In classical probability theory, the term "cutoff" describes the property of some Markov chains to jump from (close to) their initial configuration to (close to) completely mixed in a very narrow window of time. We investigate how coherent quantum evolution affects the mixing properties in two fermionic quantum models (the "gain/loss" and "topological" models), whose time evolution is governed by a Lindblad equation quadratic in fermionic operators, allowing for a straightforward exact solution. We check that the phenomenon of cutoff extends to the quantum case and examine with some care how the mixing properties depend on the initial state, drawing different regimes of our models with qualitatively different behaviour. In the topological case, we further show how the mixing properties are affected by the presence of a long-lived edge zero mode when taking open boundary conditions.

中文翻译：

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开放二次铁离子系统中的混合时间和截止

在经典概率论中，“截断”一词描述了一些马尔可夫链在很短的时间窗口内从（接近）其初始构型跃迁到（接近）完全混合的特性。我们研究相干量子演化如何影响两个铁氧体量子模型（“增益/损失”和“拓扑”模型）中的混合特性，它们的时间演化受铁氧体算子中二次方的Lindblad方程支配，从而提供了一种直接精确的解决方案。我们检查了截止现象是否扩展到量子情况，并仔细检查了混合特性如何依赖于初始状态，从而得出了模型具有质性不同的不同状态。在拓扑情况下，