Order in de Broglie - Bohm quantum mechanics

A usual assumption in the so-called {\it de Broglie - Bohm} approach to quantum dynamics is that the quantum trajectories subject to typical `guiding' wavefunctions turn to be quite irregular, i.e. {\it chaotic} (in the dynamical systems' sense). In the present paper, we consider mainly cases in which the quantum trajectories are {\it ordered}, i.e. they have zero Lyapunov characteristic numbers. We use perturbative methods to establish the existence of such trajectories from a theoretical point of view, while we analyze their properties via numerical experiments. Using a 2D harmonic oscillator system, we first establish conditions under which a trajectory can be shown to avoid close encounters with a moving nodal point, thus avoiding the source of chaos in this system. We then consider series expansions for trajectories both in the interior and the exterior of the domain covered by nodal lines, probing the domain of convergence as well as how successful the series are in comparison with numerical computations or regular trajectories. We then examine a H\'{e}non - Heiles system possessing regular trajectories, thus generalizing previous results. Finally, we explore a key issue of physical interest in the context of the de Broglie - Bohm formalism, namely the influence of order in the so-called {\it quantum relaxation} effect. We show that the existence of regular trajectories poses restrictions to the quantum relaxation process, and we give examples in which the relaxation is suppressed even when we consider initial ensembles of only chaotic trajectories, provided, however, that the system as a whole is characterized by a certain degree of order.Comment: 25 pages, 12 figure

Existential Contextuality and the Models of Meyer, Kent and Clifton

It is shown that the models recently proposed by Meyer, Kent and Clifton (MKC) exhibit a novel kind of contextuality, which we term existential contextuality. In this phenomenon it is not simply the pre-existing value but the actual existence of an observable which is context dependent. This result confirms the point made elsewhere, that the MKC models do not, as the authors claim, ``nullify'' the Kochen-Specker theorem. It may also be of some independent interest.Comment: Revtex, 7 pages, 1 figure. Replaced with published versio

Gaussian superpositions in scalar-tensor quantum cosmological models

A free scalar field minimally coupled to gravity model is quantized and the Wheeler-DeWitt equation in minisuperspace is solved analytically, exhibiting positive and negative frequency modes. The analysis is performed for positive, negative and zero values of the curvature of the spatial section. Gaussian superpositions of the modes are constructed, and the quantum bohmian trajectories are determined in the framework of the Bohm-de Broglie interpretation of quantum cosmology. Oscillating universes appear in all cases, but with a characteristic scale of the order of the Planck scale. Bouncing regular solutions emerge for the flat curvature case. They contract classically from infinity until a minimum size, where quantum effects become important acting as repulsive forces avoiding the singularity and creating an inflationary phase, expanding afterwards to an infinite size, approaching the classical expansion as long as the scale factor increases. These are non-singular solutions which are viable models to describe the early Universe.Comment: 14 pages, LaTeX, 3 Postscript figures, uses graficx.st

Barium lines in high-quality spectra of two metal-poor giants in the Galactic halo

Context. Theoretical results showed the possibility that neutron capture elements were produced in the early Universe by two different sources: a frequent s-process source hosted by rotating massive stars, and a rare r-process source hosted most likely by neutron star mergers. The two sources produce barium with different isotopic compositions. Aims. We aim to investigate the lines of barium in two halo stars, HD 6268 and HD 4306. The spectra present an exquisite quality, both in terms of resolution (R > 100 000) and signal-to-noise (~400). Due to hyperfine splitting (hfs) effects, barium lines are expected to show slightly different profiles depending on the barium isotopic fraction. Methods. We applied a standard local thermodynamic equilibrium synthesis of the barium lines. We compared the synthetic results assuming an s-process isotopic pattern or an r-process isotopic pattern for the two barium lines for each star that exhibited hfs. We also applied a methodology, less dependent on the accuracy of the theoretical Ba hfs structure, that transforms the lines of HD 4306 into those we would observe if its atmospheric parameter values (i.e. Teff, log g, micro- and macro-turbulence, V sin i, and Ba abundance) were the same as those of HD 6268. Results. With both methods, our results show that the barium lines with hfs effects of HD 4306 are in agreement with an s-process composition and the lines in HD 6268 have a different profile, which is most likely linked to the presence of an r-process isotopic pattern. Conclusions. Two lines of barium of HD 6268 and HD 4306 seem to confirm the theoretical expectation that both r-process events and also s-process contribution by rotating massive stars have polluted the ancient halo of our Galaxy

A metabolomic data fusion approach to support gliomas grading

Magnetic resonance imaging (MRI) is the current gold standard for the diagnosis of brain tumors. However, despite the development of MRI techniques, the differential diagnosis of central nervous system (CNS) primary pathologies, such as lymphoma and glioblastoma or tumor-like brain lesions and glioma, is often challenging. MRI can be supported by in vivo magnetic resonance spectroscopy (MRS) to enhance its diagnostic power and multiproject-multicenter evaluations of classification of brain tumors have shown that an accuracy around 90% can be achieved for most of the pairwise discrimination problems. However, the survival rate for patients affected by gliomas is still low. The High-Resolution Magic-Angle-Spinning Nuclear Magnetic Resonance (HR-MAS NMR) metabolomics studies may be helpful for the discrimination of gliomas grades and the development of new strategies for clinical intervention. Here, we propose to use T2-filtered, diffusion-filtered and conventional water-presaturated spectra to try to extract as much information as possible, fusing the data gathered by these different NMR experiments and applying a chemometric approach based on Multivariate Curve Resolution (MCR). Biomarkers important for glioma's discrimination were found. In particular, we focused our attention on cystathionine (Cyst) that shows promise as a biomarker for the better prognosis of glioma tumors

A metabolomic data fusion approach to support gliomas grading

Magnetic resonance imaging (MRI) is the current gold standard for the diagnosis of brain tumors. However, despite the development of MRI techniques, the differential diagnosis of central nervous system (CNS) primary pathologies, such as lymphoma and glioblastoma or tumor-like brain lesions and glioma, is often challenging. MRI can be supported by in vivo magnetic resonance spectroscopy (MRS) to enhance its diagnostic power and multiproject-multicenter evaluations of classification of brain tumors have shown that an accuracy around 90% can be achieved for most of the pairwise discrimination problems. However, the survival rate for patients affected by gliomas is still low. The High-Resolution Magic-Angle-Spinning Nuclear Magnetic Resonance (HR-MAS NMR) metabolomics studies may be helpful for the discrimination of gliomas grades and the development of new strategies for clinical intervention. Here, we propose to use T2-filtered, diffusion-filtered and conventional water-presaturated spectra to try to extract as much information as possible, fusing the data gathered by these different NMR experiments and applying a chemometric approach based on Multivariate Curve Resolution (MCR). Biomarkers important for glioma's discrimination were found. In particular, we focused our attention on cystathionine (Cyst) that shows promise as a biomarker for the better prognosis of glioma tumors

Diffuse optical tomography by using time-resolved single pixel camera

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