TY - JOUR
T1 - Spectral Gaps and Midgap States in Random Quantum Master Equations
AU - Can, Tankut
AU - Oganesyan, Vadim
AU - Orgad, Dror
AU - Gopalakrishnan, Sarang
N1 - Publisher Copyright:
© 2019 American Physical Society.
PY - 2019/12/5
Y1 - 2019/12/5
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevLett.123.234103
DO - 10.1103/PhysRevLett.123.234103
M3 - Article
C2 - 31868445
AN - SCOPUS:85076642994
SN - 0031-9007
VL - 123
JO - Physical review letters
JF - Physical review letters
IS - 23
M1 - 234103
ER -