Conferences and symposia. 70th anniversary of the E.K. Zavoisky physical-technical institute, Kazan scientific center of the Russian academy of sciences
Magnus expansion paradoxes in the study of equilibrium magnetization and entanglement in multi-pulse spin locking
D.E. Feldmanb aInstitute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow Region, Russian Federation bDepartment of Physics, Brown University, Providence, Rhode Island, USA
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 ≪ T1ρ in multiple pulse spin locking (T2 is the transverse spin relaxation time, and T1ρ 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/ 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)