Dynamics of Quantum Systems with Interacting Particles

Abstract

In this thesis, I study the static properties and dynamics of a quantum system of interacting particles. For this, I employ the laws of quantum mechanics, which differ from the laws of classical mechanics used to interpret the macroscopic world around us. Quantum mechanics is a branch of physics that describes how matter and light behave on a microscopic level. My focus is on a lattice system that has on each site a localized particle with spin ½. Spins are intrinsic properties of microscopic particles that tell us how they react to magnetic fields. The basic constituents of matter, such as electrons, protons, and neutrons, have spins ½, while atoms have higher values of spins. The interactions between the spins may lead to collective behaviors with macroscopic effects, such as ferromagnetism, where the spins line up parallel to each other, and antiferromagnetism, where neighboring spins point in opposite directions.