---
_id: '14851'
abstract:
- lang: ger
  text: Die Quantenrotation ist ein spannendes Phänomen, das in vielen verschiedenen
    Systemen auftritt, von Molekülen und Atomen bis hin zu subatomaren Teilchen wie
    Neutronen und Protonen. Durch den Einsatz von starken Laserpulsen ist es möglich,
    die mathematisch anspruchsvolle Topologie der Rotation von Molekülen aufzudecken
    und topologisch geschützte Zustände zu erzeugen, die unerwartetes Verhalten zeigen.
    Diese Entdeckungen könnten Auswirkungen auf die Molekülphysik und physikalische
    Chemie haben und die Entwicklung neuer Technologien ermöglichen. Die Verbindung
    von Quantenrotation und Topologie stellt ein aufregendes, interdisziplinäres Forschungsfeld
    dar und bietet neue Wege zur Kontrolle und Nutzung von quantenmechanischen Phänomenen.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Volker
  full_name: Karle, Volker
  id: D7C012AE-D7ED-11E9-95E8-1EC5E5697425
  last_name: Karle
  orcid: 0000-0002-6963-0129
- first_name: Mikhail
  full_name: Lemeshko, Mikhail
  id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
  last_name: Lemeshko
  orcid: 0000-0002-6990-7802
citation:
  ama: Karle V, Lemeshko M. Die faszinierende Topologie rotierender Quanten. <i>Physik
    in unserer Zeit</i>. 2024;55(1):28-33. doi:<a href="https://doi.org/10.1002/piuz.202301690">10.1002/piuz.202301690</a>
  apa: Karle, V., &#38; Lemeshko, M. (2024). Die faszinierende Topologie rotierender
    Quanten. <i>Physik in unserer Zeit</i>. Wiley. <a href="https://doi.org/10.1002/piuz.202301690">https://doi.org/10.1002/piuz.202301690</a>
  chicago: Karle, Volker, and Mikhail Lemeshko. “Die faszinierende Topologie rotierender
    Quanten.” <i>Physik in unserer Zeit</i>. Wiley, 2024. <a href="https://doi.org/10.1002/piuz.202301690">https://doi.org/10.1002/piuz.202301690</a>.
  ieee: V. Karle and M. Lemeshko, “Die faszinierende Topologie rotierender Quanten,”
    <i>Physik in unserer Zeit</i>, vol. 55, no. 1. Wiley, pp. 28–33, 2024.
  ista: Karle V, Lemeshko M. 2024. Die faszinierende Topologie rotierender Quanten.
    Physik in unserer Zeit. 55(1), 28–33.
  mla: Karle, Volker, and Mikhail Lemeshko. “Die faszinierende Topologie rotierender
    Quanten.” <i>Physik in unserer Zeit</i>, vol. 55, no. 1, Wiley, 2024, pp. 28–33,
    doi:<a href="https://doi.org/10.1002/piuz.202301690">10.1002/piuz.202301690</a>.
  short: V. Karle, M. Lemeshko, Physik in unserer Zeit 55 (2024) 28–33.
date_created: 2024-01-22T08:19:36Z
date_published: 2024-01-01T00:00:00Z
date_updated: 2024-02-15T14:29:04Z
day: '01'
ddc:
- '530'
department:
- _id: MiLe
doi: 10.1002/piuz.202301690
file:
- access_level: open_access
  checksum: 3051dadcf9bc57da97e36b647c596ab1
  content_type: application/pdf
  creator: dernst
  date_created: 2024-01-23T12:18:07Z
  date_updated: 2024-01-23T12:18:07Z
  file_id: '14878'
  file_name: 2024_PhysikZeit_Karle.pdf
  file_size: 1155244
  relation: main_file
  success: 1
file_date_updated: 2024-01-23T12:18:07Z
has_accepted_license: '1'
intvolume: '        55'
issue: '1'
keyword:
- General Earth and Planetary Sciences
- General Environmental Science
language:
- iso: ger
month: '01'
oa: 1
oa_version: Published Version
page: 28-33
publication: Physik in unserer Zeit
publication_identifier:
  eissn:
  - 1521-3943
  issn:
  - 0031-9252
publication_status: published
publisher: Wiley
quality_controlled: '1'
status: public
title: Die faszinierende Topologie rotierender Quanten
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 55
year: '2024'
...
---
_id: '15004'
abstract:
- lang: eng
  text: The impulsive limit (the “sudden approximation”) has been widely employed
    to describe the interaction between molecules and short, far-off-resonant laser
    pulses. This approximation assumes that the timescale of the laser-molecule interaction
    is significantly shorter than the internal rotational period of the molecule,
    resulting in the rotational motion being instantaneously “frozen” during the interaction.
    This simplified description of the laser-molecule interaction is incorporated
    in various theoretical models predicting rotational dynamics of molecules driven
    by short laser pulses. In this theoretical work, we develop an effective theory
    for ultrashort laser pulses by examining the full time-evolution operator and
    solving the time-dependent Schrödinger equation at the operator level. Our findings
    reveal a critical angular momentum, lcrit, at which the impulsive limit breaks
    down. In other words, the validity of the sudden approximation depends not only
    on the pulse duration but also on its intensity, since the latter determines how
    many angular momentum states are populated. We explore both ultrashort multicycle
    (Gaussian) pulses and the somewhat less studied half-cycle pulses, which produce
    distinct effective potentials. We discuss the limitations of the impulsive limit
    and propose a method that rescales the effective matrix elements, enabling an
    improved and more accurate description of laser-molecule interactions.
acknowledgement: We thank Bretislav Friedrich, Marjan Mirahmadi, Artem Volosniev,
  and Burkhard Schmidt for insightful discussions. M.L. acknowledges support by the
  European Research Council (ERC) under Starting Grant No. 801770 (ANGULON).
article_number: '023101'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Volker
  full_name: Karle, Volker
  id: D7C012AE-D7ED-11E9-95E8-1EC5E5697425
  last_name: Karle
  orcid: 0000-0002-6963-0129
- first_name: Mikhail
  full_name: Lemeshko, Mikhail
  id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
  last_name: Lemeshko
  orcid: 0000-0002-6990-7802
citation:
  ama: 'Karle V, Lemeshko M. Modeling laser pulses as δ kicks: Reevaluating the impulsive
    limit in molecular rotational dynamics. <i>Physical Review A</i>. 2024;109(2).
    doi:<a href="https://doi.org/10.1103/PhysRevA.109.023101">10.1103/PhysRevA.109.023101</a>'
  apa: 'Karle, V., &#38; Lemeshko, M. (2024). Modeling laser pulses as δ kicks: Reevaluating
    the impulsive limit in molecular rotational dynamics. <i>Physical Review A</i>.
    American Physical Society. <a href="https://doi.org/10.1103/PhysRevA.109.023101">https://doi.org/10.1103/PhysRevA.109.023101</a>'
  chicago: 'Karle, Volker, and Mikhail Lemeshko. “Modeling Laser Pulses as δ Kicks:
    Reevaluating the Impulsive Limit in Molecular Rotational Dynamics.” <i>Physical
    Review A</i>. American Physical Society, 2024. <a href="https://doi.org/10.1103/PhysRevA.109.023101">https://doi.org/10.1103/PhysRevA.109.023101</a>.'
  ieee: 'V. Karle and M. Lemeshko, “Modeling laser pulses as δ kicks: Reevaluating
    the impulsive limit in molecular rotational dynamics,” <i>Physical Review A</i>,
    vol. 109, no. 2. American Physical Society, 2024.'
  ista: 'Karle V, Lemeshko M. 2024. Modeling laser pulses as δ kicks: Reevaluating
    the impulsive limit in molecular rotational dynamics. Physical Review A. 109(2),
    023101.'
  mla: 'Karle, Volker, and Mikhail Lemeshko. “Modeling Laser Pulses as δ Kicks: Reevaluating
    the Impulsive Limit in Molecular Rotational Dynamics.” <i>Physical Review A</i>,
    vol. 109, no. 2, 023101, American Physical Society, 2024, doi:<a href="https://doi.org/10.1103/PhysRevA.109.023101">10.1103/PhysRevA.109.023101</a>.'
  short: V. Karle, M. Lemeshko, Physical Review A 109 (2024).
date_created: 2024-02-18T23:01:01Z
date_published: 2024-02-01T00:00:00Z
date_updated: 2024-02-26T09:45:20Z
day: '01'
department:
- _id: MiLe
doi: 10.1103/PhysRevA.109.023101
ec_funded: 1
external_id:
  arxiv:
  - '2307.07256'
intvolume: '       109'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2307.07256
month: '02'
oa: 1
oa_version: Preprint
project:
- _id: 2688CF98-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '801770'
  name: 'Angulon: physics and applications of a new quasiparticle'
publication: Physical Review A
publication_identifier:
  eissn:
  - 2469-9934
  issn:
  - 2469-9926
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Modeling laser pulses as δ kicks: Reevaluating the impulsive limit in molecular
  rotational dynamics'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 109
year: '2024'
...
---
_id: '12788'
abstract:
- lang: eng
  text: We show that the simplest of existing molecules—closed-shell diatomics not
    interacting with one another—host topological charges when driven by periodic
    far-off-resonant laser pulses. A periodically kicked molecular rotor can be mapped
    onto a “crystalline” lattice in angular momentum space. This allows us to define
    quasimomenta and the band structure in the Floquet representation, by analogy
    with the Bloch waves of solid-state physics. Applying laser pulses spaced by 1/3
    of the molecular rotational period creates a lattice with three atoms per unit
    cell with staggered hopping. Within the synthetic dimension of the laser strength,
    we discover Dirac cones with topological charges. These Dirac cones, topologically
    protected by reflection and time-reversal symmetry, are reminiscent of (although
    not equivalent to) that seen in graphene. They—and the corresponding edge states—are
    broadly tunable by adjusting the laser strength and can be observed in present-day
    experiments by measuring molecular alignment and populations of rotational levels.
    This paves the way to study controllable topological physics in gas-phase experiments
    with small molecules as well as to classify dynamical molecular states by their
    topological invariants.
acknowledgement: M. L. acknowledges support by the European Research Council (ERC)
  Starting Grant No. 801770 (ANGULON).
article_number: '103202'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Volker
  full_name: Karle, Volker
  id: D7C012AE-D7ED-11E9-95E8-1EC5E5697425
  last_name: Karle
- first_name: Areg
  full_name: Ghazaryan, Areg
  id: 4AF46FD6-F248-11E8-B48F-1D18A9856A87
  last_name: Ghazaryan
  orcid: 0000-0001-9666-3543
- first_name: Mikhail
  full_name: Lemeshko, Mikhail
  id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
  last_name: Lemeshko
  orcid: 0000-0002-6990-7802
citation:
  ama: Karle V, Ghazaryan A, Lemeshko M. Topological charges of periodically kicked
    molecules. <i>Physical Review Letters</i>. 2023;130(10). doi:<a href="https://doi.org/10.1103/PhysRevLett.130.103202">10.1103/PhysRevLett.130.103202</a>
  apa: Karle, V., Ghazaryan, A., &#38; Lemeshko, M. (2023). Topological charges of
    periodically kicked molecules. <i>Physical Review Letters</i>. American Physical
    Society. <a href="https://doi.org/10.1103/PhysRevLett.130.103202">https://doi.org/10.1103/PhysRevLett.130.103202</a>
  chicago: Karle, Volker, Areg Ghazaryan, and Mikhail Lemeshko. “Topological Charges
    of Periodically Kicked Molecules.” <i>Physical Review Letters</i>. American Physical
    Society, 2023. <a href="https://doi.org/10.1103/PhysRevLett.130.103202">https://doi.org/10.1103/PhysRevLett.130.103202</a>.
  ieee: V. Karle, A. Ghazaryan, and M. Lemeshko, “Topological charges of periodically
    kicked molecules,” <i>Physical Review Letters</i>, vol. 130, no. 10. American
    Physical Society, 2023.
  ista: Karle V, Ghazaryan A, Lemeshko M. 2023. Topological charges of periodically
    kicked molecules. Physical Review Letters. 130(10), 103202.
  mla: Karle, Volker, et al. “Topological Charges of Periodically Kicked Molecules.”
    <i>Physical Review Letters</i>, vol. 130, no. 10, 103202, American Physical Society,
    2023, doi:<a href="https://doi.org/10.1103/PhysRevLett.130.103202">10.1103/PhysRevLett.130.103202</a>.
  short: V. Karle, A. Ghazaryan, M. Lemeshko, Physical Review Letters 130 (2023).
date_created: 2023-04-02T22:01:10Z
date_published: 2023-03-10T00:00:00Z
date_updated: 2023-08-01T14:02:06Z
day: '10'
department:
- _id: MiLe
doi: 10.1103/PhysRevLett.130.103202
ec_funded: 1
external_id:
  arxiv:
  - '2206.07067'
  isi:
  - '000957635500003'
intvolume: '       130'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2206.07067
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 2688CF98-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '801770'
  name: 'Angulon: physics and applications of a new quasiparticle'
publication: Physical Review Letters
publication_identifier:
  eissn:
  - 1079-7114
  issn:
  - 0031-9007
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
related_material:
  link:
  - description: News on the ISTA website
    relation: press_release
    url: https://ista.ac.at/en/news/topology-of-rotating-molecules/
scopus_import: '1'
status: public
title: Topological charges of periodically kicked molecules
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 130
year: '2023'
...
---
_id: '9903'
abstract:
- lang: eng
  text: Eigenstate thermalization in quantum many-body systems implies that eigenstates
    at high energy are similar to random vectors. Identifying systems where at least
    some eigenstates are nonthermal is an outstanding question. In this Letter we
    show that interacting quantum models that have a nullspace—a degenerate subspace
    of eigenstates at zero energy (zero modes), which corresponds to infinite temperature,
    provide a route to nonthermal eigenstates. We analytically show the existence
    of a zero mode which can be represented as a matrix product state for a certain
    class of local Hamiltonians. In the more general case we use a subspace disentangling
    algorithm to generate an orthogonal basis of zero modes characterized by increasing
    entanglement entropy. We show evidence for an area-law entanglement scaling of
    the least-entangled zero mode in the broad parameter regime, leading to a conjecture
    that all local Hamiltonians with the nullspace feature zero modes with area-law
    entanglement scaling and, as such, break the strong thermalization hypothesis.
    Finally, we find zero modes in constrained models and propose a setup for observing
    their experimental signatures.
acknowledgement: "We acknowledge useful discussions with V. Gritsev and A. Garkun
  and suggestions on implementation of the\r\nPPXPP model by D. Bluvstein. A. M. and
  M. S. were supported by the European Research Council (ERC) under\r\nthe European
  Union’s Horizon 2020 research and innovation program (Grant Agreement No. 850899)"
article_number: '060602'
article_processing_charge: Yes (in subscription journal)
article_type: letter_note
arxiv: 1
author:
- first_name: Volker
  full_name: Karle, Volker
  id: D7C012AE-D7ED-11E9-95E8-1EC5E5697425
  last_name: Karle
  orcid: 0000-0002-6963-0129
- first_name: Maksym
  full_name: Serbyn, Maksym
  id: 47809E7E-F248-11E8-B48F-1D18A9856A87
  last_name: Serbyn
  orcid: 0000-0002-2399-5827
- first_name: Alexios
  full_name: Michailidis, Alexios
  id: 36EBAD38-F248-11E8-B48F-1D18A9856A87
  last_name: Michailidis
  orcid: 0000-0002-8443-1064
citation:
  ama: Karle V, Serbyn M, Michailidis A. Area-law entangled eigenstates from nullspaces
    of local Hamiltonians. <i>Physical Review Letters</i>. 2021;127(6). doi:<a href="https://doi.org/10.1103/physrevlett.127.060602">10.1103/physrevlett.127.060602</a>
  apa: Karle, V., Serbyn, M., &#38; Michailidis, A. (2021). Area-law entangled eigenstates
    from nullspaces of local Hamiltonians. <i>Physical Review Letters</i>. American
    Physical Society. <a href="https://doi.org/10.1103/physrevlett.127.060602">https://doi.org/10.1103/physrevlett.127.060602</a>
  chicago: Karle, Volker, Maksym Serbyn, and Alexios Michailidis. “Area-Law Entangled
    Eigenstates from Nullspaces of Local Hamiltonians.” <i>Physical Review Letters</i>.
    American Physical Society, 2021. <a href="https://doi.org/10.1103/physrevlett.127.060602">https://doi.org/10.1103/physrevlett.127.060602</a>.
  ieee: V. Karle, M. Serbyn, and A. Michailidis, “Area-law entangled eigenstates from
    nullspaces of local Hamiltonians,” <i>Physical Review Letters</i>, vol. 127, no.
    6. American Physical Society, 2021.
  ista: Karle V, Serbyn M, Michailidis A. 2021. Area-law entangled eigenstates from
    nullspaces of local Hamiltonians. Physical Review Letters. 127(6), 060602.
  mla: Karle, Volker, et al. “Area-Law Entangled Eigenstates from Nullspaces of Local
    Hamiltonians.” <i>Physical Review Letters</i>, vol. 127, no. 6, 060602, American
    Physical Society, 2021, doi:<a href="https://doi.org/10.1103/physrevlett.127.060602">10.1103/physrevlett.127.060602</a>.
  short: V. Karle, M. Serbyn, A. Michailidis, Physical Review Letters 127 (2021).
date_created: 2021-08-13T09:27:39Z
date_published: 2021-08-06T00:00:00Z
date_updated: 2023-08-11T10:43:27Z
day: '06'
ddc:
- '539'
department:
- _id: MaSe
- _id: GradSch
- _id: MiLe
doi: 10.1103/physrevlett.127.060602
ec_funded: 1
external_id:
  arxiv:
  - '2102.13633'
  isi:
  - '000684276000002'
file:
- access_level: open_access
  checksum: 51218f302dcef99d90d1209809fcc874
  content_type: application/pdf
  creator: mserbyn
  date_created: 2021-08-13T09:28:08Z
  date_updated: 2021-08-13T09:28:08Z
  file_id: '9904'
  file_name: PhysRevLett.127.060602_SOM.pdf
  file_size: 5064231
  relation: main_file
  success: 1
file_date_updated: 2021-08-13T09:28:08Z
has_accepted_license: '1'
intvolume: '       127'
isi: 1
issue: '6'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 23841C26-32DE-11EA-91FC-C7463DDC885E
  call_identifier: H2020
  grant_number: '850899'
  name: 'Non-Ergodic Quantum Matter: Universality, Dynamics and Control'
publication: Physical Review Letters
publication_identifier:
  eissn:
  - 1079-7114
  issn:
  - 0031-9007
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
status: public
title: Area-law entangled eigenstates from nullspaces of local Hamiltonians
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: 127
year: '2021'
...
---
_id: '8741'
abstract:
- lang: eng
  text: "In ecology, climate and other fields, (sub)systems have been identified that
    can transition into a qualitatively different state when a critical threshold
    or tipping point in a driving process is crossed. An understanding of those tipping
    elements is of great interest given the increasing influence of humans on the
    biophysical Earth system. Complex interactions exist between tipping elements,
    e.g. physical mechanisms connect subsystems of the climate system. Based on earlier
    work on such coupled nonlinear systems, we systematically assessed the qualitative
    long-term behaviour of interacting tipping elements. We developed an understanding
    of the consequences of interactions\r\non the tipping behaviour allowing for tipping
    cascades to emerge under certain conditions. The (narrative) application of\r\nthese
    qualitative results to real-world examples of interacting tipping elements indicates
    that tipping cascades with profound consequences may occur: the interacting Greenland
    ice sheet and thermohaline ocean circulation might tip before the tipping points
    of the isolated subsystems are crossed. The eutrophication of the first lake in
    a lake chain might propagate through the following lakes without a crossing of
    their individual critical nutrient input levels. The possibility of emerging cascading
    tipping dynamics calls for the development of a unified theory of interacting
    tipping elements and the quantitative analysis of interacting real-world tipping
    elements."
acknowledgement: "V.K. thanks the German National Academic Foundation (Studienstiftung
  des deutschen Volkes) for financial\r\nsupport. J.F.D. is grateful for financial
  support by the Stordalen Foundation via the Planetary Boundary Research\r\nNetwork
  (PB.net), the Earth League’s EarthDoc program and the European Research Council
  Advanced Grant\r\nproject ERA (Earth Resilience in the Anthropocene). We are thankful
  for support by the Leibniz Association\r\n(project DominoES).\r\nAcknowledgements.
  This work has been performed in the context of the copan collaboration and the FutureLab
  on Earth\r\nResilience in the Anthropocene at the Potsdam Institute for Climate
  Impact Research. Furthermore, we acknowledge\r\ndiscussions with and helpful comments
  by N. Wunderling, J. Heitzig and M. Wiedermann."
article_number: '200599'
article_processing_charge: No
article_type: original
author:
- first_name: Ann Kristin
  full_name: Klose, Ann Kristin
  last_name: Klose
- first_name: Volker
  full_name: Karle, Volker
  id: D7C012AE-D7ED-11E9-95E8-1EC5E5697425
  last_name: Karle
  orcid: 0000-0002-6963-0129
- first_name: Ricarda
  full_name: Winkelmann, Ricarda
  last_name: Winkelmann
- first_name: Jonathan F.
  full_name: Donges, Jonathan F.
  last_name: Donges
citation:
  ama: 'Klose AK, Karle V, Winkelmann R, Donges JF. Emergence of cascading dynamics
    in interacting tipping elements of ecology and climate: Cascading dynamics in
    tipping elements. <i>Royal Society Open Science</i>. 2020;7(6). doi:<a href="https://doi.org/10.1098/rsos.200599">10.1098/rsos.200599</a>'
  apa: 'Klose, A. K., Karle, V., Winkelmann, R., &#38; Donges, J. F. (2020). Emergence
    of cascading dynamics in interacting tipping elements of ecology and climate:
    Cascading dynamics in tipping elements. <i>Royal Society Open Science</i>. The
    Royal Society. <a href="https://doi.org/10.1098/rsos.200599">https://doi.org/10.1098/rsos.200599</a>'
  chicago: 'Klose, Ann Kristin, Volker Karle, Ricarda Winkelmann, and Jonathan F.
    Donges. “Emergence of Cascading Dynamics in Interacting Tipping Elements of Ecology
    and Climate: Cascading Dynamics in Tipping Elements.” <i>Royal Society Open Science</i>.
    The Royal Society, 2020. <a href="https://doi.org/10.1098/rsos.200599">https://doi.org/10.1098/rsos.200599</a>.'
  ieee: 'A. K. Klose, V. Karle, R. Winkelmann, and J. F. Donges, “Emergence of cascading
    dynamics in interacting tipping elements of ecology and climate: Cascading dynamics
    in tipping elements,” <i>Royal Society Open Science</i>, vol. 7, no. 6. The Royal
    Society, 2020.'
  ista: 'Klose AK, Karle V, Winkelmann R, Donges JF. 2020. Emergence of cascading
    dynamics in interacting tipping elements of ecology and climate: Cascading dynamics
    in tipping elements. Royal Society Open Science. 7(6), 200599.'
  mla: 'Klose, Ann Kristin, et al. “Emergence of Cascading Dynamics in Interacting
    Tipping Elements of Ecology and Climate: Cascading Dynamics in Tipping Elements.”
    <i>Royal Society Open Science</i>, vol. 7, no. 6, 200599, The Royal Society, 2020,
    doi:<a href="https://doi.org/10.1098/rsos.200599">10.1098/rsos.200599</a>.'
  short: A.K. Klose, V. Karle, R. Winkelmann, J.F. Donges, Royal Society Open Science
    7 (2020).
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