Quantum breaking time near classical equilibrium points

By using numerical and semiclassical methods, we evaluate the quantum breaking, or Ehrenfest time for a wave packet localized around classical equilibrium points of autonomous one-dimensional systems with polynomial potentials. We find that the Ehrenfest time diverges logarithmically with the inverse of the Planck constant whenever the equilibrium point is exponentially unstable. For stable equilibrium points, we have a power law divergence with exponent determined by the degree of the potential near the equilibrium point.Comment: 4 pages, 5 figure

Bistable equilibrium points of mercury body burden

In the last century mercury levels in the global environment have tripled as a result of increased pollution from industrial, occupational, medicinal and domestic uses \cite{BaMe03}. Glutathione is known to be the main agent responsible for the excretion of mercury (we refer to \cite{Thim05}, \cite{ZalBar99} and \cite{Lyn02}). It has also been shown that mercury inhibits glutathione synthetase (an enzyme acting in the synthesization of Glutathione), therefore leading to decreased glutathione levels (we refer to \cite{Thim05}, \cite{GeGe05}, \cite{GeGe06} and \cite{RDeth04}). Mercury also interferes with the production of heme in the porphyrin pathway \cite{WoMaEc93}. Heme is needed for biological energy production and ability to detox organic toxins via the P450 enzymes \cite{Boy06}. The purpose of this paper is to show that body's response to mercury exposure is hysteretic, i.e. when this feedback of mercury on its main detoxifying agents is strong enough then mercury body burden has two points of equilibrium: one with normal abilities to detoxify and low levels of mercury and one with inhibited abilities to detoxify and high levels of mercury. Furthermore, a small increase of body's mercury burden may not be sufficient to trigger observable neurotoxic effects but it may be sufficient to act as a switch leading to an accumulation of mercury in the body through environmental exposure until its toxicity becomes manifest.Comment: To appear in Journal of Biological System

Equilibria of point charges on convex curves

We study the equilibrium positions of three points on a convex curve under influence of the Coulomb potential. We identify these positions as orthotripods, three points on the curve having concurrent normals. This relates the equilibrium positions to the caustic (evolute) of the curve. The concurrent normals can only meet in the core of the caustic, which is contained in the interior of the caustic. Moreover, we give a geometric condition for three points in equilibrium with positive charges only. For the ellipse we show that the space of orthotripods is homeomorphic to a 2-dimensional bounded cylinder.Comment: minor correction