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Spectral Gaps and Midgap States in Random Quantum Master Equations
Tankut Can1, Vadim Oganesyan1,2, Dror Orgad3
1Initiative for the Theoretical Sciences, The Graduate Center, CUNY, New York, New York 10012, USA.
Physical Review Letters
|December 24, 2019
Summary
Chaotic quantum systems coupled to noise exhibit non-zero decay rates even in the thermodynamic limit. For finite systems, a critical dissipation strength reveals isolated midgap states, impacting quantum dynamics.
Area of Science:
- Quantum Chaos
- Open Quantum Systems
- Random Matrix Theory
Background:
- Understanding the dynamics of chaotic quantum systems interacting with noisy environments is crucial.
- Previous studies have explored spectral properties but often without a focus on asymptotic decay rates in the thermodynamic limit.
Purpose of the Study:
- To investigate the decay rates of chaotic quantum systems coupled to noise.
- To analyze the spectral properties of the Liouvillian superoperator under various random-matrix ensembles.
- To identify the emergence and nature of spectral gaps and midgap states.
Main Methods:
- Modeling the Hamiltonian and system-noise coupling using random N×N Hermitian matrices.
- Studying the spectral properties of the Liouvillian superoperator.
- Analyzing various random-matrix ensembles and their thermodynamic limits (N→∞).
Main Results:
- The asymptotic decay rate remains non-zero in the thermodynamic limit, indicating a gapped spectrum.
- For finite N, the probability of a small spectral gap vanishes exponentially with system size N.
- A sharp transition occurs with increasing dissipation strength, leading to isolated midgap states.
Conclusions:
- Chaotic quantum systems coupled to noise maintain a non-zero decay rate, ensuring stability.
- The existence of midgap states beyond a critical dissipation strength has implications for quantum information processing.
- These findings are relevant for both theoretical understanding and experimental realization in quantum systems.
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