A note on black hole entropy, area spectrum, and evaporation

We argue that a process where a fuzzy space splits in two others can be used to explain the origin of the black hole entropy, and why a "generalized second law of thermodynamics" appears to hold in the presence of black holes. We reach the Bekenstein-Hawking formula from the count of the microstates of a black hole modeled by a fuzzy space. In this approach, a discrete area spectrum for the black hole, which becomes increasingly spaced as the black hole approaches the Planck scale, is obtained. We show that, as a consequence of this, the black hole radiation becomes less and less entropic as the black hole evaporates, in a way that some information about its initial state could be recovered.Comment: 4 pages, 2 figure

The Role of Ivabradine in the Management of Angina Pectoris

Stable angina pectoris affects 2–4 % of the population in Western countries and entails an annual risk of death and nonfatal myocardial infarction of 1–2 % and 3 %, respectively. Heart rate (HR) is linearly related to myocardial oxygen consumption and coronary blood flow, both at rest and during stress. HR reduction is a key target for the prevention of ischemia/angina and is an important mechanism of action of drugs which are recommended as first line therapy for the treatment of angina in clinical guidelines. However, many patients are often unable to tolerate the doses of beta blocker or non-dihydropyridine calcium antagonists required to achieve the desired symptom control. The selective pacemaker current inhibitor ivabradine was developed as a drug for the management of patients with angina pectoris, through its ability to reduce HR specifically. The available data suggest that ivabradine is a well-tolerated and effective anti-anginal agent and it is recommended as a second-line agent for relief of angina in guidelines. However, recent clinical trials of ivabradine have failed to show prognostic benefit and have raised potential concerns about safety. This article will review the available evidence base for the current role of ivabradine in the management of patients with symptomatic angina pectoris in the context of stable coronary artery disease

Magnetic monopole and string excitations in a two-dimensional spin ice

We study the magnetic excitations of a square lattice spin-ice recently produced in an artificial form, as an array of nanoscale magnets. Our analysis, based upon the dipolar interaction between the nanomagnetic islands, correctly reproduces the ground-state observed experimentally. In addition, we find magnetic monopole-like excitations effectively interacting by means of the usual Coulombic plus a linear confining potential, the latter being related to a string-like excitation binding the monopoles pairs, what indicates that the fractionalization of magnetic dipoles may not be so easy in two dimensions. These findings contrast this material with the three-dimensional analogue, where such monopoles experience only the Coulombic interaction. We discuss, however, two entropic effects that affect the monopole interactions: firstly, the string configurational entropy may loose the string tension and then, free magnetic monopoles should also be found in lower dimensional spin ices; secondly, in contrast to the string configurational entropy, an entropically driven Coulomb force, which increases with temperature, has the opposite effect of confining the magnetic defects.Comment: 8 pages. Accepted by Journal of Applied Physics (2009

Magnetization reversals in a disk-shaped small magnet with an interface

We consider a nanodisk possessing two coupled materials with different ferromagnetic exchange constant. The common border line of the two media passes at the disk center dividing the system exactly in two similar half-disks. The vortex core motion crossing the interface is investigated with a simple description based on a two-dimensional model which mimics a very thin real material with such a line defect. The main result of this study is that, depending on the magnetic coupling which connects the media, the vortex core can be dramatically and repeatedly flipped from up to down and vice versa by the interface. This phenomenon produces burst-like emission of spin waves each time the switching process takes place.Comment: 11 pages, 10 figure