---
_id: '8198'
abstract:
- lang: eng
  text: We investigate how the critical driving amplitude at the Floquet many-body
    localized (MBL) to ergodic phase transition differs between smooth and nonsmooth
    drives. To this end, we numerically study a disordered spin-1/2 chain which is
    periodically driven by a sine or square-wave drive over a wide range of driving
    frequencies. In both cases the critical driving amplitude increases monotonically
    with the frequency, and at large frequencies it is identical for the two drives.
    However, at low and intermediate frequencies the critical amplitude of the square-wave
    drive depends strongly on the frequency, while that of the sinusoidal drive is
    almost constant over a wide frequency range. By analyzing the density of drive-induced
    resonances we conclude that this difference is due to resonances induced by the
    higher harmonics which are present (absent) in the Fourier spectrum of the square-wave
    (sine) drive. Furthermore, we suggest a numerically efficient method for estimating
    the frequency dependence of the critical driving amplitudes for different drives
    which is based on calculating the density of drive-induced resonances. We conclude
    that delocalization occurs once the density of drive-induced resonances reaches
    a critical value determined only by the static system.
acknowledgement: We thank Y. Bar Lev, T. Biadse, and, particularly, E. Bairey and
  B. Katzir for illuminating discussions and their many insights and help. The authors
  thank N. Lindner for his support throughout this project. We are further grateful
  to M. Serbyn, A. Kamenev, A. Turner, and S. de Nicola for reading the manuscript
  and providing good feedback and suggestions. We acknowledge financial support from
  the Defense Advanced Research Projects Agency through the DRINQS program, Grant
  No. D18AC00025. T.G. was in part supported by an Aly Kaufman Fellowship at the Technion.
  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
  Marie SkłodowskaCurie Grant Agreement No. 754411.under the Marie Skłodowska-Curie
  Grant Agreement No.754411.
article_number: '214204'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Asaf A.
  full_name: Diringer, Asaf A.
  last_name: Diringer
- first_name: Tobias
  full_name: Gulden, Tobias
  id: 1083E038-9F73-11E9-A4B5-532AE6697425
  last_name: Gulden
  orcid: 0000-0001-6814-7541
citation:
  ama: Diringer AA, Gulden T. Impact of drive harmonics on the stability of Floquet
    many-body localization. <i>Physical Review B</i>. 2021;103(21). doi:<a href="https://doi.org/10.1103/PhysRevB.103.214204">10.1103/PhysRevB.103.214204</a>
  apa: Diringer, A. A., &#38; Gulden, T. (2021). Impact of drive harmonics on the
    stability of Floquet many-body localization. <i>Physical Review B</i>. American
    Physical Society. <a href="https://doi.org/10.1103/PhysRevB.103.214204">https://doi.org/10.1103/PhysRevB.103.214204</a>
  chicago: Diringer, Asaf A., and Tobias Gulden. “Impact of Drive Harmonics on the
    Stability of Floquet Many-Body Localization.” <i>Physical Review B</i>. American
    Physical Society, 2021. <a href="https://doi.org/10.1103/PhysRevB.103.214204">https://doi.org/10.1103/PhysRevB.103.214204</a>.
  ieee: A. A. Diringer and T. Gulden, “Impact of drive harmonics on the stability
    of Floquet many-body localization,” <i>Physical Review B</i>, vol. 103, no. 21.
    American Physical Society, 2021.
  ista: Diringer AA, Gulden T. 2021. Impact of drive harmonics on the stability of
    Floquet many-body localization. Physical Review B. 103(21), 214204.
  mla: Diringer, Asaf A., and Tobias Gulden. “Impact of Drive Harmonics on the Stability
    of Floquet Many-Body Localization.” <i>Physical Review B</i>, vol. 103, no. 21,
    214204, American Physical Society, 2021, doi:<a href="https://doi.org/10.1103/PhysRevB.103.214204">10.1103/PhysRevB.103.214204</a>.
  short: A.A. Diringer, T. Gulden, Physical Review B 103 (2021).
date_created: 2020-08-04T13:03:40Z
date_published: 2021-06-21T00:00:00Z
date_updated: 2023-08-04T10:56:33Z
day: '21'
department:
- _id: MaSe
doi: 10.1103/PhysRevB.103.214204
ec_funded: 1
external_id:
  arxiv:
  - '2007.14879'
  isi:
  - '000664429700005'
intvolume: '       103'
isi: 1
issue: '21'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2007.14879
month: '06'
oa: 1
oa_version: Preprint
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Physical Review B
publication_identifier:
  eissn:
  - '24699969'
  issn:
  - '24699950'
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
status: public
title: Impact of drive harmonics on the stability of Floquet many-body localization
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 103
year: '2021'
...
---
_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
arxiv: 1
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.
    <i>Entropy</i>. 2021;23(1). doi:<a href="https://doi.org/10.3390/e23010125">10.3390/e23010125</a>
  apa: Gulden, T., &#38; Kamenev, A. (2021). Dynamics of ion channels via non-hermitian
    quantum mechanics. <i>Entropy</i>. MDPI. <a href="https://doi.org/10.3390/e23010125">https://doi.org/10.3390/e23010125</a>
  chicago: Gulden, Tobias, and Alex Kamenev. “Dynamics of Ion Channels via Non-Hermitian
    Quantum Mechanics.” <i>Entropy</i>. MDPI, 2021. <a href="https://doi.org/10.3390/e23010125">https://doi.org/10.3390/e23010125</a>.
  ieee: T. Gulden and A. Kamenev, “Dynamics of ion channels via non-hermitian quantum
    mechanics,” <i>Entropy</i>, 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.” <i>Entropy</i>, vol. 23, no. 1, e23010125, MDPI, 2021, doi:<a
    href="https://doi.org/10.3390/e23010125">10.3390/e23010125</a>.
  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
license: https://creativecommons.org/licenses/by/4.0/
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'
...
---
_id: '8199'
abstract:
- lang: eng
  text: We investigate a mechanism to transiently stabilize topological phenomena
    in long-lived quasi-steady states of isolated quantum many-body systems driven
    at low frequencies. We obtain an analytical bound for the lifetime of the quasi-steady
    states which is exponentially large in the inverse driving frequency. Within this
    lifetime, the quasi-steady state is characterized by maximum entropy subject to
    the constraint of fixed number of particles in the system's Floquet-Bloch bands.
    In such a state, all the non-universal properties of these bands are washed out,
    hence only the topological properties persist.
acknowledgement: "N.L., T.G. and E.B. acknowledge support from the European Research
  Council (ERC) under\r\nthe European Union Horizon 2020 Research and Innovation Programme
  (Grant Agreement\r\nNo. 639172). T.G. was in part supported by an Aly Kaufman Fellowship
  at the Technion. T.G.\r\nacknowledges funding from the Institute of Science and
  Technology (IST) Austria, and from\r\nthe European Union’s Horizon 2020 research
  and innovation programme under the Marie\r\nSkłodowska-Curie Grant Agreement No.
  754411. N.L. acknowledges support from the People Programme (Marie Curie Actions)
  of the European Unions Seventh Framework 546 Programme (FP7/20072013), under REA
  Grant Agreement No. 631696, and by the Israeli Center\r\nof Research Excellence
  (I-CORE) Circle of Light funded by the Israel Science Foundation (Grant\r\nNo. 1802/12).
  M.R. gratefully acknowledges the support of the European Research Council\r\n(ERC)
  under the European Union Horizon 2020 Research and Innovation Programme (Grant\r\nAgreement
  No. 678862). M.R. acknowledges the support of the Villum Foundation. M.R. and\r\nE.B.
  acknowledge support from CRC 183 of the Deutsche Forschungsgemeinschaft"
article_number: '015'
article_processing_charge: No
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: Erez
  full_name: Berg, Erez
  last_name: Berg
- first_name: Mark Spencer
  full_name: Rudner, Mark Spencer
  last_name: Rudner
- first_name: Netanel
  full_name: Lindner, Netanel
  last_name: Lindner
citation:
  ama: Gulden T, Berg E, Rudner MS, Lindner N. Exponentially long lifetime of universal
    quasi-steady states in topological Floquet pumps. <i>SciPost Physics</i>. 2020;9.
    doi:<a href="https://doi.org/10.21468/scipostphys.9.1.015">10.21468/scipostphys.9.1.015</a>
  apa: Gulden, T., Berg, E., Rudner, M. S., &#38; Lindner, N. (2020). Exponentially
    long lifetime of universal quasi-steady states in topological Floquet pumps. <i>SciPost
    Physics</i>. SciPost Foundation. <a href="https://doi.org/10.21468/scipostphys.9.1.015">https://doi.org/10.21468/scipostphys.9.1.015</a>
  chicago: Gulden, Tobias, Erez Berg, Mark Spencer Rudner, and Netanel Lindner. “Exponentially
    Long Lifetime of Universal Quasi-Steady States in Topological Floquet Pumps.”
    <i>SciPost Physics</i>. SciPost Foundation, 2020. <a href="https://doi.org/10.21468/scipostphys.9.1.015">https://doi.org/10.21468/scipostphys.9.1.015</a>.
  ieee: T. Gulden, E. Berg, M. S. Rudner, and N. Lindner, “Exponentially long lifetime
    of universal quasi-steady states in topological Floquet pumps,” <i>SciPost Physics</i>,
    vol. 9. SciPost Foundation, 2020.
  ista: Gulden T, Berg E, Rudner MS, Lindner N. 2020. Exponentially long lifetime
    of universal quasi-steady states in topological Floquet pumps. SciPost Physics.
    9, 015.
  mla: Gulden, Tobias, et al. “Exponentially Long Lifetime of Universal Quasi-Steady
    States in Topological Floquet Pumps.” <i>SciPost Physics</i>, vol. 9, 015, SciPost
    Foundation, 2020, doi:<a href="https://doi.org/10.21468/scipostphys.9.1.015">10.21468/scipostphys.9.1.015</a>.
  short: T. Gulden, E. Berg, M.S. Rudner, N. Lindner, SciPost Physics 9 (2020).
date_created: 2020-08-04T13:04:15Z
date_published: 2020-07-29T00:00:00Z
date_updated: 2023-08-22T08:28:24Z
day: '29'
ddc:
- '530'
department:
- _id: MaSe
doi: 10.21468/scipostphys.9.1.015
ec_funded: 1
external_id:
  isi:
  - '000557362300008'
file:
- access_level: open_access
  content_type: application/pdf
  creator: dernst
  date_created: 2020-08-06T08:56:06Z
  date_updated: 2020-08-06T08:56:06Z
  file_id: '8202'
  file_name: 2020_SciPostPhys_Gulden.pdf
  file_size: 531137
  relation: main_file
  success: 1
file_date_updated: 2020-08-06T08:56:06Z
has_accepted_license: '1'
intvolume: '         9'
isi: 1
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: SciPost Physics
publication_identifier:
  issn:
  - 2542-4653
publication_status: published
publisher: SciPost Foundation
quality_controlled: '1'
scopus_import: '1'
status: public
title: Exponentially long lifetime of universal quasi-steady states in topological
  Floquet pumps
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: 9
year: '2020'
...