Numerical solutions to open Hubbard models

• Autor(a) principal: Rodrigo Ferreira Saliba
• Data de Publicação: 2023
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/63993
• topic: Open quantum systems; Many body quantum systems; Hubbard model; Quantum trajectories; Open many body quantum systems; Continuous quantum Zeno effect; State preparation; Hubbard, Modelo de; Física do estado sólido

The dynamics of closed (ideal) quantum systems, i.e., systems which are not considered to be interacting with an external media (environment), are governed by unitary evolution which can be generally described by the Schrödinger -or, in the language of density operators, the von-Neunmann - equation. Nevertheless, real systems, i.e., systems which can be measured in the laboratory, are never completely closed and are inevitably going to interact with the various degrees of freedom of their environments. In this scenario, Schrödinger’s equation is only a valid description of the system’s evolution for small periods of time and a new description of its dynamics becomes necessary. One of the ways to do this is through the use of master equations, which are equations of motion that consider the dissipative effects in the system due to interactions with its environment. The Lindblad master equation is one of the most extensively studied. It describes Markovian evolutions, which are usually the case in the regime of weak interactions between system and environment. It has been successfully applied in many contexts, such as those of continuous measurement and quantum optics. In the context of open quantum many body problems it is not always possible to describe the system dynamics through a master equation in Lindblad form. Nonetheless, this approxmation can be used in a special class of atomic, molecular and optical (AMO) systems. The goal of these thesis is to study the dynamics of open many body quantum AMO systems which are approximately described by the Hubbard model through the use of numerical methods. To that end we will focus our attention on a particular simulational technique known as quantum trajectories which in many contexts proves to be very efficient - even more so if we integrate this method with others such as Tensor Networks, t-DMRG and exact diagonalization.