Exact solutions of interacting dissipative systems via weak symmetries

Abstract

We demonstrate how the presence of continuous weak symmetry can be used to analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method can be viewed as implementing an exact, sector-dependent mean-field decoupling, or alternatively, as a kind of quantum-to-classical mapping. We focus on two canonical examples: a nonlinear bosonic mode subject to incoherent loss and pumping, and an inhomogeneous quantum Ising model with arbitrary connectivity and local dissipation. In both cases, we calculate and analyze the full dissipation spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.

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

“…[10] and references therein for an updated review on the subject). Although there are some analytical techniques based on third quantization [11,12], resummation of perturbative series [13,14], weak symmetries [15], or flow equations [16], open quantum systems are generally characterized numerically, e.g., via exact diagonalization or time Density-Matrix-Renormalization-Group methods [17][18][19][20][21][22][23][24][25], which prevent in many cases a simple understanding of the phenomena.…”