Xiong, Bo2022-11-142022-11-142022-08https://hdl.handle.net/11299/243162University of Minnesota Ph.D. dissertation. August 2022. Major: Physics. Advisor: Fiona Burnell. 1 computer file (PDF); ix, 165 pages.In this dissertation, I investigate discuss constrained boundary Lindblad dynamics of the integrable, PXPand GOE systems coupled to a bath described by the PXP-type Hamiltonian. Two types of constraints are imposed on the system: (a) constrained Ising Hilbert space which is lack of a tensor product structure and (b) kinetic constraints imposed not only inside the systems but also at the boundary between the system and the bath. In all of the three systems, we observe a strong dependence of relaxation rates on the initial eigenstates. In particular, two types of slow states are observed and investigated. The impact of exponentially large zero energy space on the open-system dynamics is proved to be small.enThesis or Dissertation