Estudo da dinâmica de Langevin para um potencial quártico com composição harmônica

Abstract

The study of the mechanisms involved in dynamic transitions in bistable systems dates back to the early twentieth century with the pioneering work of Svante Arrhenius and Antoine Kramers. Due to the wide application spectrum of these models in areas such as solid state, chemistry and biological systems and the attempt to understand the dependence of transport mechanisms on the roughness of the energy surface that describes them, interest in these phenomena has experienced renewed attention from the scientific community. Usually three approaches are applied in the investigation of this problem: the Fokker-Planck Equation method, the Master Equation and the Langevin Equation. In this dissertation we developed the study of the stochastic dynamics of particles under the action of a bistable quartic potential decomposed in Fourier series. In analogy to previous works, this strategy allows us to investigate the role of potential surface roughness on the transition dynamics. In order to characterize the process, we determined by means of computational simulations via Langevin dynamics and numerical calculus, the behavior of the average position hxi, the average first pass time h i and their respective fluctuations x2 and the susceptibility as a function of T temperature and roughness. associated to the harmonic deformations of the potential surface. The behaviors of the investigated quantities suggest a possible non-equilibrium phase transition.