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Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics

by 1 and 2,3,*
1
Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria
2
School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA
3
William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, MN 55455, USA
*
Author to whom correspondence should be addressed.
Entropy 2021, 23(1), 125; https://doi.org/10.3390/e23010125
Received: 2 December 2020 / Revised: 12 January 2021 / Accepted: 15 January 2021 / Published: 19 January 2021
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. View Full-Text
Keywords: non-Hermitian Hamiltonians; algebraic topology; semiclassical methods; nanopores; ion transport; statistical mechanics non-Hermitian Hamiltonians; algebraic topology; semiclassical methods; nanopores; ion transport; statistical mechanics
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MDPI and ACS Style

Gulden, T.; Kamenev, A. Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics. Entropy 2021, 23, 125. https://doi.org/10.3390/e23010125

AMA Style

Gulden T, Kamenev A. Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics. Entropy. 2021; 23(1):125. https://doi.org/10.3390/e23010125

Chicago/Turabian Style

Gulden, Tobias; Kamenev, Alex. 2021. "Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics" Entropy 23, no. 1: 125. https://doi.org/10.3390/e23010125

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