Microscopic Models and Simulations of Local Activation Processes

Abstract

The classical reaction theory of Kramers describes transitions over a potential barrier (activation processes) by Fokker-Planck equations or the corresponding Langevin equations. Kramers model is based on the assumption of uncorrelated stochastic forces. In this work simple but more realistic microscopic models for transitions are developed. The physical forces leading to transitions are studied by means of molecular dynamics simulations. The investigation is restricted to two-dimensional systems. In particular we study local energy excitations of soft molecules solved in liquids. This investigation makes use of an analogy to Toda lattices. For Toda systems it was shown in earlier work that soliton excitations and soliton fusion at the soft sites may lead to local energy spots. The basic configuration studied here is a soft reacting site imbedded into a thermal bath of hard molecules. In the first part we develop a microscopic model for Kramers bistable potential well and calculate the transition rates by MD-simulations. In the following parts we study models for the dissociation of molecules and for the fusion of molecules.

Bound states of electrons with soliton-like excitations in thermal systems - adiabatic approximations

“…We demonstrated this in figure 1 on the example of the specific heat, taken from an earlier work based on molecular dynamics simulations for Lennard-Jones-like molecules on a plane [16][17][18]. The calculation of the mean potential energy per molecule shows deviations from the ideal low-temperature Dulong-Petit value for a linear lattice, first an increase with temperature and only then a decrease to the ideal gas value.…”

“…Further, it is of relevance whether these excitations are observed in thermal systems. Some evidence for the occurrence of such thermal compression waves comes from earlier simulations for two-dimensional Lennard-Jones systems [16][17][18] Figure 3. Two-dimensional system of 100 Morse molecules (Bσ = 2) with periodic boundary conditions heated to the temperature T = 0.2 (in units of 2D).…”

“…This and other papers, e. g., [14,15] give us a hint that indeed in two-dimensional systems soliton-like excitations occur. Some evidence for the occurrence of thermal compression waves also comes from computer simulations for two-dimensional Lennard-Jones systems [16][17][18]. In these systems energy-rich hard excitations were observed which are capable of activating the imbedded impurities.…”

Nonlinear Dynamics of Active Brownian Particles

“…Superposition of solitons corresponds to multiple collisions in these systems. In higher dimensions a weak localisation of potential energy was observed also at the bindings of the bath molecules and was connected to a transition between different lattice configurations [17,18,19]. We introduce interactions described by the potential U (r 1 , ..., r N ); then the dynamics of Brownian particles is determined by the Langevin equation:…”

Harvesting thermal fluctuations: Activation process induced by a nonlinear chain in thermal equilibrium

“…There has been a surge of recent activity in an attempt to understand the thermal conductivity of nonlinear chains [24][25][26] The connection between the study of perfect nonlinear arrays and the Kramers problem arises because such arrays may themselves serve as models for a heat bath for other systems connected to them. [27][28][29] Albeit in different contexts, "perfect" arrays serving as energy storage and transfer assemblies for chemical or photochemical processes are not uncommon, [30][31][32][33] and literature on the subject goes back for two decades. [34][35][36] We thus consider the following variant of the Kramers problem: a bistable system connected to a nonlinear chain, which is in turn connected to a heat bath in the usual Langevin manner (see Fig.…”