Dresden 2020 – wissenschaftliches Programm
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TT 9.6: Vortrag
Montag, 16. März 2020, 11:30–11:45, HÜL 186
Hierarchy of relaxation timescales in local random Liouvillians — Kevin Wang1, •Francesco Piazza2, and David Luitz2 — 1Department of Physics, Stanford University, Stanford, California 94305, USA — 2Max Planck Institute for the Physics of Complex Systems, Noethnitzer Str. 38, Dresden, Germany
To characterize the generic behavior of open quantum systems, we consider random, purely dissipative Liouvillians with a notion of locality. We find that the positivity of the map implies a sharp separation of the relaxation timescales according to the locality of observables. Specifically, we analyze a spin-1/2 system of size ℓ with up to n-body Lindblad operators, which are n-local in the complexity-theory sense. Without locality (n=ℓ), the complex Liouvillian spectrum densely covers a “lemon”-shaped support, in agreement with recent findings [Phys. Rev. Lett. 123, 140403;arXiv:1905.02155]. However, for local Liouvillians (n<ℓ), we find that the spectrum is composed of several dense clusters with random matrix spacing statistics, each featuring a lemon-shaped support wherein all eigenvectors correspond to n-body decay modes. This implies a hierarchy of relaxation timescales of n-body observables, which we verify to be robust in the thermodynamic limit.