--- _id: '9020' abstract: - lang: eng text: '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. ' acknowledgement: "A.K. was supported by NSF grants DMR-2037654. T.G. acknowledges funding from the Institute of Science and Technology (IST) Austria, and from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 754411.\r\nWe are indebted to Boris Shklovskii for introducing us to the problem, and Alexander Gorsky and Peter Koroteev for introducing us to the Picard-Fuchs methods. A very special thanks goes to Michael Janas for several years of excellent collaboration on these topics. TG thanks Michael Kreshchuk for introduction to the exact WKB method and great collaboration on related projects. Figure 3 and Figure 4 are reproduced from Reference [25] with friendly permission by the Russian Academy of Sciences. Figure 2, Figure 4, Figure 5, Figure 6, and Figure 8 are reproduced from Reference [26] with friendly permission by IOP Publishing." article_number: e23010125 article_processing_charge: Yes article_type: original author: - first_name: Tobias full_name: Gulden, Tobias id: 1083E038-9F73-11E9-A4B5-532AE6697425 last_name: Gulden orcid: 0000-0001-6814-7541 - first_name: Alex full_name: Kamenev, Alex last_name: Kamenev citation: ama: Gulden T, Kamenev A. Dynamics of ion channels via non-hermitian quantum mechanics. Entropy. 2021;23(1). doi:10.3390/e23010125 apa: Gulden, T., & Kamenev, A. (2021). Dynamics of ion channels via non-hermitian quantum mechanics. Entropy. MDPI. https://doi.org/10.3390/e23010125 chicago: Gulden, Tobias, and Alex Kamenev. “Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics.” Entropy. MDPI, 2021. https://doi.org/10.3390/e23010125. ieee: T. Gulden and A. Kamenev, “Dynamics of ion channels via non-hermitian quantum mechanics,” Entropy, vol. 23, no. 1. MDPI, 2021. ista: Gulden T, Kamenev A. 2021. Dynamics of ion channels via non-hermitian quantum mechanics. Entropy. 23(1), e23010125. mla: Gulden, Tobias, and Alex Kamenev. “Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics.” Entropy, vol. 23, no. 1, e23010125, MDPI, 2021, doi:10.3390/e23010125. short: T. Gulden, A. Kamenev, Entropy 23 (2021). date_created: 2021-01-19T11:12:06Z date_published: 2021-01-19T00:00:00Z date_updated: 2023-08-07T13:34:18Z day: '19' ddc: - '530' department: - _id: MaSe doi: 10.3390/e23010125 ec_funded: 1 external_id: arxiv: - '2012.01390' isi: - '000610122000001' file: - access_level: open_access checksum: 6cd0e706156827c45c740534bd32c179 content_type: application/pdf creator: tgulden date_created: 2021-01-19T11:11:14Z date_updated: 2021-01-19T11:11:14Z file_id: '9021' file_name: Final published paper.pdf file_size: 981285 relation: main_file file_date_updated: 2021-01-19T11:11:14Z has_accepted_license: '1' intvolume: ' 23' isi: 1 issue: '1' language: - iso: eng month: '01' oa: 1 oa_version: Published Version project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Entropy publication_identifier: eissn: - 1099-4300 publication_status: published publisher: MDPI quality_controlled: '1' status: public title: Dynamics of ion channels via non-hermitian quantum mechanics tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 23 year: '2021' ...