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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]

Early detection of anomalies in machine system is essential for prevention of production accidents. Among various anomaly detection methods, symbolic time series analysis has been widely used. The effectiveness of this method is heavily dependent on the procedure of symbol sequence generation. This paper presents a novel partitioning method called probability density space partitioning for the symbol sequence generation. In this partitioning approach, a time series is divided into several equal-sized regions based on the probability density distribution and each region is represented by a symbol. To verify the effectiveness of the symbolic time series analysis which is based on probability density space partitioning, the test-to-fatigue experiments are conducted. The experimental results indicate that probability-density-based method is more sensitive to detect bearing anomaly than the traditional partition based methods. [ABSTRACT FROM AUTHOR]