Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains

• URL: http://arxiv.org/abs/2202.07674v1
• Date: Tue, 15 Feb 2022 19:00:09 GMT
• Title: Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains
• Authors: \'Alvaro G\'omez-Le\'on and Tom\'as Ramos and Diego Porras and Alejandro Gonz\'alez-Tudela
• Abstract summary: Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
• Score: 62.997667081978825
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) 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 (dissipative) lattice Green's function with a real-space decimation technique. Compared to other methods, such technique enables obtaining 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 non-trivial topology, which manifests in directional amplification.

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