Spectral Gaps and Midgap States in Random Quantum Master Equations

Tankut Can, Vadim Oganesyan, Dror Orgad, Sarang Gopalakrishnan

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We discuss the decay rates of chaotic quantum systems coupled to noise. We model both the Hamiltonian and the system-noise coupling by random N×N Hermitian matrices, and study the spectral properties of the resulting Liouvillian superoperator. We consider various random-matrix ensembles, and find that for all of them the asymptotic decay rate remains nonzero in the thermodynamic limit; i.e., the spectrum of the superoperator is gapped as N→∞. For finite N, the probability of finding a very small gap vanishes as P(Δ)∼ΔcN, where c is insensitive to the dissipation strength. A sharp spectral transition takes place as the dissipation strength is increased: for dissipation beyond a critical strength, the slowest-decaying eigenvalues of the Liouvillian correspond to isolated "midgap" states. We give evidence that midgap states exist also for nonrandom system-noise coupling and discuss some experimental implications of the above results.

Original languageAmerican English
Article number234103
JournalPhysical Review Letters
Issue number23
StatePublished - 5 Dec 2019

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© 2019 American Physical Society.


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