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Towards a Theory of Metastability in Open Quantum Dynamics
Katarzyna Macieszczak1,2, Mădălin Guţă1, Igor Lesanovsky2
1School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom.
Physical Review Letters
|July 2, 2016
Summary
We introduce a theory for metastability in quantum systems, revealing how systems partially relax into long-lived states. This theory leverages spectral properties for low-dimensional approximations of quantum dynamics.
Area of Science:
- Quantum Physics
- Statistical Mechanics
- Dynamical Systems Theory
Background:
- Classical stochastic dynamics provides a framework for understanding metastability.
- Open quantum systems exhibit complex dynamics influenced by their environment.
Purpose of the Study:
- Establish a theory of metastability for Markovian open quantum systems.
- Develop methods for approximating complex quantum dynamics.
Main Methods:
- Generalize concepts from classical stochastic dynamics.
- Analyze the spectral properties of the generator of quantum dynamics.
- Construct low-dimensional approximations using metastable state manifolds.
Main Results:
- Identify partial relaxation into metastable states distinct from the stationary state.
- Demonstrate that spectral splitting underlies time-scale separation.
- Show that metastable manifolds can be approximated using low-lying eigenmatrices.
Conclusions:
- Metastability in open quantum systems can be theoretically described.
- Spectral analysis provides a powerful tool for simplifying quantum dynamics.
- The metastable manifold may comprise disjoint states, noiseless subsystems, or decoherence-free subspaces.
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