Product formulas in the framework of mean ergodic theorems
An extension of Chernoff’s product formula for one-parameter functions taking values in the space of bounded linear operators on a Banach space is given. Essentially, the n-th one-parameter function in the product formula is mapped by the n-th iterate of a contraction acting on the space of the one-parameter functions. The motivation to study this specific product formula lies in the growing field of dynamical control of quantum systems, involving the procedure of dynamical decoupling and also the Quantum Zeno effect.
KeywordsChernoff’s product formula Mean ergodic theorems Strongly continuous semigroups
Mathematics Subject Classification47D03 47A35 47N50
This work is supported by the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No. 732894 (FET Proactive HOT).