---
_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'
...