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The free creation and annihilation operators as the central limit of the quantum Bernoulli process. (English) Zbl 0927.60066

The authors propose a new method of construction of free creation and annihilation operators with the help of the simplest spin model. They demonstrate that, based on the quantum Bernoulli process which is determined on the tensor product of the 2-dimensional Hilbert space, one can define two sequences of quantum random variables (operators) \(\{T_k, k\geq 1\}\) and \(\{T_k^*, k\geq 1\}\) such that the central limit of \((1/\sqrt{n})\sum_{k=1}^n T_k^*\) is free creation operator while the central limit of \((1/\sqrt{n})\sum_{k=1}^n T_k\) is annihilation operator.

MSC:

60H25 Random operators and equations (aspects of stochastic analysis)
81P20 Stochastic mechanics (including stochastic electrodynamics)
47N55 Applications of operator theory in statistical physics (MSC2000)
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