Spectral Gaps and Midgap States in Random Quantum Master Equations
Abstract
We discuss the decay rates of chaotic quantum systems coupled to noise. We model both the Hamiltonian and the systemnoise coupling by random N ×N Hermitian matrices, and study the spectral properties of the resulting Liouvillian superoperator. We consider various randommatrix 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 )∼Δ^{c N}, 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 slowestdecaying eigenvalues of the Liouvillian correspond to isolated "midgap" states. We give evidence that midgap states exist also for nonrandom systemnoise coupling and discuss some experimental implications of the above results.
 Publication:

Physical Review Letters
 Pub Date:
 December 2019
 DOI:
 10.1103/PhysRevLett.123.234103
 arXiv:
 arXiv:1902.01414
 Bibcode:
 2019PhRvL.123w4103C
 Keywords:

 Quantum Physics;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Statistical Mechanics
 EPrint:
 5+13 pages, 14 figures