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.

UR - http://www.scopus.com/inward/record.url?scp=85076642994&partnerID=8YFLogxK

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 -