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We discuss several features of the classical quantum potential appearing in Covariant Quantum Mechanics. In particular, we compare the “observed potential” A [ K , G , o ] of the joined spacetime connection K with the potential A ↑ of the cosymplectic phase 2-form Ω [ K , G ] and with the potential A ↑ of the upper quantum connection Ч ↑ . Moreover, we discuss the distinguished observer o [ Ψ ] and the distinguished timelike potential A [ Ψ ] associated with a non-vanishing quantum section Ψ. We show that the above objects play a natural role in the context of the kinetic quantum momentum Q [ Ψ ] , of the quantum probability current J [ Ψ ] , of the Schrödinger operator S [ Ψ ] and of the classical fluid associated with a non-vanishing quantum section Ψ. [ABSTRACT FROM AUTHOR]

In an elementary variational treatment of the electronic structure of H2+, Eyring, Walter, and Kimball (EWK) serendipitously discovered charge migration (CM) in 1944. Using an analytic expression for the electronic probability density (EPD), they found that if the electron is initially localized on one of the protons (by taking the initial state to be a superposition of the ground and first excited electronic energy eigenstates), then it oscillates adiabatically between fixed protons with a period T inversely proportional to the energy gap between the eigenstates. At the equilibrium internuclear separation, T = 550.9 as. As shown here, the EWK model also yields an analytic formula for the electronic flux density (EFD). While the EPD indicates where the electron is at any instant, the EFD reveals the pathways the electron follows during its migration. Thus, the EFD complements the EPD, providing valuable new insight into the mechanism of CM. The formula for the EFD is a simple product of a time factor and a spatial factor. This factoring exposes a plethora of spatial-temporal symmetry relations which imply novel and surprising properties. An especially significant finding is that, in contrast to multielectron systems, where electron correlation may play a role in CM, in the EWK model of H2+, CM is due strictly to quantum interference between the ground and first excited electronic states. [ABSTRACT FROM AUTHOR]

Subjects observing many samples from a Bernoulli distribution are able to perceive an estimate of the generating parameter. A question of fundamental importance is how the current percept-what we think the probability now is-depends on the sequence of observed samples. Answers to this question are strongly constrained by the manner in which the current percept changes in response to changes in the hidden parameter. Subjects do not update their percept trial-by-trial when the hidden probability undergoes unpredictable and unsignaled step changes; instead, they update it only intermittently in a step-hold pattern. It could be that the step-hold pattern is not essential to the perception of probability and is only an artifact of step changes in the hidden parameter. However, we now report that the step-hold pattern obtains even when the parameter varies slowly and smoothly. It obtains even when the smooth variation is periodic (sinusoidal) and perceived as such. We elaborate on a previously published theory that accounts for: (i) the quantitative properties of the step-hold update pattern; (ii) subjects' quick and accurate reporting of changes; (iii) subjects' second thoughts about previously reported changes; (iv) subjects' detection of higher-order structure in patterns of change. We also call attention to the challenges these results pose for trial-by-trial updating theories. [ABSTRACT FROM AUTHOR]

Learning introductory quantum physics is challenging, in part due to the different paradigms in classical mechanics and quantum physics. Classical mechanics is deterministic in that the equations of motion and the initial conditions fully determine a particle's trajectory. Quantum physics is an inherently probabilistic theory in that only probabilities for measurement outcomes can be determined. Prior to studying quantum physics, students will typically have little experience with probabilistic analyses of physical systems, and thus probability may be a conceptual hurdle for introductory quantum physics students. This article describes two interactive simulations developed as part of the QuVis Quantum Mechanics Visualization Project that aim to bridge the gap between classical mechanics and quantum physics using probabilistic analyses of classical systems. The simulations illustrate how a probability density can be obtained for two classical systems well known to students. The key learning goals of the simulations are to introduce students to probability densities and to help students distinguish between a probability and a probability density. The simulations build on previous work by Bao and Redish, who developed an activity that used pseudo-random video frames of a glider in harmonic motion to derive a classical probability density for this system, and a University of Washington quantum mechanics tutorial focusing on probability and probability density for a classical system. Interactive simulations allow students to easily carry out experiments and change variables that would be difficult to do with real equipment, and help students connect multiple representations by showing explicitly how they are linked. The simulations described here only require basic knowledge of algebra and classical mechanics. They run on touchscreen devices as well as desktop computers, and can be run in a standard web browser from the QuVis website or downloaded for offline use. [ABSTRACT FROM AUTHOR]

The traditional sweep width model can not accurately predicate the impact of target magnetic feature, ambient noise on the airborne magnetic anomaly detection sweep width, the traditional sweep width model is improved by adding the idea of probability distribution, and a new sweep width model is proposed based on signal to noise ratio detection criterion. On the basis of establishing airborne magnetic anomaly detection encounter model based on magnetic dipole model, submarine magnetic signature model, ambient magnetic noise model and signal detection model, the calculation method and corresponding procedure for the new sweep width model are presented. Simulation results show that the improved model is effective and accurate in evaluating the effect of submarine magnetic features, geomagnetic dip angle, ambient magnetic noise and detection platform on sweep width of airborne magnetic anomaly detection. The improved model is more effective and accurate in estimating the sweep width of airborne magnetic anomaly detection compared with traditional sweep width model. [ABSTRACT FROM AUTHOR]

The GUM and its supplements one and two have come to be regarded as de facto standards for evaluating measurement uncertainty. The latter documents have stressed the benefits of deriving probability density functions (PDFs) for the output quantities instead of just evaluating the standard and expanded uncertainties associated with their best estimates. Those supplements, however, present a brute force numerical method for obtaining the output PDFs. In this paper, we rely instead on the use of the change-of-variables theorem as a way of obtaining analytical expressions for PDFs in the form of integrals that, at least in principle, can be numerically evaluated. But more importantly, the GUM supplements do not include situations in which the available information is more than enough, in the sense that by separately considering its various components one may arrive at concurrent PDFs for the quantity or quantities of interest. In some situations these PDFs will be largely similar, so that implementing some form of merging method would perhaps be reasonable. But it may also happen that significant discrepancies between those PDFs are apparent, in which case a modification of the measurement model might make all information appear to be consistent. Herein we review two procedures for merging concurrent and not too dissimilar PDFs. We also discuss some elements to be considered if extending the measurement model appears to be a better alternative. [ABSTRACT FROM PUBLISHER]

A standard result in quantum mechanics is this: if two observables are commuting then they have a classical joint distribution in every state. A converse is demonstrated here: If a classical joint distribution for the pair agrees with standard quantum facts, then the observables must commute. This has consequences for some historical and recent quantum nonlocal models: they are analytically disallowed without the need for experiment, as they imply that all local observables must commute among themselves. [ABSTRACT FROM AUTHOR]

The conditional mean estimator for a n-state linear system with additive Cauchy measurement and process noises is developed. It is shown that although the Cauchy densities, which model the initial state, the process noise and the measurement noise have undefined first moments and an infinite second moment, the probability density function conditioned on the measurement history does have a finite conditional mean and conditional variance. For the multivariable system state, the characteristic function of the unnormalized conditional probability density function is sequentially propagated through measurement updates and dynamic state propagation, while expressing the resulting characteristic function in a closed analytical form. Once the characteristic function of the unnormalized conditional probability density function is obtained, the probability density function of the measurement history, the conditional mean, and conditional variance are easily computed from the characteristic function and its continuous first and second derivatives, evaluated at the origin in the spectral variables' domain. These closed form expressions yield the sequential state estimator. A three-state dynamic system example demonstrates numerically the performance of the Cauchy estimator. [ABSTRACT FROM AUTHOR]

This paper explores the study on mixture of a class of probability density functions under type-I censoring scheme. In this paper, we mold a heterogeneous population by means of a two-component mixture of the class of probability density functions. The parameters of the class of mixture density functions are estimated and compared using the Bayes estimates under the squared-error and precautionary loss functions. A censored mixture dataset is simulated by probabilistic mixing for the computational purpose considering particular case of the Maxwell distribution. Closed-form expressions for the Bayes estimators along with their posterior risks are derived for censored as well as complete samples. Some stimulating comparisons and properties of the estimates are presented here. A factual dataset has also been for illustration. [ABSTRACT FROM AUTHOR]

The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical structure of quantum theory. This review paper tries to present the framework and recent results to a broader readership in an accessible manner. To achieve this, we follow a constructive approach. Starting from a few basic physically motivated assumptions we show how a given set of observations can be manifested in an operational theory. Furthermore, we characterize consistency conditions limiting the range of possible extensions. In this framework classical and quantum theory appear as special cases, and the aim is to understand what distinguishes quantum mechanics as the fundamental theory realized in nature. It turns out that non-classical features of single systems can equivalently result from higher-dimensional classical theories that have been restricted. Entanglement and non-locality, however, are shown to be genuine non-classical features. [ABSTRACT FROM AUTHOR]