Statistical theory and microscopic simulations
of local activation processes
Werner Ebeling and Victor Yu. Podlipchuk
Institute of Physics, Humboldt University Berlin,
D - 10115 Berlin, Germany
The strong interest in local excitations is especially inspired by the theory of reaction rates [1]. The standard theory models the stochastic transitions over a high energy barrier. of potential energy. We discuss a class of observations of activation processes where the standard theory fails [2], and propose several mechanisms leading to non-standard energy rich events. Our special interest is devoted to local energy spots and to the high energy tails of the distributions. The main idea is, that catalytic activity in complex reaction systems is supported by nonlinear excitations capable to localize energy at special reaction sites. At first we discuss several 1D-systems which are analytically tractable and show in this way the importance of hard (soliton-like) excitations [3]. We show that, similar to stochastic resonance phenomena, a window of temperature exists, where activation processes and transitions are enhanced. These analytical findings for the 1D case are supported by molecular dynamics simulations for the 2D and the 3D case [4,5]. The simple model which we study in detail consists of one soft molecule simulating the reactive site, which is imbedded into a bath of hard molecules (the solvent). The simulatins show again, that hard soliton-like excitations and soliton fusion at the excitation sites may lead to local energy spots. It is shown that in thermal equilibrium a region of temperatures exists, where a kind of stochastic resonance is observed, i.e. high-energy events and transition rates are enhanced. Here the energy distributions of the active sites have long high-energy tails. Further the time-correlation functions of the forces and velocities at the active site is calculated and their relation to assumptions of the standard theory is discussed. In the final part the influence of quantum mechanical effects is discussed.