[{"scopus_import":"1","month":"08","intvolume":" 195","abstract":[{"text":"We give a detailed and easily accessible proof of Gromov’s Topological Overlap Theorem. Let X be a finite simplicial complex or, more generally, a finite polyhedral cell complex of dimension d. Informally, the theorem states that if X has sufficiently strong higher-dimensional expansion properties (which generalize edge expansion of graphs and are defined in terms of cellular cochains of X) then X has the following topological overlap property: for every continuous map (Formula presented.) there exists a point (Formula presented.) that is contained in the images of a positive fraction (Formula presented.) of the d-cells of X. More generally, the conclusion holds if (Formula presented.) is replaced by any d-dimensional piecewise-linear manifold M, with a constant (Formula presented.) that depends only on d and on the expansion properties of X, but not on M.","lang":"eng"}],"oa_version":"Published Version","volume":195,"related_material":{"record":[{"id":"1378","status":"public","relation":"earlier_version"}]},"issue":"1","license":"https://creativecommons.org/licenses/by/4.0/","publication_status":"published","file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"d2f70fc132156504aa4c626aa378a7ab","file_id":"5835","creator":"kschuh","date_updated":"2020-07-14T12:47:58Z","file_size":412486,"date_created":"2019-01-15T13:44:05Z","file_name":"s10711-017-0291-4.pdf"}],"language":[{"iso":"eng"}],"type":"journal_article","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)"},"status":"public","pubrep_id":"912","_id":"742","department":[{"_id":"UlWa"}],"file_date_updated":"2020-07-14T12:47:58Z","date_updated":"2023-09-27T12:29:57Z","ddc":["514","516"],"quality_controlled":"1","publisher":"Springer","oa":1,"page":"307–317","doi":"10.1007/s10711-017-0291-4","date_published":"2018-08-01T00:00:00Z","date_created":"2018-12-11T11:48:16Z","isi":1,"has_accepted_license":"1","year":"2018","day":"01","publication":"Geometriae Dedicata","project":[{"name":"Embeddings in Higher Dimensions: Algorithms and Combinatorics","grant_number":"PP00P2_138948","_id":"25FA3206-B435-11E9-9278-68D0E5697425"}],"author":[{"full_name":"Dotterrer, Dominic","last_name":"Dotterrer","first_name":"Dominic"},{"full_name":"Kaufman, Tali","last_name":"Kaufman","first_name":"Tali"},{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli","full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","last_name":"Wagner"}],"publist_id":"6925","external_id":{"isi":["000437122700017"]},"article_processing_charge":"Yes (via OA deal)","title":"On expansion and topological overlap","citation":{"ieee":"D. Dotterrer, T. Kaufman, and U. Wagner, “On expansion and topological overlap,” Geometriae Dedicata, vol. 195, no. 1. Springer, pp. 307–317, 2018.","short":"D. Dotterrer, T. Kaufman, U. Wagner, Geometriae Dedicata 195 (2018) 307–317.","ama":"Dotterrer D, Kaufman T, Wagner U. On expansion and topological overlap. Geometriae Dedicata. 2018;195(1):307–317. doi:10.1007/s10711-017-0291-4","apa":"Dotterrer, D., Kaufman, T., & Wagner, U. (2018). On expansion and topological overlap. Geometriae Dedicata. Springer. https://doi.org/10.1007/s10711-017-0291-4","mla":"Dotterrer, Dominic, et al. “On Expansion and Topological Overlap.” Geometriae Dedicata, vol. 195, no. 1, Springer, 2018, pp. 307–317, doi:10.1007/s10711-017-0291-4.","ista":"Dotterrer D, Kaufman T, Wagner U. 2018. On expansion and topological overlap. Geometriae Dedicata. 195(1), 307–317.","chicago":"Dotterrer, Dominic, Tali Kaufman, and Uli Wagner. “On Expansion and Topological Overlap.” Geometriae Dedicata. Springer, 2018. https://doi.org/10.1007/s10711-017-0291-4."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1"},{"project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"}],"citation":{"short":"P. Nejjar, Latin American Journal of Probability and Mathematical Statistics 15 (2018) 1311–1334.","ieee":"P. Nejjar, “Transition to shocks in TASEP and decoupling of last passage times,” Latin American Journal of Probability and Mathematical Statistics, vol. 15, no. 2. Instituto Nacional de Matematica Pura e Aplicada, pp. 1311–1334, 2018.","apa":"Nejjar, P. (2018). Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. Instituto Nacional de Matematica Pura e Aplicada. https://doi.org/10.30757/ALEA.v15-49","ama":"Nejjar P. Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. 2018;15(2):1311-1334. doi:10.30757/ALEA.v15-49","mla":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” Latin American Journal of Probability and Mathematical Statistics, vol. 15, no. 2, Instituto Nacional de Matematica Pura e Aplicada, 2018, pp. 1311–34, doi:10.30757/ALEA.v15-49.","ista":"Nejjar P. 2018. Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. 15(2), 1311–1334.","chicago":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” Latin American Journal of Probability and Mathematical Statistics. Instituto Nacional de Matematica Pura e Aplicada, 2018. https://doi.org/10.30757/ALEA.v15-49."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","first_name":"Peter","full_name":"Nejjar, Peter","last_name":"Nejjar"}],"external_id":{"isi":["000460475800022"],"arxiv":["1705.08836"]},"article_processing_charge":"No","title":"Transition to shocks in TASEP and decoupling of last passage times","quality_controlled":"1","publisher":"Instituto Nacional de Matematica Pura e Aplicada","oa":1,"has_accepted_license":"1","isi":1,"year":"2018","day":"01","publication":"Latin American Journal of Probability and Mathematical Statistics","page":"1311-1334","doi":"10.30757/ALEA.v15-49","date_published":"2018-10-01T00:00:00Z","date_created":"2018-12-11T11:44:28Z","_id":"70","article_type":"original","type":"journal_article","status":"public","date_updated":"2023-10-10T13:11:29Z","ddc":["510"],"file_date_updated":"2020-07-14T12:47:46Z","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"abstract":[{"text":"We consider the totally asymmetric simple exclusion process in a critical scaling parametrized by a≥0, which creates a shock in the particle density of order aT−1/3, T the observation time. When starting from step initial data, we provide bounds on the limiting law which in particular imply that in the double limit lima→∞limT→∞ one recovers the product limit law and the degeneration of the correlation length observed at shocks of order 1. This result is shown to apply to a general last-passage percolation model. We also obtain bounds on the two-point functions of several airy processes.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"10","intvolume":" 15","publication_identifier":{"issn":["1980-0436"]},"publication_status":"published","file":[{"file_name":"2018_ALEA_Nejjar.pdf","date_created":"2019-02-14T09:44:10Z","creator":"kschuh","file_size":394851,"date_updated":"2020-07-14T12:47:46Z","file_id":"5981","checksum":"2ded46aa284a836a8cbb34133a64f1cb","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"volume":15,"issue":"2","ec_funded":1},{"date_created":"2018-12-11T11:44:19Z","doi":"10.1103/PhysRevB.98.155134","date_published":"2018-10-22T00:00:00Z","year":"2018","isi":1,"publication":"Physical Review B","day":"22","oa":1,"publisher":"American Physical Society","quality_controlled":"1","external_id":{"arxiv":["1806.10933"],"isi":["000447919100001"]},"article_processing_charge":"No","publist_id":"8010","author":[{"last_name":"Turner","full_name":"Turner, C J","first_name":"C J"},{"first_name":"Alexios","id":"36EBAD38-F248-11E8-B48F-1D18A9856A87","last_name":"Michailidis","full_name":"Michailidis, Alexios","orcid":"0000-0002-8443-1064"},{"first_name":"D A","full_name":"Abanin, D A","last_name":"Abanin"},{"id":"47809E7E-F248-11E8-B48F-1D18A9856A87","first_name":"Maksym","last_name":"Serbyn","full_name":"Serbyn, Maksym","orcid":"0000-0002-2399-5827"},{"full_name":"Papić, Z","last_name":"Papić","first_name":"Z"}],"title":"Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations","citation":{"ista":"Turner CJ, Michailidis A, Abanin DA, Serbyn M, Papić Z. 2018. Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations. Physical Review B. 98(15), 155134.","chicago":"Turner, C J, Alexios Michailidis, D A Abanin, Maksym Serbyn, and Z Papić. “Quantum Scarred Eigenstates in a Rydberg Atom Chain: Entanglement, Breakdown of Thermalization, and Stability to Perturbations.” Physical Review B. American Physical Society, 2018. https://doi.org/10.1103/PhysRevB.98.155134.","short":"C.J. Turner, A. Michailidis, D.A. Abanin, M. Serbyn, Z. Papić, Physical Review B 98 (2018).","ieee":"C. J. Turner, A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papić, “Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations,” Physical Review B, vol. 98, no. 15. American Physical Society, 2018.","ama":"Turner CJ, Michailidis A, Abanin DA, Serbyn M, Papić Z. Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations. Physical Review B. 2018;98(15). doi:10.1103/PhysRevB.98.155134","apa":"Turner, C. J., Michailidis, A., Abanin, D. A., Serbyn, M., & Papić, Z. (2018). Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations. Physical Review B. American Physical Society. https://doi.org/10.1103/PhysRevB.98.155134","mla":"Turner, C. J., et al. “Quantum Scarred Eigenstates in a Rydberg Atom Chain: Entanglement, Breakdown of Thermalization, and Stability to Perturbations.” Physical Review B, vol. 98, no. 15, 155134, American Physical Society, 2018, doi:10.1103/PhysRevB.98.155134."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_number":"155134","volume":98,"issue":"15","publication_status":"published","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1806.10933"}],"scopus_import":"1","intvolume":" 98","month":"10","abstract":[{"lang":"eng","text":"Recent realization of a kinetically constrained chain of Rydberg atoms by Bernien et al., [Nature (London) 551, 579 (2017)] resulted in the observation of unusual revivals in the many-body quantum dynamics. In our previous work [C. J. Turner et al., Nat. Phys. 14, 745 (2018)], such dynamics was attributed to the existence of “quantum scarred” eigenstates in the many-body spectrum of the experimentally realized model. Here, we present a detailed study of the eigenstate properties of the same model. We find that the majority of the eigenstates exhibit anomalous thermalization: the observable expectation values converge to their Gibbs ensemble values, but parametrically slower compared to the predictions of the eigenstate thermalization hypothesis (ETH). Amidst the thermalizing spectrum, we identify nonergodic eigenstates that strongly violate the ETH, whose number grows polynomially with system size. Previously, the same eigenstates were identified via large overlaps with certain product states, and were used to explain the revivals observed in experiment. Here, we find that these eigenstates, in addition to highly atypical expectation values of local observables, also exhibit subthermal entanglement entropy that scales logarithmically with the system size. Moreover, we identify an additional class of quantum scarred eigenstates, and discuss their manifestations in the dynamics starting from initial product states. We use forward scattering approximation to describe the structure and physical properties of quantum scarred eigenstates. Finally, we discuss the stability of quantum scars to various perturbations. We observe that quantum scars remain robust when the introduced perturbation is compatible with the forward scattering approximation. In contrast, the perturbations which most efficiently destroy quantum scars also lead to the restoration of “canonical” thermalization."}],"acknowledged_ssus":[{"_id":"ScienComp"}],"oa_version":"Preprint","department":[{"_id":"MaSe"}],"date_updated":"2023-10-10T13:28:49Z","type":"journal_article","status":"public","_id":"44"},{"date_published":"2018-03-19T00:00:00Z","doi":"10.1103/PhysRevLett.120.124501","date_created":"2018-12-11T11:45:51Z","day":"19","publication":"Physical Review Letters","isi":1,"year":"2018","quality_controlled":"1","publisher":"American Physical Society","oa":1,"acknowledgement":"The authors thank Philipp Maier and the IST Austria workshop for their dedicated technical support.","title":"Exceeding the asymptotic limit of polymer drag reduction","publist_id":"7537","author":[{"full_name":"Choueiri, George H","last_name":"Choueiri","id":"448BD5BC-F248-11E8-B48F-1D18A9856A87","first_name":"George H"},{"first_name":"Jose M","id":"40770848-F248-11E8-B48F-1D18A9856A87","last_name":"Lopez Alonso","full_name":"Lopez Alonso, Jose M","orcid":"0000-0002-0384-2022"},{"last_name":"Hof","orcid":"0000-0003-2057-2754","full_name":"Hof, Björn","first_name":"Björn","id":"3A374330-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","external_id":{"isi":["000427804000005"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Choueiri GH, Lopez Alonso JM, Hof B. 2018. Exceeding the asymptotic limit of polymer drag reduction. Physical Review Letters. 120(12), 124501.","chicago":"Choueiri, George H, Jose M Lopez Alonso, and Björn Hof. “Exceeding the Asymptotic Limit of Polymer Drag Reduction.” Physical Review Letters. American Physical Society, 2018. https://doi.org/10.1103/PhysRevLett.120.124501.","short":"G.H. Choueiri, J.M. Lopez Alonso, B. Hof, Physical Review Letters 120 (2018).","ieee":"G. H. Choueiri, J. M. Lopez Alonso, and B. Hof, “Exceeding the asymptotic limit of polymer drag reduction,” Physical Review Letters, vol. 120, no. 12. American Physical Society, 2018.","ama":"Choueiri GH, Lopez Alonso JM, Hof B. Exceeding the asymptotic limit of polymer drag reduction. Physical Review Letters. 2018;120(12). doi:10.1103/PhysRevLett.120.124501","apa":"Choueiri, G. H., Lopez Alonso, J. M., & Hof, B. (2018). Exceeding the asymptotic limit of polymer drag reduction. Physical Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.120.124501","mla":"Choueiri, George H., et al. “Exceeding the Asymptotic Limit of Polymer Drag Reduction.” Physical Review Letters, vol. 120, no. 12, 124501, American Physical Society, 2018, doi:10.1103/PhysRevLett.120.124501."},"project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"},{"grant_number":"306589","name":"Decoding the complexity of turbulence at its origin","_id":"25152F3A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"article_number":"124501","volume":120,"issue":"12","ec_funded":1,"language":[{"iso":"eng"}],"publication_status":"published","month":"03","intvolume":" 120","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1703.06271"}],"oa_version":"Preprint","acknowledged_ssus":[{"_id":"SSU"}],"abstract":[{"lang":"eng","text":"The drag of turbulent flows can be drastically decreased by adding small amounts of high molecular weight polymers. While drag reduction initially increases with polymer concentration, it eventually saturates to what is known as the maximum drag reduction (MDR) asymptote; this asymptote is generally attributed to the dynamics being reduced to a marginal yet persistent state of subdued turbulent motion. Contrary to this accepted view, we show that, for an appropriate choice of parameters, polymers can reduce the drag beyond the suggested asymptotic limit, eliminating turbulence and giving way to laminar flow. At higher polymer concentrations, however, the laminar state becomes unstable, resulting in a fluctuating flow with the characteristic drag of the MDR asymptote. Our findings indicate that the asymptotic state is hence dynamically disconnected from ordinary turbulence. © 2018 American Physical Society."}],"department":[{"_id":"BjHo"}],"date_updated":"2023-10-10T13:27:44Z","status":"public","type":"journal_article","_id":"328"},{"title":"Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow","author":[{"last_name":"Suri","full_name":"Suri, Balachandra","id":"47A5E706-F248-11E8-B48F-1D18A9856A87","first_name":"Balachandra"},{"full_name":"Tithof, Jeffrey","last_name":"Tithof","first_name":"Jeffrey"},{"first_name":"Roman","full_name":"Grigoriev, Roman","last_name":"Grigoriev"},{"full_name":"Schatz, Michael","last_name":"Schatz","first_name":"Michael"}],"external_id":{"arxiv":["1808.02088"],"isi":["000441466800010"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Suri, Balachandra, et al. “Unstable Equilibria and Invariant Manifolds in Quasi-Two-Dimensional Kolmogorov-like Flow.” Physical Review E, vol. 98, no. 2, American Physical Society, 2018, doi:10.1103/PhysRevE.98.023105.","apa":"Suri, B., Tithof, J., Grigoriev, R., & Schatz, M. (2018). Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow. Physical Review E. American Physical Society. https://doi.org/10.1103/PhysRevE.98.023105","ama":"Suri B, Tithof J, Grigoriev R, Schatz M. Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow. Physical Review E. 2018;98(2). doi:10.1103/PhysRevE.98.023105","ieee":"B. Suri, J. Tithof, R. Grigoriev, and M. Schatz, “Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow,” Physical Review E, vol. 98, no. 2. American Physical Society, 2018.","short":"B. Suri, J. Tithof, R. Grigoriev, M. Schatz, Physical Review E 98 (2018).","chicago":"Suri, Balachandra, Jeffrey Tithof, Roman Grigoriev, and Michael Schatz. “Unstable Equilibria and Invariant Manifolds in Quasi-Two-Dimensional Kolmogorov-like Flow.” Physical Review E. American Physical Society, 2018. https://doi.org/10.1103/PhysRevE.98.023105.","ista":"Suri B, Tithof J, Grigoriev R, Schatz M. 2018. Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow. Physical Review E. 98(2)."},"date_published":"2018-08-13T00:00:00Z","doi":"10.1103/PhysRevE.98.023105","date_created":"2018-12-11T11:44:49Z","day":"13","publication":"Physical Review E","isi":1,"year":"2018","publisher":"American Physical Society","quality_controlled":"1","oa":1,"department":[{"_id":"BjHo"}],"date_updated":"2023-10-10T13:29:10Z","status":"public","type":"journal_article","_id":"136","volume":98,"issue":"2","language":[{"iso":"eng"}],"publication_status":"published","month":"08","intvolume":" 98","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1808.02088","open_access":"1"}],"oa_version":"Submitted Version","abstract":[{"text":"Recent studies suggest that unstable, nonchaotic solutions of the Navier-Stokes equation may provide deep insights into fluid turbulence. In this article, we present a combined experimental and numerical study exploring the dynamical role of unstable equilibrium solutions and their invariant manifolds in a weakly turbulent, electromagnetically driven, shallow fluid layer. Identifying instants when turbulent evolution slows down, we compute 31 unstable equilibria of a realistic two-dimensional model of the flow. We establish the dynamical relevance of these unstable equilibria by showing that they are closely visited by the turbulent flow. We also establish the dynamical relevance of unstable manifolds by verifying that they are shadowed by turbulent trajectories departing from the neighborhoods of unstable equilibria over large distances in state space.","lang":"eng"}]}]