20.500.12556/RUL-124026 Spectral transitions and universal steady states in random Kraus maps and circuits The study of dissipation and decoherence in generic open quantum systems recently led to the investigation of spectral and steady-state properties of random Lindbladian dynamics. A natural question is then how realistic and universal those properties are. Here, we address these issues by considering a different description of dissipative quantum systems, namely, the discrete-time Kraus map representation of completely positive quantum dynamics. Through random matrix theory (RMT) techniques and numerical exact diagonalization, we study random Kraus maps, allowing for a varying dissipation strength, and their local circuit counterpart. We find the spectrum of the random Kraus map to be either an annulus or a disk inside the unit circle in the complex plane, with a transition between the two cases taking place at a critical value of dissipation strength. The eigenvalue distribution and the spectral transition are well described by a simplified RMT model that we can solve exactly in the thermodynamic limit, by means of non-Hermitian RMT and quaternionic free probability. The steady state, on the contrary, is not affected by the spectral transition. It has, however, a perturbative crossover regime at small dissipation, inside which the steady state is characterized by uncorrelated eigenvalues. At large dissipation (or for any dissipation for a large-enough system), the steady state is well described by a random Wishart matrix. The steady-state properties thus coincide with those already observed for random Lindbladian dynamics, indicating their universality. Quite remarkably, the statistical properties of the local Kraus circuit are qualitatively the same as those of the nonlocal Kraus map, indicating that the latter, which is more tractable, already captures the realistic and universal physical properties of generic open quantum systems. nonequilibrium statistical mechanics open quantum systems neravnovesna statistična mehanika odprti kvantni sistemi true false false Angleški jezik Slovenski jezik Neznano 2020-12-21 11:50:48 2020-12-21 11:50:49 2022-09-04 03:57:12 0000-00-00 00:00:00 2020 0 0 Str. 134310-1-134310-13 iss. 13 Vol. 102 2020 0000-00-00 PostprintKoncna Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 536.93 2469-9950 10.1103/PhysRevB.102.134310 42982147 2997348 RAZ_Sa_Lucas_2020.pdf RAZ_Sa_Lucas_2020.pdf 1 735516A9737EFB78BF3B190A13570388 181d3c3ed0d45fe9ab5211f0689b52880795087c3e99bc9441ba5169f6c6a5b5 74f3ab78-a1bb-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=139405 https://journals.aps.org/prb/abstract/10.1103/PhysRevB.102.134310 1 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=140144 Fakulteta za matematiko in fiziko 0 0 0