Minimum Uncertainty Research Articles

Refractive index distribution of the ice-layer in ICF target from the interference method

In the inertial confinement fusion (ICF) system, the uniformity of the target is important to the successful ignition. A method based on the phase-shifting interferometry and ray tracing is proposed to obtain the 2D (two-dimensional) refractive index distributions of the ice-layer at three wavelengths (532 nm, 785 nm, 1064 nm), from which the 2D density distribution of the ice-layer is got. A differential method is utilized to get the reference refractive index, based on which the refractive index distribution of the layer is retrieved. For targets with uniform refractive index in the ice-layer, simulations show that the relative retrieval accuracies are better than 10 ppb. Experiments show that the refractive index distributions have good consistency at different wavelengths for the same target. The detectable normalized RMS (root mean square) of the refractive index distributions is at least 2.9E-4. The relative accuracies of the average refractive indexes of the shells are better than 1.5% for all three wavelengths. The optimal selection of the two rings on the wavefront map that yields minimal uncertainty to the reference refractive index is discussed. It is concluded that the proposed method and system poses great potential in the in-situ measurement of the refractive index and density distribution of the ICF target layers.

Composite particles with minimum uncertainty in spacetime

Composite particles---atoms, molecules, or microspheres---are unique tools for testing joint quantum and general relativistic effects, macroscopic limits of quantum mechanics, and searching for new physics. However, all studies of the free propagation of these particles find that they delocalise into separate internal energy components, destroying their spatial coherence. This renders them unsuitable for experimental applications, as well as theoretical studies where they are used as idealised test masses or clocks. Here we solve this problem by introducing a new class of states with minimal uncertainty in space-time that fully overcome the delocalisation. The relevant physics comes from minimising the uncertainty between position and velocity, rather than position and momentum, while directly accounting for mass as an operator. Our results clarify the nature of composite particles, providing a currently missing theoretical tool with direct relevance for studies of joint foundations of quantum and relativistic phenomena, which removes a roadblock that could limit near-future quantum tests using composite particles.

The use of ASH-15 flowstone as a matrix-matched reference material for laser-ablation U − Pb geochronology of calcite

Abstract. Latest advances in laser ablation inductively coupled plasma mass spectrometer (LA-ICPMS) allow for accurate in situ U−Pb dating of carbonate material, with final age uncertainties usually >3 % 2σ. Cross-laboratory reference materials (RMs) used for sample-bracketing are currently limited to WC1 calcite with an age of 254.4±6.5 (2σ). The minimum uncertainty on any age determination with the LA-ICPMS method is therefore ≥2.5 %, and validation by secondary RMs is usually performed on in-house standards. This contribution presents a new reference material, ASH-15, a flowstone that is dated here by isotope dilution (ID) thermal ionization mass spectrometry (TIMS) analysis using 37 sub-samples, 1–7 mg each. Age results presented here are slightly younger compared to previous ID isotope ratio mass spectrometry (IRMS) U−Pb dates of ASH-15 but within uncertainties and in agreement with in situ analyses using WC1 as the primary RM. We provide new correction parameters to be used as primary or secondary standardization. The suggested 238U∕206Pb apparent age, not corrected for disequilibrium and without common-lead anchoring, is 2.965±0.011 Ma (uncertainties are 95 % confidence intervals). The new results could improve the propagated uncertainties on the final age with a minimal value of 0.4 %, which is approaching the uncertainty of typical ID analysis on higher-U materials such as zircon. We show that although LA-ICPMS spot analyses of ASH-15 exhibit significant scatter in their isotopic ratios, the down-hole fractionation of ASH-15 is similar to that of other reference materials. This high-U (≈1 ppm) and low-Pb (<0.01 ppm) calcite is most appropriate as a reference material for other speleothem-type carbonates but requires more-sensitive ICP-MS instruments such as the new generation of single-collector and multi-collector ICP-MS. Reference materials with high-Pb and low-U or both low-U and low-Pb compositions are still needed to fully cover the compositional range of carbonate material but may introduce analytical challenges.

Spatiotemporal effects on squeezing measurements

The role of the spatiotemporal degrees of freedom in the preparation and observation of squeezed photonic states, produced by parametric down-conversion, is investigated. The analysis is done with the aid of a functional approach under the semi-classical approximation and the thin-crystal approximation. It is found that the squeezed state loses its minimum uncertainty property as the efficiency of down-conversion is increased, in a way that depends on the conditions of the homodyne measurements with which the amount of squeezing is determined.

A minimal length uncertainty approach to cosmological constant problem

AbstractBased on quantum mechanical framework for the minimal length uncertainty, we demonstrate that the generalized uncertainty principle (GUP) parameter could be best constrained by recent gravitational waves observations on one hand. On the other hand, this suggests modified dispersion relations (MDRs) enabling an estimation for the difference between the group velocity of gravitons and that of photons. Utilizing features of the UV/IR correspondence and the obvious similarities between GUP (including non‐gravitating and gravitating impacts on Heisenberg uncertainty principle) and the discrepancy between the theoretical and the observed cosmological constant (apparently manifesting gravitational influences on the vacuum energy density), we suggest a possible solution for the cosmological constant problem.

Information Optimal Control for Single Particle Tracking Microscopy.

We consider the problem of designing a control policy for a laser scanning microscope (LSM) which will minimize the estimation uncertainty when identifying the state and motion model of a fluorescent biological particle. Using the information optimal design framework we pose an optimization problem which seeks to maximize the Fisher information of the particle's state. We then apply optimal control methods to determine the laser trajectory that maximizes a criterion based on the Fisher information. The resulting optimal control policy is a Bang-Singular control which moves the laser to the set of measurement locations that maximize the rate of information accumulation. Simulations demonstrate the ability of the resulting control system to position the laser to measure the particles location with a minimum uncertainty.

Consequences of minimal length discretization on line element, metric tensor, and geodesic equation

When minimal length uncertainty emerging from a generalized uncertainty principle (GUP) is thoughtfully implemented, it is of great interest to consider its impacts on gravitational Einstein field equations (gEFEs) and to try to assess consequential modifications in metric manifesting properties of quantum geometry due to quantum gravity. GUP takes into account the gravitational impacts on the noncommutation relations of length (distance) and momentum operators or time and energy operators and so on. On the other hand, gEFE relates classical geometry or general relativity gravity to the energy–momentum tensors, that is, proposing quantum equations of state. Despite the technical difficulties, we intend to insert GUP into the metric tensor so that the line element and the geodesic equation in flat and curved space are accordingly modified. The latter apparently encompasses acceleration, jerk, and snap (jounce) of a particle in the quasi‐quantized gravitational field. Finite higher orders of acceleration apparently manifest phenomena such as accelerating expansion and transitions between different radii of curvature and so on.

Viewpoint Selection for Rover Relative Pose Estimation Driven by Minimal Uncertainty Criteria

Pose estimation is critical for mobile robots to fulfill various tasks, such as path following or mapping the environment. This is usually accomplished by simultaneous localization and mapping (SLAM). However, computationally constrained systems, such as planetary rovers, rely on less intensive guidance navigation and control (GNC) solutions generally derived solely from visual odometry (VO), wheel odometry, and the onboard inertial measurement unit. Although providing adequate localization performances, the drift accumulated overtime is not compensated by loop closing capabilities, typical of SLAM. Usually, rovers send surface images to the ground station, and these images are used for multiple purposes, such as scientific and operational planning. The number of images is constrained by the communication bandwidth and power budget. The set of transmitted images can be used as a means to correct the robot’s trajectory in an off-line manner. In this work, a solution is presented to the problem of selecting the optimal set of viewpoints belonging to the planned path from which to capture and transmit images: 1) it guarantees accurate trajectory correction and 2) complies with the maximum number of images that can be transmitted to ground control given the available data budget. To this end, it is proposed: 1) a delocalized/decentralized sensor fusion approach based on pose graph optimization and structure from motion and 2) a strategy to select a minimal set of viewpoints along the trajectory that, given a tentative geometry of the environment and the global path that the rover must follow, minimizes the uncertainty of all the robot poses. Optimal camera viewpoint positions are selected as a function of the planned trajectory, the approximate scene geometry, and the maximum transmittable number of images. The proposed method has been tested on a dataset of stereo-images collected in a representative Martian environment, the ALTEC Mars Terrain Simulator (MTS), with the ExoMars testing rover (ExoTeR—European Space Agency, Paris, France, property). Rover stereo-images ground truth was given with millimetric accuracy by a motion capture (MC) system.

Hyperbolic reflectors determined from peak echoes of ground penetrating radar

Ground penetrating radar has recently been used to detect subsurface structures of extraterrestrial bodies, but in situ physical properties (permittivity, density, porosity, etc.) of planetary materials are not well constrained, so that geological interpretations for a given radar observation can be widely different. Hyperbolic reflectors in radargrams obtained by ground penetrating radars are caused by subsurface materials that have a different permittivity, and these reflectors are important agent to deduce the physical properties of materials at smaller depths. The geometry of hyperbolic reflectors is critical for such calculations. Manual extraction, image analyses, and peak echoes have been used to extract the geometry of hyperbolic reflectors, but uncertainties caused by these different methods have not been systematically investigated. Here we compare differences caused by the three methods based on both modelled and observed hyperbolic reflectors in radargrams. Our results suggest that minor differences in the extracted geometry could yield significant uncertainty in the estimated bulk permittivities, leading to dramatically different interpretations. For the interpretation of the top-most radargram that was obtained by the high-frequency lunar penetrating radar onboard the Chang'E-3 mission, uncertainties caused by the different extraction techniques are trivial. However, for radargrams obtained by both the Chang'E-4 and the first Chinese Mars missions, uncertainties of depth estimations can be tens of meters based on the different extraction methods. Such uncertainties should be considered as the minimum inherent uncertainty of radar detection, because hyperbolic reflectors in radargrams are formed by peak echoes of reflected electromagnetic waves, and in actual worlds, their geometry normally deviates from ideal forms of hyperbolas. We recommend extracting hyperbolas using the peak echo method.

Efficient two-dimensional atom localization in a five-level conductive chiral atomic medium via birefringence beam absorption spectrum

We have theoretically investigated two-dimensional atom localization using the absorption spectra of birefringence beams of light in a single wavelength domain. The atom localization is controlled and modified through tunneling effect in a conductive chiral atomic medium with absorption spectra of birefringent beams. The significant localization peaks are investigated in the left and right circularly polarized beam. Single and double localized peaks are observed in different quadrants with minimum uncertainty and significant probability. The localized probability is modified by controlling birefringence and tunneling conditions. These results may be useful for the capability of optical microscopy and atom imaging.

The spin-one DKP equation with a nonminimal vector interaction in the presence of minimal uncertainty in momentum

In this work, we consider the relativistic Duffin–Kemmer–Petiau equation for spin-one particles with a nonminimal vector interaction in the presence of minimal uncertainty in momentum. By using the position space representation, we exactly determine the bound-states spectrum and the corresponding eigenfunctions. We discuss the effects of the deformation and nonminimal vector coupling parameters on the energy spectrum analytically and numerically.

Robust data‐driven fixed‐order controller synthesis: Model matching approach

In this paper, a new data-driven fixed-order H ∞ controller design method based on convex optimisation is proposed for linear single input single output systems. The proposed non-parametric frequency domain data based approach renders the need for a mathematical model of the controlled plant unnecessary. First, a semi-definite convex optimisation algorithm is proposed to simultaneously compute a minimal uncertainty model and an optimal nominal model from the experimental data. Then the H ∞ robust performance condition, control input constraints and the closed-loop model matching objective are described by convex functions with respect to the parameters of the controller. The usefulness and efficiency of the proposed approach are verified experimentally with application to the control of a thrust vector control system.

Addressing School Bullying with a Multi-tiered System of Support Approach

ABSTRACT School bullying undermines students’ participation and functioning and is within the scope of practice for school-based occupational therapists to address. The Multi-Tiered System of Support (MTSS) approach has the potential to guide the work occupational therapists do in addressing bullying. However, to date, how occupational therapists are addressing school bullying with an MTSS approach is unknown. We, therefore, conducted an exploratory qualitative interpretive study to gain an understanding of how occupational therapists are addressing school bullying with an MTSS approach. The methods we used included semi-structured one-on-one interviews with eight occupational therapists (seven women, one man) working in public schools in New York City. We used the qualitative data management tool Taguette and thematic analysis for data analysis. Themes illuminate occupational therapists’ minimal involvement and uncertainty with bullying prevention and intervention efforts being implemented through MTSS in their schools. They attributed their minimal involvement to not having sufficient experience and a lack of recognition from school staff on occupational therapy’s mental health expertise and distinct contribution that could be brought to anti-bullying efforts. In conclusion, this study emphasizes the need for occupational therapists to have access to occupation-based anti-bullying interventions, appropriate mentorship, workload support, recognition from school staff, and professional development to be part of an interprofessional team in schools that addresses bullying. For this to occur, a systematic process of capacity building, advocacy, and planning across system levels (i.e., entry-level education programs, individual school sites, state occupational therapy associations, professional association) is needed.

Information-theoretic aspects of Werner states

In a seminal study of quantum states with Einstein–Podolsky–Rosen correlations (entanglement) admitting a hidden-variable model (Werner, 1989), Werner introduced the dichotomy of entanglement/separability and devised a family of highly symmetric states, now termed the Werner states, some of which exhibit entanglement but no Bell nonlocality. It turns out that the Werner states have a rich structure of correlations and constitute a paradigm which has played an innovative role in both theoretical and experimental explorations of quantum information. Given the theoretical significance and wide applications of the Werner states, here we first give a concise review of information contents of the Werner states, and then present an information-theoretic characterization of them in terms of the Wigner–Yanase skew information: The Werner states are identified as the states with the minimum quantum uncertainty with respect to a natural family of observables (i.e., the generators of the diagonal unitary group). For this purpose, we introduce a measure of quantum uncertainty which is of independent interest in studying asymmetry, coherence, and uncertainty, and reveal its fundamental properties. We further identify the Bell triplet states as the opposite states of the Werner states in the sense that they have the maximal amount of quantum uncertainty. Analogously, we provide a similar characterization of the isotropic states as the minimum quantum uncertainty states with respect to a closely related family of operators.

Exploration of entropic uncertainty bound in a symmetric multi-qubit system under noisy channels

Considering one of the particles as a quantum memory in a bipartite system can remarkably improve the measurement accuracy for two incompatible observables. Herein, we study quantum-memory-assisted entropic uncertainty bound for an arbitrary two-qubit X-state, and then we get a clear formula as the entropic uncertainty bound. In the following, we examine analytically and numerically the dynamics of entropic uncertainty bound in a symmetric multi-qubit system under four types of noisy channels, i.e. phase-flip, amplitude damping, phase-damping, and depolarizing channels. Our results show that the entropic uncertainty bound dynamics is related to the number of particles and especially the noise channel used. Noteworthy, our remarks reveal that under the amplitude damping channel, the entropic uncertainty bound can be suppressed during the time. It turns out that under an amplitude damping channel, these results can be important in practical goals where the minimum uncertainty is required such as quantum computation.

Geometric aspects of analog quantum search evolutions

We use geometric concepts originally proposed by Anandan and Aharonov to show that the Farhi-Gutmann time optimal analog quantum search evolution between two orthogonal quantum states is characterized by unit efficiency dynamical trajectories traced on a projective Hilbert space. In particular, we prove that these optimal dynamical trajectories are the shortest geodesic paths joining the initial and the final states of the quantum evolution. In addition, we verify they describe minimum uncertainty evolutions specified by an uncertainty inequality that is tighter than the ordinary time-energy uncertainty relation. We also study the effects of deviations from the time optimality condition from our proposed Riemannian geometric perspective. Furthermore, after pointing out some physically intuitive aspects offered by our geometric approach to quantum searching, we mention some practically relevant physical insights that could emerge from the application of our geometric analysis to more realistic time-dependent quantum search evolutions. Finally, we briefly discuss possible extensions of our work to the geometric analysis of the efficiency of thermal trajectories of relevance in quantum computing tasks.

Aspects of nonperturbative GUP models

We review on further new developments of Generalized Uncertainty Principle (GUP) and implications for the cosmological vacuum energy. First, we introduce basic aspects of GUP as well as several possible different and viable formulation of it. Second, we move on discussing two recent new types of higher D-dimensional nonperturbative GUP models; which we dub D-Type-I and D-Type-II GUPs. The D-Type-I and D-Type-II GUPs are both related to the existence of a critical conspiracy between a minimal uncertainty length and a maximal observable momentum. Finally, we show direct implications of D-Type-I and D-Type-II on the cosmological vacuum energy obtained in quantum mechanical systems such as the typical quantum harmonic oscillator. Such a computation goes through investigations of the density of states for D-dimensional coordinate systems in the momentum space. We will also comment on several possible connections with fundamental issues of quantum gravity such as black hole physics and gravitational radiative aspects.

A Comprehensive Quality Assurance Program of Small Animal Irradiators for Preclinical Radiation Research

Draeger et al. (Red Journal, 2020) raised awareness on the importance of the standardization of dosimetry protocols in pre-clinical radiobiology research and the inclusion of physicists on the research team. At our institute, a QA program of the small animal radiation research platform (SARRP, Xstrahl) that includes daily, monthly and annual tests have been implemented to ensure minimal delivery uncertainties. Details of the QA procedures, feasibility and results will be reported. End-to-end imaging and radiation isocenter coincidence testing using a Winston-Lutz phantom and EBT3 films, as well as CBCT imaging quality visual check, were performed daily by the research team. Monthly QA (mechanical and dosimetric tests such as the star-shot test and output constancy of the reference field), and annual QA (TG61 absolute dosimetry, imaging quality phantom check, output factor, beam profiles and percent depth dose measurements) were performed by the physics staff. The estimated time to complete the daily, monthly and annual tests were twenty minutes, one and two hours, respectively. The frequency of each QA item had been established based on the failure occurrence rate. The tolerance results of the daily, monthly and annual testing are displayed in the table. The results of the daily isocenter coincidence check show a discrepancy between the radiation isocenter and set-up center combined with the uncertainty from the couch movement of the image-guided system smaller than 1.5 mm. This test has successfully caught failures in the entire delivery process. For the monthly QA, diameter of the radiation isocenter was consistently smaller than 0.5 mm and the output has been measured to be within ±1% of baseline. The results of the annual QA, using an ion chamber and EBT3 films, match the beam data of the treatment planning system as well as the data from our in-house Monte Carlo calculation within the tolerance. Additionally, we used EBT3 films and a mouse solid water phantom as tools for verification of dosimetrically complex plans. The maximum dosimetry error observed has been consistently within 2%. With the implemented QA program, the fidelity of overall system delivery was ensured for robust and accurate small animal radiation studies without excess burden on the medical physicists and research team.Tabled 1Abstract 2596; TableProcedureToleranceDailyEnd to end imaging and radiation isocenter coincidence2 mmCBCT imaging quality visual checkBaselineLocalizing lasers1 mmMonthlyOutput constancy2%Isocentricity1 mmGantry position check1 mmAnnualOutput, flatness and symmetry, PDD, output factor1%CBCT imaging quality phantom checkBaseline Open table in a new tab

A Bayesian Logistic Regression for Probabilistic Forecasts of the Minimum September Arctic Sea Ice Cover

AbstractThis study introduces a Bayesian logistic regression framework that is capable of providing skillful probabilistic forecasts of Arctic sea ice cover, along with quantifying the attendant uncertainties. The presence or absence of ice (absence defined as ice concentration below 15%) is modeled using a categorical regression model, with atmospheric, oceanic, and sea ice covariates at 1‐ to 7‐month lead times. The model parameters are estimated in a Bayesian framework, thus enabling the posterior predictive probabilities of the minimum sea ice cover and parametric uncertainty quantification. The model is fitted and validated to September minimum sea ice cover data from 1980 through 2018. Results show overall skillful forecasts of the minimum sea ice cover at all lead times, with higher skills at shorter lead times, along with a direct measure of forecast uncertainty to aide in assessing the reliability.

Зведення задачі мінімаксного керування лінійними нестаціонарними системами до – робастного шляхом динамічної гри

The problem of synthesis of minimax control for the dynamic, described by the linear system of differential equations (taking into account the state, controls, perturbations and initial conditions, with the given equation of observation inclusive) of objects functioning in accordance with the integral-quadratic quality criterion in uncertainty is solved in the work. External perturbations, errors, and initial conditions were assumed to belong to a number of uncertainties. The task of finding optimal control in the form of a feedback object that minimizes the performance criterion is presented in the form of a minimum maximal uncertainty control problem. In the absence of ready-made solution paths, this problem is reduced to a -control problem under the most unfavorable disturbances, and in addition to a dynamic game problem with zero sum and a certain price for the game, and a strategy for solving it is proposed that offers a way to new results. The problem of finding the optimal control and the initial state that maximize the quality criterion is considered in the framework of the optimization problem solved by the Lagrange multiplier method after introducing the auxiliary scalar function, the Hamiltonian. It is shown that to find the maximum value of the criterion, either the necessary condition of the extremum of the first kind can be used, which depends on the ratio of the first variation of the criterion and the first variations of the control vectors and the initial state, or also the necessary condition of the extremum of the second kind, which depends on the sign of the second variation. For the first and second variations, formulas are given that can be used for calculations. It is suggested to solve the control search problem in two steps: search for an intermediate solution at fixed values of control vectors and errors, and then search for final optimal control. Consideration is also given to solving -optimal control for infinite control time with respect to the signal from the compensator output, as well as solving the corresponding Riccati matrix algebraic equations.