| Abstract: | We study the statistical mechanics of open quantum systems coupled to external baths at their edges. We treat the dynamics of such systems using the Lindblad formalism and focus on a class of problems that allow for analytical solutions of the steady state and equilibration properties. In particular, we examine the quantum XY model and the transverse field Ising model in 1D, with the outer spins coupled to external baths. We study the relaxation time to steady state, and compute the steady state correlations in these system. Furthermore, we develop a method to extract the exact density matrix at the steady state. We use these techniques to analyze the properties of these systems under various configurations of the external baths. |