We present new criteria, based on commutator methods, for the strong mixingproperty of discrete flows $\{U^N\}_{N\in\mathbb Z}$ and continuous flows$\{{\rm e}^{-itH}\}_{t\in\mathbb R}$ induced by unitary operators $U$ andself-adjoint operators $H$ in a Hilbert space $\mathcal H$. Our approach putinto evidence a general definition for the topological degree of the curves$N\mapsto U^N$ and $t\mapsto{\rm e}^{-itH}$ in the unitary group of $\mathcalH$. Among other examples, our results apply to skew products of compact Liegroups, time changes of horocycle flows and adjacency operators on graphs.
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机译：我们基于换向器方法提出了新的标准，用于离散流$ \ {U ^ N \} _ {N \ in \ mathbb Z} $和连续流$ \ {{\ rm e} ^ {-itH } \} _ {t \ in \ mathbb R} $由希尔伯特空间$ \ mathcal H $中的unit算子$ U $和自伴算子$ H $引起。我们的方法证明了在$ \ mathcalH $单一组中，曲线$ N \ mapsto U ^ N $和$ t \ mapsto {\ rm e} ^ {-itH} $的拓扑度的一般定义。除其他示例外，我们的结果适用于紧致李群的偏积，热循环的时间变化以及图形上的邻接算子。
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