[{"oa":1,"quality_controlled":"1","publisher":"Wiley","publication":"Physik in unserer Zeit","day":"01","year":"2024","has_accepted_license":"1","date_created":"2024-01-22T08:19:36Z","date_published":"2024-01-01T00:00:00Z","doi":"10.1002/piuz.202301690","page":"28-33","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Karle V, Lemeshko M. 2024. Die faszinierende Topologie rotierender Quanten. Physik in unserer Zeit. 55(1), 28–33.","chicago":"Karle, Volker, and Mikhail Lemeshko. “Die faszinierende Topologie rotierender Quanten.” Physik in unserer Zeit. Wiley, 2024. https://doi.org/10.1002/piuz.202301690.","ieee":"V. Karle and M. Lemeshko, “Die faszinierende Topologie rotierender Quanten,” Physik in unserer Zeit, vol. 55, no. 1. Wiley, pp. 28–33, 2024.","short":"V. Karle, M. Lemeshko, Physik in unserer Zeit 55 (2024) 28–33.","apa":"Karle, V., & Lemeshko, M. (2024). Die faszinierende Topologie rotierender Quanten. Physik in unserer Zeit. Wiley. https://doi.org/10.1002/piuz.202301690","ama":"Karle V, Lemeshko M. Die faszinierende Topologie rotierender Quanten. Physik in unserer Zeit. 2024;55(1):28-33. doi:10.1002/piuz.202301690","mla":"Karle, Volker, and Mikhail Lemeshko. “Die faszinierende Topologie rotierender Quanten.” Physik in unserer Zeit, vol. 55, no. 1, Wiley, 2024, pp. 28–33, doi:10.1002/piuz.202301690."},"title":"Die faszinierende Topologie rotierender Quanten","article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"Volker","id":"D7C012AE-D7ED-11E9-95E8-1EC5E5697425","orcid":"0000-0002-6963-0129","full_name":"Karle, Volker","last_name":"Karle"},{"first_name":"Mikhail","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6990-7802","full_name":"Lemeshko, Mikhail","last_name":"Lemeshko"}],"oa_version":"Published Version","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."}],"intvolume":" 55","month":"01","language":[{"iso":"ger"}],"file":[{"file_size":1155244,"date_updated":"2024-01-23T12:18:07Z","creator":"dernst","file_name":"2024_PhysikZeit_Karle.pdf","date_created":"2024-01-23T12:18:07Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"3051dadcf9bc57da97e36b647c596ab1","file_id":"14878"}],"publication_status":"published","publication_identifier":{"eissn":["1521-3943"],"issn":["0031-9252"]},"issue":"1","volume":55,"_id":"14851","keyword":["General Earth and Planetary Sciences","General Environmental Science"],"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","ddc":["530"],"date_updated":"2024-02-15T14:29:04Z","file_date_updated":"2024-01-23T12:18:07Z","department":[{"_id":"MiLe"}]},{"publisher":"American Physical Society","quality_controlled":"1","oa":1,"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).","date_published":"2024-02-01T00:00:00Z","doi":"10.1103/PhysRevA.109.023101","date_created":"2024-02-18T23:01:01Z","day":"01","publication":"Physical Review A","year":"2024","project":[{"_id":"2688CF98-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Angulon: physics and applications of a new quasiparticle","grant_number":"801770"}],"article_number":"023101","title":"Modeling laser pulses as δ kicks: Reevaluating the impulsive limit in molecular rotational dynamics","author":[{"id":"D7C012AE-D7ED-11E9-95E8-1EC5E5697425","first_name":"Volker","orcid":"0000-0002-6963-0129","full_name":"Karle, Volker","last_name":"Karle"},{"full_name":"Lemeshko, Mikhail","orcid":"0000-0002-6990-7802","last_name":"Lemeshko","first_name":"Mikhail","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","external_id":{"arxiv":["2307.07256"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","chicago":"Karle, Volker, and Mikhail Lemeshko. “Modeling Laser Pulses as δ Kicks: Reevaluating the Impulsive Limit in Molecular Rotational Dynamics.” Physical Review A. American Physical Society, 2024. https://doi.org/10.1103/PhysRevA.109.023101.","ieee":"V. Karle and M. Lemeshko, “Modeling laser pulses as δ kicks: Reevaluating the impulsive limit in molecular rotational dynamics,” Physical Review A, vol. 109, no. 2. American Physical Society, 2024.","short":"V. Karle, M. Lemeshko, Physical Review A 109 (2024).","ama":"Karle V, Lemeshko M. Modeling laser pulses as δ kicks: Reevaluating the impulsive limit in molecular rotational dynamics. Physical Review A. 2024;109(2). doi:10.1103/PhysRevA.109.023101","apa":"Karle, V., & Lemeshko, M. (2024). Modeling laser pulses as δ kicks: Reevaluating the impulsive limit in molecular rotational dynamics. Physical Review A. American Physical Society. https://doi.org/10.1103/PhysRevA.109.023101","mla":"Karle, Volker, and Mikhail Lemeshko. “Modeling Laser Pulses as δ Kicks: Reevaluating the Impulsive Limit in Molecular Rotational Dynamics.” Physical Review A, vol. 109, no. 2, 023101, American Physical Society, 2024, doi:10.1103/PhysRevA.109.023101."},"month":"02","intvolume":" 109","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2307.07256"}],"oa_version":"Preprint","abstract":[{"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.","lang":"eng"}],"issue":"2","volume":109,"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2469-9926"],"eissn":["2469-9934"]},"publication_status":"published","status":"public","type":"journal_article","article_type":"original","_id":"15004","department":[{"_id":"MiLe"}],"date_updated":"2024-02-26T09:45:20Z"},{"date_updated":"2023-08-01T14:02:06Z","department":[{"_id":"MiLe"}],"_id":"12788","type":"journal_article","article_type":"original","status":"public","publication_status":"published","publication_identifier":{"eissn":["1079-7114"],"issn":["0031-9007"]},"language":[{"iso":"eng"}],"ec_funded":1,"issue":"10","related_material":{"link":[{"description":"News on the ISTA website","relation":"press_release","url":"https://ista.ac.at/en/news/topology-of-rotating-molecules/"}]},"volume":130,"abstract":[{"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.","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2206.07067","open_access":"1"}],"scopus_import":"1","intvolume":" 130","month":"03","citation":{"ista":"Karle V, Ghazaryan A, Lemeshko M. 2023. Topological charges of periodically kicked molecules. Physical Review Letters. 130(10), 103202.","chicago":"Karle, Volker, Areg Ghazaryan, and Mikhail Lemeshko. “Topological Charges of Periodically Kicked Molecules.” Physical Review Letters. American Physical Society, 2023. https://doi.org/10.1103/PhysRevLett.130.103202.","apa":"Karle, V., Ghazaryan, A., & Lemeshko, M. (2023). Topological charges of periodically kicked molecules. Physical Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.130.103202","ama":"Karle V, Ghazaryan A, Lemeshko M. Topological charges of periodically kicked molecules. Physical Review Letters. 2023;130(10). doi:10.1103/PhysRevLett.130.103202","short":"V. Karle, A. Ghazaryan, M. Lemeshko, Physical Review Letters 130 (2023).","ieee":"V. Karle, A. Ghazaryan, and M. Lemeshko, “Topological charges of periodically kicked molecules,” Physical Review Letters, vol. 130, no. 10. American Physical Society, 2023.","mla":"Karle, Volker, et al. “Topological Charges of Periodically Kicked Molecules.” Physical Review Letters, vol. 130, no. 10, 103202, American Physical Society, 2023, doi:10.1103/PhysRevLett.130.103202."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"isi":["000957635500003"],"arxiv":["2206.07067"]},"article_processing_charge":"No","author":[{"id":"D7C012AE-D7ED-11E9-95E8-1EC5E5697425","first_name":"Volker","last_name":"Karle","full_name":"Karle, Volker"},{"full_name":"Ghazaryan, Areg","orcid":"0000-0001-9666-3543","last_name":"Ghazaryan","first_name":"Areg","id":"4AF46FD6-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Mikhail","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","last_name":"Lemeshko","orcid":"0000-0002-6990-7802","full_name":"Lemeshko, Mikhail"}],"title":"Topological charges of periodically kicked molecules","article_number":"103202","project":[{"grant_number":"801770","name":"Angulon: physics and applications of a new quasiparticle","_id":"2688CF98-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"year":"2023","isi":1,"publication":"Physical Review Letters","day":"10","date_created":"2023-04-02T22:01:10Z","date_published":"2023-03-10T00:00:00Z","doi":"10.1103/PhysRevLett.130.103202","acknowledgement":"M. L. acknowledges support by the European Research Council (ERC) Starting Grant No. 801770 (ANGULON).","oa":1,"quality_controlled":"1","publisher":"American Physical Society"},{"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."}],"oa_version":"Published Version","intvolume":" 127","month":"08","publication_status":"published","publication_identifier":{"eissn":["1079-7114"],"issn":["0031-9007"]},"language":[{"iso":"eng"}],"file":[{"creator":"mserbyn","date_updated":"2021-08-13T09:28:08Z","file_size":5064231,"date_created":"2021-08-13T09:28:08Z","file_name":"PhysRevLett.127.060602_SOM.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"51218f302dcef99d90d1209809fcc874","file_id":"9904","success":1}],"ec_funded":1,"volume":127,"issue":"6","_id":"9903","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"letter_note","type":"journal_article","status":"public","date_updated":"2023-08-11T10:43:27Z","ddc":["539"],"department":[{"_id":"MaSe"},{"_id":"GradSch"},{"_id":"MiLe"}],"file_date_updated":"2021-08-13T09:28:08Z","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)","oa":1,"quality_controlled":"1","publisher":"American Physical Society","year":"2021","has_accepted_license":"1","isi":1,"publication":"Physical Review Letters","day":"06","date_created":"2021-08-13T09:27:39Z","doi":"10.1103/physrevlett.127.060602","date_published":"2021-08-06T00:00:00Z","article_number":"060602","project":[{"call_identifier":"H2020","_id":"23841C26-32DE-11EA-91FC-C7463DDC885E","grant_number":"850899","name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control"}],"citation":{"ista":"Karle V, Serbyn M, Michailidis A. 2021. Area-law entangled eigenstates from nullspaces of local Hamiltonians. Physical Review Letters. 127(6), 060602.","chicago":"Karle, Volker, Maksym Serbyn, and Alexios Michailidis. “Area-Law Entangled Eigenstates from Nullspaces of Local Hamiltonians.” Physical Review Letters. American Physical Society, 2021. https://doi.org/10.1103/physrevlett.127.060602.","ama":"Karle V, Serbyn M, Michailidis A. Area-law entangled eigenstates from nullspaces of local Hamiltonians. Physical Review Letters. 2021;127(6). doi:10.1103/physrevlett.127.060602","apa":"Karle, V., Serbyn, M., & Michailidis, A. (2021). Area-law entangled eigenstates from nullspaces of local Hamiltonians. Physical Review Letters. American Physical Society. https://doi.org/10.1103/physrevlett.127.060602","short":"V. Karle, M. Serbyn, A. Michailidis, Physical Review Letters 127 (2021).","ieee":"V. Karle, M. Serbyn, and A. Michailidis, “Area-law entangled eigenstates from nullspaces of local Hamiltonians,” Physical Review Letters, vol. 127, no. 6. American Physical Society, 2021.","mla":"Karle, Volker, et al. “Area-Law Entangled Eigenstates from Nullspaces of Local Hamiltonians.” Physical Review Letters, vol. 127, no. 6, 060602, American Physical Society, 2021, doi:10.1103/physrevlett.127.060602."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"isi":["000684276000002"],"arxiv":["2102.13633"]},"article_processing_charge":"Yes (in subscription journal)","author":[{"id":"D7C012AE-D7ED-11E9-95E8-1EC5E5697425","first_name":"Volker","full_name":"Karle, Volker","orcid":"0000-0002-6963-0129","last_name":"Karle"},{"first_name":"Maksym","id":"47809E7E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2399-5827","full_name":"Serbyn, Maksym","last_name":"Serbyn"},{"id":"36EBAD38-F248-11E8-B48F-1D18A9856A87","first_name":"Alexios","last_name":"Michailidis","orcid":"0000-0002-8443-1064","full_name":"Michailidis, Alexios"}],"title":"Area-law entangled eigenstates from nullspaces of local Hamiltonians"},{"department":[{"_id":"MiLe"}],"file_date_updated":"2020-11-09T09:07:11Z","date_updated":"2024-03-12T12:31:30Z","ddc":["530","550"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public","_id":"8741","volume":7,"issue":"6","publication_status":"published","publication_identifier":{"eissn":["20545703"]},"language":[{"iso":"eng"}],"file":[{"date_created":"2020-11-09T09:07:11Z","file_name":"2020_RoyalSocOpenScience_Klose.pdf","date_updated":"2020-11-09T09:07:11Z","file_size":1611485,"creator":"dernst","checksum":"5505c445de373bfd836eb4d3b48b1f37","file_id":"8748","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"scopus_import":"1","intvolume":" 7","month":"06","abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","article_processing_charge":"No","external_id":{"isi":["000545625200001"],"arxiv":["1910.12042"]},"author":[{"first_name":"Ann Kristin","last_name":"Klose","full_name":"Klose, Ann Kristin"},{"last_name":"Karle","orcid":"0000-0002-6963-0129","full_name":"Karle, Volker","id":"D7C012AE-D7ED-11E9-95E8-1EC5E5697425","first_name":"Volker"},{"last_name":"Winkelmann","full_name":"Winkelmann, Ricarda","first_name":"Ricarda"},{"full_name":"Donges, Jonathan F.","last_name":"Donges","first_name":"Jonathan F."}],"title":"Emergence of cascading dynamics in interacting tipping elements of ecology and climate: Cascading dynamics in tipping elements","citation":{"mla":"Klose, Ann Kristin, et al. “Emergence of Cascading Dynamics in Interacting Tipping Elements of Ecology and Climate: Cascading Dynamics in Tipping Elements.” Royal Society Open Science, vol. 7, no. 6, 200599, The Royal Society, 2020, doi:10.1098/rsos.200599.","apa":"Klose, A. K., Karle, V., Winkelmann, R., & Donges, J. F. (2020). Emergence of cascading dynamics in interacting tipping elements of ecology and climate: Cascading dynamics in tipping elements. Royal Society Open Science. The Royal Society. https://doi.org/10.1098/rsos.200599","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. Royal Society Open Science. 2020;7(6). doi:10.1098/rsos.200599","short":"A.K. Klose, V. Karle, R. Winkelmann, J.F. Donges, Royal Society Open Science 7 (2020).","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,” Royal Society Open Science, vol. 7, no. 6. The Royal Society, 2020.","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.” Royal Society Open Science. The Royal Society, 2020. https://doi.org/10.1098/rsos.200599.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_number":"200599","date_created":"2020-11-08T23:01:25Z","doi":"10.1098/rsos.200599","date_published":"2020-06-01T00:00:00Z","year":"2020","isi":1,"has_accepted_license":"1","publication":"Royal Society Open Science","day":"01","oa":1,"quality_controlled":"1","publisher":"The Royal Society","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."}]