Geodesic
Generalized Coherent States and Random Shift Operators
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Noncommutative Analysis and Quantum Information Theory, Tome 324 (2024), pp. 124-131

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We study the Chernoff averages for random generalized shift operators in the case of noncanonical commutation relations between creation and annihilation operators. We introduce the concepts of shift-dual ladder operators and generalized shift operators. As an example, we consider a one-parameter family of commutation relations for which generalized shift operators are unitary and satisfy the semigroup property on straight lines passing through the origin. For this family, we prove that the sequence of expectations of Feynman–Chernoff iterations of random shift operators converges to a limit strongly continuous semigroup.
Keywords: generalized coherent states, Feynman–Chernoff iterations, random operators, strongly continuous one-parameter semigroups. 
@article{TM_2024_324_a11,
     author = {R. Sh. Kalmetev and Yu. N. Orlov and V. Zh. Sakbaev},
     title = {Generalized {Coherent} {States} and {Random} {Shift} {Operators}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {124--131},
     publisher = {mathdoc},
     volume = {324},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2024_324_a11/}
}
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R. Sh. Kalmetev; Yu. N. Orlov; V. Zh. Sakbaev. Generalized Coherent States and Random Shift Operators. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Noncommutative Analysis and Quantum Information Theory, Tome 324 (2024), pp. 124-131. http://geodesic.mathdoc.fr/item/TM_2024_324_a11/