Generalized Coherent States and Random Shift Operators

Pub Date : 2024-07-11 DOI:10.1134/s0081543824010127
R. Sh. Kalmetev, Yu. N. Orlov, V. Zh. Sakbaev
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Abstract

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.

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广义相干态和随机移位算子
摘要 我们研究了在创造算子和湮灭算子之间存在非经典换向关系的情况下,随机广义移位算子的切尔诺夫平均数。我们引入了移位双梯形算子和广义移位算子的概念。作为一个例子,我们考虑了换向关系的一个参数族,对于这个族,广义移位算子是单元的,并且满足通过原点的直线上的半群性质。对于这个族,我们证明了随机移位算子的费曼-切尔诺夫迭代期望序列收敛于一个极限强连续半群。
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