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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.
Physical Review Letters
|February 4, 2022
Summary
Researchers used continuous weak symmetry to analytically diagonalize complex quantum systems. This method provides an exact description of dynamics and the dissipative spectrum for driven-dissipative quantum systems.
Area of Science:
- Quantum mechanics
- Statistical physics
- Condensed matter theory
Background:
- Markovian dissipative systems with strong interactions or nonlinearity present challenges for exact analytical solutions.
- Understanding the full dynamics and dissipative spectrum is crucial for characterizing these complex quantum systems.
Purpose of the Study:
- To develop a novel analytical method for diagonalizing the Liouvillian of a specific class of Markovian dissipative systems.
- To enable an exact description of the full dynamics and dissipative spectrum in these systems.
Main Methods:
- Utilizing the presence of continuous weak symmetry to analytically diagonalize the Liouvillian.
- Applying an exact, sector-dependent mean-field decoupling or a quantum-to-classical mapping approach.
- Focusing on canonical examples: a nonlinear bosonic mode and an inhomogeneous quantum Ising model.
Main Results:
- Successfully demonstrated the analytical diagonalization of the Liouvillian for the studied systems.
- Obtained an exact description of the full dynamics and the complete dissipative spectrum.
- Analyzed the dissipation spectrum for both the nonlinear bosonic mode and the quantum Ising model.
Conclusions:
- The developed method, based on continuous weak symmetry, provides a powerful tool for analyzing complex driven-dissipative quantum systems.
- This approach offers an exact description of system dynamics and spectral properties, applicable to various other systems.
- It facilitates a deeper understanding of quantum systems with strong interactions or nonlinearity under dissipation.
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