4.8 Article

Spectral Gaps and Midgap States in Random Quantum Master Equations

Journal

PHYSICAL REVIEW LETTERS
Volume 123, Issue 23, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.123.234103

Keywords

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Funding

  1. NSF [DMR-1653271, DMR-1508538]
  2. United States-Israel Binational Science Foundation [2018159]

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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 x 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 -> infinity. For finite N, the probability of finding a very small gap vanishes as P(Delta) similar to Delta(cN), 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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