Non-Universal Behavior of the k-Body Embedded Gaussian Unitary Ensemble of Random Matrices

Using a novel approach, we investigate the shape of the average spectrum and the spectral fluctuations of the $k$-body embedded unitary ensemble in the limit of large matrix dimension. We identify the transition point between semicircle and Gaussian shape. The transition also affects the spectral fluctuations which deviate from Wigner-Dyson form and become Poissonian in the limit $k << m << l$. Here $m$ is the number of Fermions and $l$ the number of degenerate single-particle states.Comment: 4 pages, no figures, revised version including a new proof of one of our main claim

Phase-Space Volume of Regions of Trapped Motion: Multiple Ring Components and Arcs

The phase--space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, sudden reductions in the phase-space volume or gaps are observed at specific values of the parameter which tunes the dynamics; these locations are approximated by the stability resonances. The latter are defined by a resonant condition on the stability exponents of a central linearly stable periodic orbit. We show that, for more than two degrees of freedom, these resonances can be excited opening up gaps, which effectively separate and reduce the regions of trapped motion in phase space. Using the scattering approach to narrow rings and a billiard system as example, we demonstrate that this mechanism yields rings with two or more components. Arcs are also obtained, specifically when an additional (mean-motion) resonance condition is met. We obtain a complete representation of the phase-space volume occupied by the regions of trapped motion.Comment: 19 pages, 17 figure

Non-Ergodic Behaviour of the k-Body Embedded Gaussian Random Ensembles for Bosons

We investigate the shape of the spectrum and the spectral fluctuations of the $k$-body Embedded Gaussian Ensemble for Bosons in the dense limit, where the number of Bosons $m \to \infty$ while both $k$, the rank of the interaction, and $l$, the number of single-particle states, are kept fixed. We show that the relative fluctuations of the low spectral moments do not vanish in this limit, proving that the ensemble is non-ergodic. Numerical simulations yield spectra which display a strong tendency towards picket-fence type. The wave functions also deviate from canonical random-matrix behaviourComment: 7 pages, 5 figures, uses epl.cls (included

Food, Acid Supplementation and Drug Absorption - a Complicated Gastric Mix: a Randomized Control Trial.

PURPOSE:The purpose of this study was to determine the impact of food on gastric pH and the ability of over the counter betaine hydrochloride (BHCl) acid to reacidify gastric pH after food-induced elevations in gastric pH. METHODS:This open-label cross over clinical study (NCT02758015) included 9 subjects who were randomly assigned to one of 16 possible, 4-period cross-over sequences to determine the impact and relationship of food and gastric pH with acid supplementation. Subjects were administered various doses (1500&nbsp;mg, 3000&nbsp;mg and 4500&nbsp;mg) of betaine hydrochloride (BHCl) to determine the ability of acid supplementation to reacidify gastric pH after the elevation of gastric pH caused by the ingestion of food. RESULTS:Following the administration of food and the resulting elevation in gastric pH, time to return to baseline gastric pH levels without acid supplementation was 49.7 ± 14.0&nbsp;min. Administering 4500&nbsp;mg of BHCl acid in capsules was able to reacidify gastric pH levels back to baseline following the administration of food in approximately 17.3 ± 5.9&nbsp;min. AUCpH of each treatment were similar and not statistically different. Mean max pH following the administration of food was 3.20 ± 0.55. CONCLUSION:The ability of food to elevate and maintain gastric pH levels in the presence of acid supplementation was made evident throughout the study. A 4500&nbsp;mg dose of BHCl was required to reacidify gastric pH after the administration of food. This study details the difficulty faced by clinicians in dosing a poorly soluble, weakly basic drug to patients receiving acid reducing agents where administration with food is recommended to avoid gastric side effects. TRIAL REGISTRATION:https://clinicaltrials.gov/ct2/show/NCT02758015

Alteración de las biotitas y biotitas clorizadas de la granodiorita de Collserola (Barcelona)

[ES] Se estudia la alteración natural experimentada por las biotitas y biotitas cloritizadas de la granodiorita de la Serra de Collcerola (Barcelona), bajo clima mediterráneo. Se muestrearon nueve perfiles, separándose magnéticamente las biotitas de la fracción arena, analizándose químicamente (elementos totales), por difractometría de R.X. y microscopia electrónica de barrido. También se estudiaron con el microscopio petrográfico láminas delgadas de muestras no perturbadas. Las biotitas evolucionan progresivamente primero a interestratificados biotita-vermiculita y después a vermiculita, apreciándose una tendencia a la esmectización, sugiriendo que las condiciones medioambitentales en las que se ha producido la alteración son muy similares a las actuales. La fase clorita procedente de las biotitas cloritizadas permanece inalterada en dicho medio.[EN] The weathering of biotites and cloritized biotites from a granodiorite from Serra de Collcerola (Barcelona, Spain), under mediterranean climate, has been studied. The sand fraction from the horizons of nine pedological profiles were sampled and the biotites magnetically separated and analysed by XRD, SEM and chemically. Thin sections of undisturbed samples were also studied. The weathering sequence from non-cloritized biotites was Biotite - Interlayer B-V - Vermiculite with a trend towards smectitization. The chlorite mineral from chloritized biotites remains unchanged in this environment. These results suggest tliat the weathering environment has been quite similar to the present one.Peer reviewe

Nearest-Neighbor Distributions and Tunneling Splittings in Interacting Many-Body Two-Level Boson Systems

We study the nearest-neighbor distributions of the $k$-body embedded ensembles of random matrices for $n$ bosons distributed over two-degenerate single-particle states. This ensemble, as a function of $k$, displays a transition from harmonic oscillator behavior ($k=1$) to random matrix type behavior ($k=n$). We show that a large and robust quasi-degeneracy is present for a wide interval of values of $k$ when the ensemble is time-reversal invariant. These quasi-degenerate levels are Shnirelman doublets which appear due to the integrability and time-reversal invariance of the underlying classical systems. We present results related to the frequency in the spectrum of these degenerate levels in terms of $k$, and discuss the statistical properties of the splittings of these doublets.Comment: 13 pages (double column), 7 figures some in color. The movies can be obtained at http://link.aps.org/supplemental/10.1103/PhysRevE.81.03621

Disjoining Pressure and the Film-Height-Dependent Surface Tension of Thin Liquid Films: New Insight from Capillary Wave Fluctuations

In this paper we review simulation and experimental studies of thermal capillary wave fluctuations as an ideal means for probing the underlying disjoining pressure and surface tensions, and more generally, fine details of the Interfacial Hamiltonian Model. We discuss recent simulation results that reveal a film-height-dependent surface tension not accounted for in the classical Interfacial Hamiltonian Model. We show how this observation may be explained bottom-up from sound principles of statistical thermodynamics and discuss some of its implications.Comment: File is accepted version with 70 pages and 13 figures. Submitted 23/08/2013; Accepted 06/11/2013; Online 17/11/201