Computational Physics II

This textbook is intended for master's degree students and is a follow-up to the Computational Physics I course studied at the bachelor's level. The content of the textbook Computational Physics II focuses on stochastic methods of solving physical problems, mainly on Monte Carlo (MC) simulation of many-particle systems. The focus on this computationally intensive approach is motivated by the gradual increase in the computing capacities of ordinary computers as well as the introduction of high-performance computing clusters. This has led to significant progress in the development of new simulation techniques, thanks to which MC simulations have found application in various areas of research and application practice. Considering the main research focus of the department, this text is particularly devoted to the presentation of basic and more advanced MC simulation techniques applied to a simple Ising spin model in order to investigate its magnetic, thermodynamic and critical properties. The next part is devoted to MC simulations of random processes. It focuses on the simplest but also the most basic random walk process and demonstrates its applications in financial analysis and the solution of a quantum system described by the time-dependent Schrödinger equation. The last part is dedicated to the basics of molecular dynamics, applied to simulating the classical movement of atoms in a given force field. By mastering the problems addressed in this course, students will obtain a potential tool for working out of their diploma theses, or a methodology useful for their further scientific and research practice in the field of investigating of complex systems. The lectured topic is subsequently exercised in the form of preparing projects implemented in the freely distributable software Octave, which is easy on the user's programming skills and which students have the opportunity to familiarize themselves with in the previous study.