20.500.12556/RUL-155002 Phantom relaxation rate of the average purity evolution in random circuits due to Jordan non-Hermitian skin effect and magic sums Phantom relaxation is relaxation with a rate that is not given by a finite spectral gap. Studying the average purity dynamics in a staircase random Haar circuit and the spectral decomposition of a nonsymmetric matrix describing the underlying Markovian evolution, we explain how that can arise out of an ordinary-looking spectrum. Crucial are alternating expansion coefficients that diverge in the thermodynamic limit due to the non-Hermitian skin effect in the matrix describing the average purity dynamics under an overall unitary evolution. The mysterious phantom relaxation emerges out of localized generalized eigenvectors describing the Jordan normal form kernel, and, independently, also out of interesting trigonometric sums due to localized true eigenvectors. All this shows that when dealing with non-Hermitian matrices it can happen that the spectrum is not the relevant object; rather, it is the pseudospectrum or, equivalently, a delicate cancellation enabled by localized eigenvectors. quantum mechanics kvantna mehanika true false true Angleški jezik Slovenski jezik Članek v reviji 2024-03-13 13:48:33 2024-03-13 13:48:34 2024-03-28 12:36:05 0000-00-00 00:00:00 2023 0 0 Str. 033145-1-033145-17 iss. 3 Vol. 5 2023 0000-00-00 Zaloznikova NiDoloceno NiDoloceno 0000-00-00 0000-00-00 2023-09-01 530.145 2643-1564 10.1103/PhysRevResearch.5.033145 188725251 PhysRevResearch.5.033145.pdf PhysRevResearch.5.033145.pdf 1 5CF611260A4B84A06C4592490A286D90 90b34e6c6ac5c73ffe4e33f36b40ec8c29c0dfde9ebee34818c22917a6ff7ec5 0507cb6b-e13a-11ee-88aa-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=181705 https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.033145 0 158036ca-e13a-11ee-88aa-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=181706 Fakulteta za matematiko in fiziko 0 0 0