Partial Integrability of 3-d Bohmian Trajectories

In this paper we study the integrability of 3-d Bohmian trajectories of a system of quantum harmonic oscillators. We show that the initial choice of quantum numbers is responsible for the existence (or not) of an integral of motion which confines the trajectories on certain invariant surfaces. We give a few examples of orbits in cases where there is or there is not an integral and make some comments on the impact of partial integrability in Bohmian Mechanics. Finally, we make a connection between our present results for the integrability in the 3-d case and analogous results found in the 2-d and 4-d cases.Comment: 18 pages, 3 figure

Origin of chaos in 3-d Bohmian trajectories

We study the 3-d Bohmian trajectories of a quantum system of three harmonic oscillators. We focus on the mechanism responsible for the generation of chaotic trajectories. We demonstrate the existence of a 3-d analogue of the mechanism found in earlier studies of 2-d systems, based on moving 2-d `nodal point - X-point complexes'. In the 3-d case, we observe a foliation of nodal point - X-point complexes, forming a `3-d structure of nodal and X-points'. Chaos is generated when the Bohmian trajectories are scattered at one or more close encounters with such a structure.Comment: 7 pages, 8 figure

Perturbed precessing ellipses as the building blocks of spiral arms in a barred galaxy with two pattern speeds

Observations and simulations of barred spiral galaxies have shown that, in general, the spiral arms rotate at a different pattern speed to that of the bar. The main conclusion from the bibliography is that the bar rotates faster than the spiral arms with a double or even a triple value of angular velocity. The theory that prevails in explaining the formation of the spiral arms in the case of a barred spiral galaxy with two pattern speeds is the manifold theory, where the orbits that support the spiral density wave are chaotic, and are related to the manifolds emanating from the Lagrangian points L_1 and L_2 at the end of the bar. In the present study, we consider an alternative scenario in the case where the bar rotates fast enough in comparison with the spiral arms and the bar potential can be considered as a perturbation of the spiral potential. In this case, the stable elliptical orbits that support the spiral density wave (in the case of grand design galaxies) are transformed into quasiperiodic orbits (or 2D tori) with a certain thickness. The superposition of these perturbed preccesing ellipses for all the energy levels of the Hamiltonian creates a slightly perturbed symmetrical spiral density wave.Comment: 9 pages, 7 figure

Microvascular resistance predicts myocardial salvage and infarct characteristics in ST-elevation myocardial infarction

<b>Background:</b> The pathophysiology of myocardial injury and repair in patients with ST‐elevation myocardial infarction is incompletely understood. We investigated the relationships among culprit artery microvascular resistance, myocardial salvage, and ventricular function.<p></p> <b>Methods and Results:</b> The index of microvascular resistance (IMR) was measured by means of a pressure‐ and temperature‐sensitive coronary guidewire in 108 patients with ST‐elevation myocardial infarction (83% male) at the end of primary percutaneous coronary intervention. Paired cardiac MRI (cardiac magnetic resonance) scans were performed early (2 days; n=108) and late (3 months; n=96) after myocardial infarction. T2‐weighted‐ and late gadolinium–enhanced cardiac magnetic resonance delineated the ischemic area at risk and infarct size, respectively. Myocardial salvage was calculated by subtracting infarct size from area at risk. Univariable and multivariable models were constructed to determine the impact of IMR on cardiac magnetic resonance–derived surrogate outcomes. The median (interquartile range) IMR was 28 (17–42) mm Hg/s. The median (interquartile range) area at risk was 32% (24%–41%) of left ventricular mass, and the myocardial salvage index was 21% (11%–43%). IMR was a significant multivariable predictor of early myocardial salvage, with a multiplicative effect of 0.87 (95% confidence interval 0.82 to 0.92) per 20% increase in IMR; P<0.001. In patients with anterior myocardial infarction, IMR was a multivariable predictor of early and late myocardial salvage, with multiplicative effects of 0.82 (95% confidence interval 0.75 to 0.90; P<0.001) and 0.92 (95% confidence interval 0.88 to 0.96; P<0.001), respectively. IMR also predicted the presence and extent of microvascular obstruction and myocardial hemorrhage.<p></p> <b>Conclusion:</b> Microvascular resistance measured during primary percutaneous coronary intervention significantly predicts myocardial salvage, infarct characteristics, and left ventricular ejection fraction in patients with ST‐elevation myocardial infarction.<p></p&gt