论文标题
在开放的二次费米子系统中混合时间和截止
Mixing times and cutoffs in open quadratic fermionic systems
论文作者
论文摘要
在经典概率理论中，“截止”一词描述了一些马尔可夫链的属性，从（接近）其初始配置跳到（接近）完全混合的时间窗口。我们研究了两个费米子量子模型（“增益/损失”和“拓扑”模型）中的相干量子演化如何影响混合性能，它们的时间演变受费米子操作员的lindblad方程二次控制，允许直接精确解决方案。我们检查截止现象是否扩展到量子案例，并在某种程度上检查混合特性如何依赖于初始状态，从而以质量不同的行为来绘制模型的不同状态。在拓扑情况下，我们进一步展示了在采取开放边界条件时长期存在零模式的混合特性如何受到的影响。
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.
