Sharif Digital Repository

Non-equilibrium systems refer to systems in which, unlike equilibrium systems, the initial condition plays an important role. Conventional methods in quantum field theory cannot be used to study these systems because they do not necessarily have a convergent perturbative expansion.In this thesis, we first briefly introduce the Ising model and fermions in the lattice gauge theory. We then introduce the two-particle irreducible (2PI) method as a tool to investigate nonequilibrium systems. Finally, using this method, we reformulate the Ising model for a system out of equilibrium  

Out-of-equilibrium systems have garnered increasing interest in recent years. These many-body systems do not exhibit ergodic behavior, even in the presence of generic interactions, allowing locally stored quantum information to remain accessible for extended periods through local observables. Due to these exotic characteristics, such systems are ideal candidates for the realization of quantum computing. Many-body localized systems serve as a prime example of these non-ergodic systems. In the absence of thermalization, long-range quantum order can persist even in highly excited states, contrasting with thermal systems where long-range order can only exist in the ground state of gapped...