Asymptotic Exceptional Steady States in Dissipative Dynamics
Yu-Min Hu1, Jan Carl Budich1,2
1Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany.
Physical Review Letters
|January 20, 2026
Summary
Dissipative quantum systems can exhibit exceptional steady states, challenging previous theories. This study links computational complexity to scaling towards these states, revealing dynamical instability at W=1.
Area of Science:
- Quantum Dynamics
- Non-Hermitian Physics
- Computational Complexity
Background:
- Spectral degeneracies in Liouvillian generators typically manifest as exceptional points.
- A no-go theorem excludes nondiagonalizable degeneracies in steady states (zero modes).
Purpose of the Study:
- Investigate the connection between diverging timescales in dissipative state preparation and exceptional steady states.
- Explore the relationship between computational complexity and the finite-size scaling towards exceptional steady states.
Main Methods:
- Analysis of Liouvillian generators and non-Hermitian operators.
- Case studies involving NP-complete problems encoded in quantum master equations.
- Examination of dissipative preparation of symmetry-protected topological phases.
- Parameter-dependent analysis of quantum jump weights (W) in the Lindblad master equation.
Main Results:
- Diverging timescales in dissipative state preparation approach an exceptional steady state in the thermodynamic limit.
- Computational complexity (exponential and polynomial scaling) correlates with finite-size scaling towards exceptional steady states.
- Exceptional steady states at W=1 signify a critical point of dynamical instability.
Conclusions:
- Steady states can exhibit nondiagonalizable degeneracies, contrary to prior no-go theorems.
- Exceptional steady states are linked to computational complexity and dynamical instability.
- The Lindblad master equation's parameter W=1 marks the onset of instability in dissipative systems.
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