开放二次费米子系统的混合时间和截断
Mixing times and cutoffs in open quadratic fermionic systems
摘要：
在经典概率论中，术语“截断”描述了一些马尔可夫链在非常窄的时间窗口内从（接近）其初始配置跳到（接近）完全混合的属性。我们研究相干量子演化如何影响两个费米量子模型（“增益/损失”和“拓扑”模型）的混合特性，其时间演化是由一个林德布拉德方程二次费米子运营商，允许一个简单的精确解。我们检查，截断的现象延伸到量子的情况下，并检查与一些照顾如何混合属性依赖于初始状态，绘制不同的制度，我们的模型与定性不同的行为。在拓扑的情况下，我们进一步展示了如何混合性能的影响，当采取开放的边界条件时，存在一个长寿命的边缘零模式。
英文摘要：
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.
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