Authors: Gomez-Leon, Alvaro; Ramos, Tomas; Porras, Diego; Gonzalez-Tudela, Alejandro
Journal: PHYSICAL REVIEW A
Publication date: 2022/05/26
Abstract: The unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (nonunitary) dynamics, which can be radically different from closed-system scenarios. Such open quantum system dynamics is generally described by Lindblad master equations, whose dynamical and steady-state properties are challenging to obtain, especially in the many-particle regime. Here, we introduce a method to deal with these systems based on the calculation of a (dissipative) lattice Green???s function with a real-space decimation technique. Compared to other methods, such a technique enables us to obtain compact analytical expressions for the dynamics and steady-state properties, such as asymptotic decays or correlation lengths. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity, including the Hatano-Nelson model. The latter is especially illustrative because its surface and bulk dissipative behavior are linked due to its nontrivial topology, which manifests in directional amplification.