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 )∼Δc 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 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.
Physical Review Letters
- Pub Date:
- December 2019
- Quantum Physics;
- Condensed Matter - Mesoscale and Nanoscale Physics;
- Condensed Matter - Statistical Mechanics
- 5+13 pages, 14 figures