The present thesis is devoted to the dynamics in open or closed many-body bosonic systems, with the use of beyond mean-field methods. In the first part, inspired by the state-of-the-art experiments, we study the dynamics of a Bose-Einstein condensation which is loaded in an optical lattice with localized loss channels for the atoms. We prove that the particular form of the dissipation can help us to control the many-body dynamics. The loss allows the local manipulation of the system’s coherence properties and creates attractive fixed points in the classical (mean-field) phase space. We predict the dynamical creation of stable nonlinear structures like discrete bright and dark solitons. Furthermore, for specific initial states, the systems produces highly entangled and long-living states, which are of high relevance for practical applications. The first part of this thesis ends with the study of non-equilibrium bosonic transport across optical one-dimensional lattices. In the second part, we present techniques for bosonic many-body systems which are based on path integrals. We analyze the Bose-Einstein condensation phenomenon by using tools from quantum information theory and field theory. Finally, we introduce a coherent state path integral formalism in the continuum, which allows us the systematic development of approximate methods for the study of bosons in optical lattices.
The present thesis is devoted to the dynamics in open or closed manybodybosonic systems, with the use of beyond mean-eld methods.In the rst part, inspired by the state-of-the-art experiments, we study thedynamics of a Bose-Einstein condensation which is loaded in an optical latticewith localized loss channels for the atoms. We prove that the particularform of the dissipation can help us to control the many-body dynamics. Theloss allows the local manipulation of the system's coherence properties andcreates attractive xed points in the classical (mean-eld) phase space. Wepredict the dynamical creation of stable nonlinear structures like discretebright and dark solitons. Furthermore, for specic initial states, the systemsproduces highly entangled and long-living states, which are of high relevancefor practical applications. The rst part of this thesis ends with the study ofnon-equilibrium bosonic transport across optical one-dimensional lattices.In the second part, we present techniques for bosonic many-body systemswhich are based on path integrals. We analyze the Bose-Einstein condensationphenomenon by using tools from quantum information theory and eldtheory. Finally, we introduce a coherent state path integral formalism inthe continuum, which allows us the systematic development of approximatemethods for the study of bosons in optical lattices.
Open many‐body quantum systems have recently gained renewed interest in the context of quantum information science and quantum transport with biological clusters and ultracold atomic gases. A series of results in diverse setups is presented, based on a Master equation approach to describe the dissipative dynamics of ultracold bosons in a one‐dimensional lattice. The creation of mesoscopic stable many‐body structures in the lattice is predicted and the non‐equilibrium transport of neutral atoms in the regime of strong and weak interactions is studied.