跨维度漏斗增强高维随机系统中的拓扑保护振荡
An interdimensional funnel enhances topologically protected oscillations in high-dimensional stochastic systems
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- University College London（伦敦大学学院）
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中文总结 AI 辅助
本文发现高维随机系统中的跨维度漏斗可增强拓扑保护振荡，通过量子化Zak相位标识拓扑转变，并展现出独特的非厄米趋肤效应，为生化系统相干动力学提供新机制。
中文摘要 AI 辅助
诸如蛋白质复合物之类的生化系统通常占据其维度随分子组分数量增长的构型空间。尽管高维通常被视为相干动力学的障碍，但在这里我们表明高维可以增强拓扑保护的振荡。在拓扑区域中，具有 $D$ 维构型空间的随机系统会发展出局限于一维边缘环的稳态电流。$D$ 维体相与一维环之间的边界面形成一个跨维度漏斗，依次将系统推向更低维度的面，直至一维环。因此，增加 $D$ 会增强漏斗，从而改善一维局域化和振荡相干性。量子化的双正交 Zak 相位标识了向拓扑区域的转变，该区域还表现出高度结构化的非厄米趋肤效应。与先前在随机系统中实现的拓扑态相比，我们揭示的现象在量子凝聚态或活性物质系统中没有对应物。
英文摘要
Biochemical systems such as protein complexes often occupy configuration spaces whose dimensionality grows with the number of molecular components. Although usually viewed as an obstacle to coherent dynamics, here we show that high dimensionality can enhance topologically protected oscillations. In the topological regime, a stochastic system with a $D$-dimensional configuration space develops a steady-state current confined to a one-dimensional edge cycle. The intervening boundary faces between the $D$-dimensional bulk and the one-dimensional cycle form an interdimensional funnel, sequentially pushing the system towards lower dimensional faces, down to the one-dimensional cycle. As a consequence, increasing $D$ enhances the funnel, leading to improved one-dimensional localization and oscillatory coherence. A quantized biorthogonal Zak phase identifies the transition to the topological regime, which additionally exhibits a highly structured non-Hermitian skin effect. In contrast with previous realizations of topological states in stochastic systems, the phenomena we uncover have no counterpart in quantum condensed matter or active matter systems.
