Behavioral states alternate between wakefulness (wk), rapid eye movement (rem) and non-rem (nrem) sleep at time scale of hours i.e., light and dark cycle rhythms and from several tens of minutes to seconds (i.e., brief awakenings during sleep). Using statistical analysis of bout duration, Markov chains of sleep-wk dynamics and quantitative EEG analysis, we evaluated the influence of light/dark ...

The Wentzel-Kramers-Brillouin (WKB) perturbative series, a widely used technique for solving linear waves, is typically divergent and, at best, asymptotic, thus impeding predictions beyond the first few leading-order effects. Here, we report closed-form formula that exactly resums WKB series to all orders two turning point problems. elegantly interpreted as action evaluated using product of spa...

Path integral derivations are presented for two recently developed complex trajectory techniques for the propagation of wave packets, Complex WKB and BOMCA. Complex WKB is derived using a standard saddle point approximation of the path integral, but taking into account the h̄ dependence of both the amplitude and the phase of the intial wave function, thus giving rise to the need for complex clas...

The quantum mechanical tunnelling in a smooth symmetric double-well potential is a long-standing and well-known problem. Three methods have been proposed to calculate the energy splitting: the instanton method @1,2#, the WKB approximation @3,4# and numerical calculation @4–6#. The instanton method is helpful to understand the physical insight of quantum tunnelling, but the validity is restricte...

We study the stability and oscillation of traveling fronts in a three-component, advection-reaction biodegradation model. The three components are pollutant, nutrient , and bacteria concentrations. Under an explicit condition on the biomass growth and decay coeecients, we derive reduced, two-component, semilinear hyperbolic models through a relaxation procedure, during which biomass is slaved t...