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Updated: Oct 4, 2025

Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
Exact Solutions of Interacting Dissipative Systems via Weak Symmetries
A McDonald1,2, A A Clerk1
1Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA.
Abstract:
We demonstrate how the presence of continuous weak symmetry can be used to analytically diagonalize the Liouvillian of a class of Markovian dissipative systems with 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.
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