Metaestabilidade na cruz

Abstract

Statistical Mechanics appeared in the middle of 1850, is based on the attempt of the use of microscopic models, with the intention of describing macroscopic phenomena. In general, such models have stochastic dynamics. That is, the micro-system particles evolve stochastically. In this work we are interested in certain systems which are called Markov Chains at continuous time, where the particles are located at points of the cartesian plane Z2. In our work, the dynamics used is that of Kawasaki, the original con guration of the particles is distributed in the format a cross. In models of statistical mechanics there is a function that is called by many by function energy (H). At each movement of the particles we have a new energy value for this new con guration. The system addressed in this work is such that it always seeks the lowest state of energy. In this search the system may be stuck in a certain valley for a long time (such phenomenon characterizes a metastate). However, for a very long time interval the system converges to a real state of equilibrium called the macro state. In our work we aim to verify the metastability of the particle system, starting from the simplest case, where the system is composed of only twelve particles and later we will study the system metastability of a larger number of particles. As a result of the work we will get the probability of the particle system reaching a certain macro state.