equation of Kossakowski-Gorini-Sudarshan-Lindblad type and give a characterization of the convex set of steady states of such systems based on the generalized Bloch representation. It is shown that an isolated steady state of the Bloch equation cannot be a center, i.e., that the existence of a unique steady state implies attractivity and global asymptotic stability. Necessary and sufficient conditions for the existence of a unique steady state are derived and applied to different physical models including two- and four-level atoms, (truncated) harmonic oscillators, composite and decomposable systems. It is shown how these criteria could be exploited in principle for quantum reservoir engineeing via coherent control and direct feedback to stabilize the system to a desired steady state. We also discuss the question of limit points of the dynamics. Despite the non-existence of isolated centers, open quantum systems can have nontrivial invariant sets. These invariant sets are center manifolds that arise when the Bloch superoperator has purely imaginary eigenvalues and are closely related to decoherence-free subspaces.Comment: 16 pages, 4 figures, marginally revised version, mainly fixed some notational inconsistencies that had crept in when we change the notation in some figures without changing the captions and tex

Supernova Hydrodynamicas Experiments Using the Nova Laser

We are developing experiments using the Nova laser to investigate (1) compressible nonlinear hydrodynamic mixing relevant to the first few hours of the supernova (SN) explosion and (2) ejecta-ambient plasma interactions relevant to the early SN remnant phase. The experiments and astrophysical implications are discussed

Analysis of the shearing instability in nonlinear convection and magnetoconvection

Numerical experiments on two-dimensional convection with or without a vertical magnetic field reveal a bewildering variety of periodic and aperiodic oscillations. Steady rolls can develop a shearing instability, in which rolls turning over in one direction grow at the expense of rolls turning over in the other, resulting in a net shear across the layer. As the temperature difference across the fluid is increased, two-dimensional pulsating waves occur, in which the direction of shear alternates. We analyse the nonlinear dynamics of this behaviour by first constructing appropriate low-order sets of ordinary differential equations, which show the same behaviour, and then analysing the global bifurcations that lead to these oscillations by constructing one-dimensional return maps. We compare the behaviour of the partial differential equations, the models and the maps in systematic two-parameter studies of both the magnetic and the non-magnetic cases, emphasising how the symmetries of periodic solutions change as a result of global bifurcations. Much of the interesting behaviour is associated with a discontinuous change in the leading direction of a fixed point at a global bifurcation; this change occurs when the magnetic field is introduced

Hydrodynamic Instability Experiments on the Nova Laser

Hydrodynamic instabilities in compressible plasmas play a critical role in the fields of inertial confinement fusion (ICF), astrophysics, and high energy-density physics. We are, investigating hydrodynamic instabilities such as the Rayleigh-Taylor (RT) instability, at high compression at the Nova laser in a series of experiments, both in planar and in spherical geometry. In the indirect drive approach, a thermal x-ray drive is generated by focusing the Nova laser beams into a Au cylindrical radiation cavity (hohlraum). Issues in the instability evolution that we are examining are shock propagation and foil compression, RT growth of 2D versus 3D single-mode perturbations, drive pulse shape, perturbation location at the ablation front versus at an embedded interface, and multimode perturbation growth and nonlinear saturation. The effects of convergence on RT growth are being investigated both with hemispherical implosions of packages mounted on the hohlraum wall and with spherical implosions of capsules at the center of the hohlraum. Single-mode perturbations are pre-imposed at the ablation front of these capsules as a seed for the RT growth. In our direct drive experiments, we are investigating the effect of laser imprinting and subsequent RT growth on planar foils, both at {lambda}{sub Laser} = 1/3 {mu}m and 1/2 {mu}m. An overview is given describing recent progress in each of these areas

Incomplete approach to homoclinicity in a model with bent-slow manifold geometry

The dynamics of a model, originally proposed for a type of instability in plastic flow, has been investigated in detail. The bifurcation portrait of the system in two physically relevant parameters exhibits a rich variety of dynamical behaviour, including period bubbling and period adding or Farey sequences. The complex bifurcation sequences, characterized by Mixed Mode Oscillations, exhibit partial features of Shilnikov and Gavrilov-Shilnikov scenario. Utilizing the fact that the model has disparate time scales of dynamics, we explain the origin of the relaxation oscillations using the geometrical structure of the bent-slow manifold. Based on a local analysis, we calculate the maximum number of small amplitude oscillations, $s$, in the periodic orbit of $L^s$ type, for a given value of the control parameter. This further leads to a scaling relation for the small amplitude oscillations. The incomplete approach to homoclinicity is shown to be a result of the finite rate of `softening' of the eigen values of the saddle focus fixed point. The latter is a consequence of the physically relevant constraint of the system which translates into the occurrence of back-to-back Hopf bifurcation.Comment: 14 Figures(Postscript); To Appear in Physica D : Nonlinear Phenomen

Variability of the sheep lung microbiota

Sequencing technologies have recently facilitated the characterisation of bacterial communities present in lungs during health and disease. However, there is currently a dearth of information concerning the variability of such data in health both between and within subjects. This study seeks to examine such variability using healthy adult sheep as our model system. Protected specimen brush samples were collected from three spatially disparate segmental bronchi of six adult sheep (age 20 months) on three occasions (day 0, one month and three months). To further explore the spatial variability of the microbiota, more extensive brushings (n=16) and a throat swab were taken from a separate sheep. The V2-V3 hypervariable regions of the bacterial 16S rRNA gene were amplified and sequenced via Illumina MiSeq. DNA sequences were analysed using the MOTHUR software package. Quantitative PCR was performed to quantify total bacterial DNA. Some sheep lungs contained dramatically different bacterial communities at different sampling sites whereas in others airway microbiota appeared similar across the lung. In our spatial variability study, clustering was observed related to the depth within the lung from which samples were taken. Lung depth refers to increasing distance from the glottis progressing in a caudal direction. We conclude that both host influence and local factors have an impact on the composition of the sheep lung microbiota

Laser Imprint and Implications for Direct Drive Ignition With the National Ignition Facility

For direct drive ICF, nonuniformities in laser illumination can seed ripples at the ablation front in a process called imprint. Such nonuniformities will grow during the capsule implosion and can penetrate the capsule shell impede ignition, or degrade burn. We have simulated imprint for a number of experiments on tile Nova laser. Results are in generally good agreement with experimental data. We leave also simulated imprint upon National Ignition Facility (NIF) direct drive ignition capsules. Imprint modulation amplitude comparable to the intrinsic surface finish of {approximately}40 nm is predicted for a laser bandwidth of 0.5 THz. Ablation front modulations experience growth factors up to several thousand, carrying modulation well into the nonlinear regime. Saturation modeling predicts that the shell should remain intact at the time of peak velocity, but penetration at earlier times appears more marginal

Non-chaotic dynamics in general-relativistic and scalar-tensor cosmology

In the context of scalar-tensor models of dark energy and inflation, the dynamics of vacuum scalar-tensor cosmology are analysed without specifying the coupling function or the scalar field potential. A conformal transformation to the Einstein frame is used and the dynamics of general relativity with a minimally coupled scalar field are derived for a generic potential. It is shown that the dynamics are non-chaotic, thus settling an existing debate.Comment: 20 pages, LaTeX, to appear in Class. Quantum Gra

Scaling supernova hydrodynamics to the laboratory

Supernova (SN) 1987A focused attention on the critical role of hydrodynamic instabilities in the evolution of supernovae. To test the modeling of these instabilities, we are developing laboratory experiments of hydrodynamic mixing under conditions relevant to supernovae. Initial results were reported in J. Kane et al. [Astrophys. J. 478, L75 (1997) and B. A. Remington et al., Phys. Plasmas 4, 1994 (1997)]. The Nova laser is used to generate a 10–15 Mbar shock at the interface of a two-layer planar target, which triggers perturbation growth due to the Richtmyer–Meshkov instability, and to the Rayleigh–Taylor instability as the interface decelerates. This resembles the hydrodynamics of the He-H interface of a Type II supernova at intermediate times, up to a few ×103 s.×103s. The scaling of hydrodynamics on microscopic laser scales to the SN-size scales is presented. The experiment is modeled using the hydrodynamics codes HYADES [J. T. Larson and S. M. Lane, J. Quant. Spect. Rad. Trans. 51, 179 (1994)] and CALE [R. T. Barton, Numerical Astrophysics (Jones and Bartlett, Boston, 1985), pp. 482–497], and the supernova code PROMETHEUS [P. R. Woodward and P. Collela, J. Comp. Phys. 54, 115 (1984)]. Results of the experiments and simulations are presented. Analysis of the spike-and-bubble velocities using potential flow theory and Ott thin-shell theory is presented, as well as a study of 2D versus 3D differences in perturbation growth at the He-H interface of SN 1987A.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69672/2/PHPAEN-6-5-2065-1.pd

Outcomes of reablement and their measurement : findings from an evaluation of English reablement services

Reablement – or restorative care – is a central feature of many western governments’ approaches to supporting and enabling older people to stay in their own homes and minimise demand for social care. Existing evidence supports this approach although further research is required to strengthen the certainty of conclusions being drawn. In countries where reablement has been rolled out nationally, an additional research priority – to develop an evidence base on models of delivery – is emerging. This paper reports a prospective cohort study of individuals referred to three English social care reablement services, each representing a different model of service delivery. Outcomes included healthcare- and social care–related quality of life, functioning, mental health and resource use (service costs, informal carer time, out-of-pocket costs). In contrast with the majority of other studies, self-report measures were the predominant source of outcomes and resource use data. Furthermore, no previous evaluation has used a global measure of mental health. Outcomes data were collected on entry to the service, discharge and 6 months post discharge. A number of challenges were encountered during the study and insufficient individuals were recruited in two research sites to allow a comparison of service models. Findings from descriptive analyses of outcomes align with previous studies and positive changes were observed across all outcome domains. Improvements observed at discharge were, for most, retained at 6 months follow-up. Patterns of change in functional ability point to the importance of assessing functioning in terms of basic and extended activities of daily living. Findings from the economic evaluation highlight the importance of collecting data on informal carer time and also demonstrate the viability of collecting resource use data direct from service users. The study demonstrates challenges, and value, of including self-report outcome and resource use measures in evaluations of reablement