It is generally accepted that unstable systems decay according to an exponential law which has been experimentally verified on many quantum systems. However, deviation from exponential decay have been predicted for short as well as for very long decay times. The short-time deviation turns out to be very interesting due to its consequences leading to the so-called quantum Zeno effect – the inhib...

Spontaneous emission from reaction centers of photosynthetic bacteria has been recorded with a time resolution of 50 fs. Excitation was made directly into both the special-pair band (850 nm) and the Qx band of bacteriochlorophylls (608 nm). Rhodobacter sphaeroides R26, Rhodobacter capsulatus wild type, and four mutants of Rb. capsulatus were studied. In all cases the fluorescence decay was not ...

In this paper, I explore the exponential Rosenbrock-type method of order two. It is an explicit method that solves stiff ODEs. The method linearizes the equation with each step, then uses a matrix exponential to solve the linearized equation exactly. Previous research has identified stability bounds and convergence results. In this paper, I explore the stiffness capabilities of this second orde...

We derive sufficient conditions for asymptotic and monotone exponential decay in mean square of solutions the geometric Brownian motion with delay. The are written terms parameters explicit case decay. For decay, they easily resolvable numerically. analytical method is based on construction a Lyapunov functional (asymptotic decay) forward-backward estimate (exponential decay).

The chaotic portion of phase space of the simplified Fermi-Ulam model is studied under the context of transport of trajectories in two scenarios: (i) the trajectories are originated from a region distant from the islands of regular motion and are transported to a region located at a high portion of phase space and (ii) the trajectories are originated from chaotic regions around the islands of r...

For a general class of exponential weights on the line and on (−1, 1), we study pointwise convergence of the derivatives of Lagrange interpolation. Our weights include even weights of smooth polynomial decay near ±∞ (Freud weights), even weights of faster than smooth polynomial decay near ±∞ (Erdős weights) and even weights which vanish strongly near ±1, for example Pollaczek type weights. 1991...