Divergence of the Magnus expansion leads to paradoxes in the spin dynamics of solid-state NMR and in quantum informatics. This review presents results on quasi-equilibrium magnetization in a system of dipole--dipole (DD) coupled spins at times T₂ ≪ t ≪ T_1ρ in multiple pulse spin locking (T₂ is the transverse spin relaxation time, and T_1ρ is the rotating-frame spin-lattice relaxation time). It is shown how the contradictions between the results obtained with the Magnus expansion and experimental data can be removed. Systems of two and three DD coupled spins in multi-pulse spin locking are considered and the entanglement evolution is investigated using both the Magnus expansion and the exact solution obtained. The critical temperature for an entangled state is also found.

Keywords: Floquet theorem, Floquet Hamiltonian, Magnus expansion, Magnus paradox, multi-pulse spin locking, average Hamiltonian theory, concurrence, quantum entanglement PACS: 03.65.−w, 03.67.Mn, 76.60.−k (all) DOI: 10.3367/UFNe.2016.02.037753 URL: https://ufn.ru/en/articles/2016/6/g/ 000386349400007 2-s2.0-84987608366 2016PhyU...59..577K Citation: Kuznetsova E I, Fel’dman É B, Feldman D E "Magnus expansion paradoxes in the study of equilibrium magnetization and entanglement in multi-pulse spin locking" Phys. Usp. 59 577–582 (2016) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 29th, February 2016, accepted: 4th, February 2016 Оригинал: Кузнецова Е И, Фельдман Э Б, Фельдман Д Э «Парадоксы ряда Магнуса при исследовании равновесной намагниченности и запутанности в многоимпульсном спиновом локинге» УФН 186 647–653 (2016); DOI: 10.3367/UFNr.2016.02.037753