Coding closed and open quantum systems in MATLAB: applications in quantum optics and condensed matter

We develop a package of numerical simulations implemented in MATLAB to solve complex many-body quantum systems. We focus on widely used examples that include the calculation of the magnetization dynamics for the closed and open Ising model, dynamical quantum phase transition in cavity QED arrays, Markovian dynamics for interacting two-level systems, and the non-Markovian dynamics of the pure-dephasing spin-boson model. These examples will be useful for undergraduate and graduate students with a medium or high background in MATLAB, and also for researches interested in numerical studies applied to quantum optics and condensed matter systems.