Note on a Product Formula Related to Quantum Zeno Dynamics

0540706 - ÚJF 2022 RIV CH eng J - Journal Article
Exner, Pavel - Ichinose, T.
Note on a Product Formula Related to Quantum Zeno Dynamics.
Annales Henri Poincare. Roč. 22, MAY (2021), s. 1669-1697. ISSN 1424-0637. E-ISSN 1424-0661
R&D Projects: GA ČR GA17-01706S
Institutional support: RVO:61389005
Keywords : Hilbert space * operator topology
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 1.338, year: 2021
Method of publishing: Limited access
https://doi.org/10.1007/s00023-020-01014-z

Given a nonnegative self-adjoint operator H acting on a separable Hilbert space and an orthogonal projection P such that H-P := ((HP)-P-1/2)((HP)-P-1/2) is densely defined, we prove that lim(n ->infinity)(Pe(-itH/n)P)(n) = e(-itHP) P holds in the strong operator topology. We also derive modifications of this product formula and its extension to the situation when P is replaced by a strongly continuous projection-valued function satisfying P(0) = P.
Permanent Link: http://hdl.handle.net/11104/0319555