A justification for the use of approximate transition amplitudes in semiclassical surface hopping

Recent work has shown that a certain surface hopping form of the wave function is capable of obtaining highly accurate transition probabilities for nonadiabatic problems. It has also been found that it is necessary to include hops in classically forbidden regions in order to obtain this level of accuracy at low energies. The amplitude for the hops in this surface hopping expansion of the wave function has the typical p^?1/2 semiclassical divergence at the turning points in the classical motion. While this singularity is an integrable divergence, the divergent behavior complicates the numerical evaluation of the integrals over hopping points that is present in the surface hopping expressions. Numerical evidence has shown that only small errors are incurred at most energies if these singular hopping amplitudes are replaced with a nonsingular approximation. This agreement is surprising, since the exact and approximate amplitudes differ greatly in the turning point region, and this region is expected to make important contributions to the transition probability at low energies. A numerical analysis is presented in this work that provides a justification as to why this numerically useful approximation works as well as it does.     

A sharper uncertainty principle

The work strengthens the result established by L. Cohen on uncertainty principle involving phase derivative. We propose stronger uncertainty principles not only in the classical setting for Fourier transform, but also for self-adjoint operators. We also deduce the conditions that give rise to the equal relation of the uncertainty principle. Examples are provided to show that the new uncertainty principle is truly sharper than the existing ones in literature.     

Direct and rapid electrochemical immunosensing system based on a conducting polymer

A system device using multifunctional conjugated copolymer poly(5-hydroxy-1,4-naphthoquinone-co-hydroxy-2-thioacetic acid-1,4-naphthoquinone) acting both as immobilizing and transducing element for reagentless immunosensor has been constructed. Its functionality was evaluated in an antigen-antibody interaction model using ovalbumin-anti-ovalbumin. It was shown that the system specifically detects via electrochemical signal the antigen-antibody immune interaction in a reagentless context. Comparison to the conventional ELISA technique relevant to performance and sensitivity was presented.     

On the convergence of the product of independent random operators

In this paper, we study infinite products of independent random operators. Conditions for the existence a.s. and the convergence in mean of order p of such infinite products are established.     

Dynamically consistent discrete metapopulation model

In this paper we construct nonstandard difference schemes, which are dynamically consistent with a metapopulation model formulated by Keymer et al. in 2000, i.e. preserve all dynamical properties of the differential equations of the model. These properties are: monotone convergence, boundedness, local asymptotic stability and especially, global stability of equilibria and non-periodicity of solutions. Numerical examples confirm the obtained theoretical results of the properties of the constructed difference schemes.     

The Extension of Distributions on Manifolds,a Microlocal Approach

Let M be a smooth manifold, \({I\subset M}\) a closed embedded submanifold of M and U an open subset of M. In this paper, we find conditions using a geometric notion of scaling for \({t\in \mathcal{D}^{\prime}(U{\setminus} I)}\) to admit an extension in \({\mathcal{D}^\prime(U)}\). We give microlocal conditions on t which allow to control the wave front set of the extension generalizing a previous result of Brunetti–Fredenhagen. Furthermore, we show that there is a subspace of extendible distributions for which the wave front of the extension is minimal which has applications for the renormalization of quantum field theory on curved spacetimes.