O problema da difusão clássica : uma abordagem via operadores da Mecânica Quântica

Abstract

This work aims to use the Master-Equation to study the delusion of particles. Initially, we summarized the simple quantum harmonic oscillator in order to formulate the application of the creation and annihilation operators. We, then, studied the Hamiltonian of the two-particle and two-site case, which was later generalized to the linear chain N site case. In the generalized case particles can jump into their closest neighbor by delusion. We also analyzed the case of the box-like behaved bosons: two particles and two boxes, one particle and three boxes, one particle and four boxes, one particle and five boxes, two particles and three boxes to obtain their probabilities and the average number of particles as a function of time. In the case of one particle and five boxes we considered that the number of particles is independent of the delusion that happens among themselves. For the case in two parts and three boxes we used the fact that the particles are uncorrelated, not having restriction for the amount of particles that _t in each box. We obtained the probability for the case of a single particle to calculate the combined probabilities for the case of many particles in a chain (N particle chain delusion).