In this paper we construct a quantum extension of the Laguerre semigroup and study its properties. In particular we show that it has a unique pure invariant state and any initial state converges to this invariant state. For initial states satisfying a finite energy condition, convergence is exponentially fast.

中文翻译：

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量子拉盖尔半群

在本文中，我们构造了 Laguerre 半群的量子扩展并研究了它的性质。特别地，我们表明它具有唯一的纯不变状态，并且任何初始状态都收敛到该不变状态。对于满足有限能量条件的初始状态，收敛速度呈指数级增长。