Interference, reduced action, and trajectories

Instead of investigating the interference between two stationary, rectilinear wave functions in a trajectory representation by examining the two rectilinear wave functions individually, we examine a dichromatic wave function that is synthesized from the two interfering wave functions. The physics of interference is contained in the reduced action for the dichromatic wave function. As this reduced action is a generator of the motion for the dichromatic wave function, it determines the dichromatic wave function's trajectory. The quantum effective mass renders insight into the behavior of the trajectory. The trajectory in turn renders insight into quantum nonlocality.Comment: 12 pages text, 5 figures. Typos corrected. Author's final submission. A companion paper to "Welcher Weg? A trajectory representation of a quantum Young's diffraction experiment", quant-ph/0605121. Keywords: interference, nonlocality, trajectory representation, entanglement, dwell time, determinis

OPERA data and The Equivalence Postulate of Quantum Mechanics

An interpretation of the recent results reported by the OPERA collaboration is that neutrinos propagation in vacuum exceeds the speed of light. It has been further been suggested that this interpretation can be attributed to the variation of the particle speed arising from the Relativistic Quantum Hamilton Jacobi Equation. I show that this is in general not the case. I derive an expression for the quantum correction to the instantaneous relativistic velocity in the framework of the relativistic quantum Hamilton-Jacobi equation, which is derived from the equivalence postulate of quantum mechanics. While the quantum correction does indicate deviations from the classical energy--momentum relation, it does not necessarily lead to superluminal speeds. The quantum correction found herein has a non-trivial dependence on the energy and mass of the particle, as well as on distance travelled. I speculate on other possible observational consequences of the equivalence postulate approach.Comment: 8 pages. Standard LaTex. References adde

Welcher Weg? A trajectory representation of a quantum Young's diffraction experiment

The double slit problem is idealized by simplifying each slit by a point source. A composite reduced action for the two correlated point sources is developed. Contours of the reduced action, trajectories and loci of transit times are developed in the region near the two point sources. The trajectory through any point in Euclidian 3-space also passes simultaneously through both point sources.Comment: 12 pages LaTeX2e, 9 figures. Typos corrected. Author's final submission. A companion paper to "Interference, reduced action, and trajectories", quant-ph/0605120. Keywords: interference, Young's experiment, entanglement, nonlocality, trajectory representation, determinis

The Quantum Reduced Action In Higher Dimensions

The solution with respect to the reduced action of the one-dimensional stationary quantum Hamilton-Jacobi equation is well known in the literature. The extension to higher dimensions in the separated variable case was proposed in contradictory formulations. In this paper we provide new insights into the construction of the reduced action. In particular, contrary to the classical mechanics case, we analytically show that the reduced action constructed as a sum of one variable functions does not contain a complete information about the quantum motion. In the same context, we also make some observations about recent results concerning quantum trajectories. Finally, we will examine the conditions in which microstates appear even in the case where the wave function is complex.Comment: 12 pages, no figur

Coherent States and Modified de Broglie-Bohm Complex Quantum Trajectories

This paper examines the nature of classical correspondence in the case of coherent states at the level of quantum trajectories. We first show that for a harmonic oscillator, the coherent state complex quantum trajectories and the complex classical trajectories are identical to each other. This congruence in the complex plane, not restricted to high quantum numbers alone, illustrates that the harmonic oscillator in a coherent state executes classical motion. The quantum trajectories are those conceived in a modified de Broglie-Bohm scheme and we note that identical classical and quantum trajectories for coherent states are obtained only in the present approach. The study is extended to Gazeau-Klauder and SUSY quantum mechanics-based coherent states of a particle in an infinite potential well and that in a symmetric Poschl-Teller (PT) potential by solving for the trajectories numerically. For the coherent state of the infinite potential well, almost identical classical and quantum trajectories are obtained whereas for the PT potential, though classical trajectories are not regained, a periodic motion results as t --> \infty.Comment: More example

Risk factors for atrial fibrillation in a multicenter United States clinical cohort of people with HIV infection

To assess atrial fibrillation risk factors in people with HIV, we identified incident atrial fibrillation in a large clinical cohort of people receiving care. Compared with 970 controls without atrial fibrillation, the 97 with adjudicated incident atrial fibrillation were older, less likely Hispanic, and had more coronary disease, heart failure, and chronic obstructive pulmonary disease. In multivariable analysis, nonuse of antiretroviral therapy and prescription of antiretroviral regimens with multiple core agents were associated with increased atrial fibrillation risk

Detrital Avalonian zircons in the Laurentian Southern Uplands Terrane, Scotland

The Silurian–Ordovician Southern Uplands terrane occupies a key position in the Caledonian orogen, yet its genesis is controversial. Marginal-basin, backarc, and forearc tectonic regimes have all been invoked as operative at the Laurentian margin of the Iapetus Ocean. Fresh andesitic detritus within turbidite sandstones has, until now, been assumed to provide evidence for an Ordovician suprasubduction volcanic arc, a central feature of most models. However, high-precision thermal-ionization mass spectrometer U-Pb and laser-ablation data for detrital zircons from the sandstone prove Neoproterozoic volcanism at 557 ± 6 Ma (2σ) and probably also at 613 ± 12 Ma (2σ). The complex crystallization history recorded by the zircons shows assimilation of 1043 ± 7 Ma (2σ) Grenvillian basement into the andesite magma. The fact that no zircons have been found having ages that overlap the Caradocian depositional age of the host sedimentary rocks undermines all extant terrane models. The age profile of the detrital zircons is typical of Gondwana and Avalonia. This finding has important implications for the paleogeography of the Iapetus Ocean during the Ordovician, because the zircon data require the introduction of Avalonian detritus into a sedimentary basin marginal to Laurentia