We study dynamics and thermodynamics of ion transport in narrow, water-filled channels, considered as effective 1D Coulomb systems. The long range nature of the inter-ion interactions comes about due to the dielectric constants mismatch between the water and the surrounding medium, confining the electric filed to stay mostly within the water-filled channel. Statistical mechanics of such Coulomb systems is dominated by entropic effects which may be accurately accounted for by mapping onto an effective quantum mechanics. In presence of multivalent ions the corresponding quantum mechanics appears to be non-Hermitian. In this review we discuss a framework for semiclassical calculations for the effective non-Hermitian Hamiltonians. Non-Hermiticity elevates WKB action integrals from the real line to closed cycles on a complex Riemann surfaces where direct calculations are not attainable. We circumvent this issue by applying tools from algebraic topology, such as the Picard-Fuchs equation. We discuss how its solutions relate to the thermodynamics and correlation functions of multivalent solutions within narrow, water-filled channels.

中文翻译：

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通过非厄米量子力学的离子通道动力学

我们研究狭窄、充满水的通道中离子传输的动力学和热力学，被认为是有效的一维库仑系统。离子间相互作用的长程性质是由于水和周围介质之间的介电常数不匹配而产生的，将电场限制在主要停留在充满水的通道内。这种库仑系统的统计力学受熵效应支配，这可以通过映射到有效量子力学来准确解释。在多价离子的存在下，相应的量子力学似乎是非厄米的。在这篇综述中，我们讨论了有效非厄米哈密顿量的半经典计算框架。在无法直接计算的复杂黎曼曲面上，非厄米性将 WKB 作用积分从实线提升到闭环。我们通过应用代数拓扑中的工具来规避这个问题，例如 Picard-Fuchs 方程。我们讨论了它的解决方案如何与狭窄的、充满水的通道内的多价解决方案的热力学和相关函数相关。