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Note on a Product Formula Related to Quantum Zeno Dynamics
- Source :
- Annales Henri Poincaré. 22:1669-1697
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- Given a nonnegative self-adjoint operator $H$ acting on a separable Hilbert space and an orthogonal projection $P$ such that $H_P := (H^{1/2}P)^*(H^{1/2}P)$ is densely defined, we prove that $\lim_{n\rightarrow \infty} (P\,\mathrm{e}^{-itH/n}P)^n = \mathrm{e}^{-itH_P}P$ 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 $P(0)=P$.<br />30 pages, no figures; to appear in Ann. H. Poincar\'e
- Subjects :
- Physics
Quantum Physics
Nuclear and High Energy Physics
81Q05, 47B25, 47D03, 47N50, 35J05
Operator (physics)
Orthographic projection
FOS: Physical sciences
Statistical and Nonlinear Physics
Mathematical Physics (math-ph)
Function (mathematics)
Extension (predicate logic)
Functional Analysis (math.FA)
Mathematics - Functional Analysis
Combinatorics
Product (mathematics)
FOS: Mathematics
Quantum Physics (quant-ph)
Mathematical Physics
Separable hilbert space
Strong operator topology
Quantum Zeno effect
Subjects
Details
- ISSN :
- 14240661 and 14240637
- Volume :
- 22
- Database :
- OpenAIRE
- Journal :
- Annales Henri Poincaré
- Accession number :
- edsair.doi.dedup.....975bdb6e8ce1a902d2f3dd5b5e10ccd1