Metastability in the Hamiltonian mean field model and Kuramoto model |
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| Institution: | 1. Dipartimento di Física, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy;2. Dipartimento di Física, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy;3. INFN and Dipartimento di Física, Università di Cagliari, Cittadella Universitaria, I-09042 Monserrato (CA), Italy;1. Instituto de Matemática, Universidade Federal Fluminense, Rua Mário Santos Braga S/N, Niterói, RJ 24020-140, Brazil;2. IMPA, Estrada Dona Castorina 110, Rio de Janeiro, RJ, 22460-320, Brazil;3. Departamento de Matemática, Universidade Federal do Espírito Santo, Av. Fernando Ferrari, 514, Goiabeiras, Vitória, 29075-910, Brazil;1. Department of Mathematics, State University of New Jersey, Rutgers, NJ 08854, USA;2. Institut de recherche en mathématique et en physique, Université catholique de Louvain, chemin du Cyclotron 2 bte L7.01.01, 1348 Louvain-la-Neuve, Belgium;3. Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong;1. School of Mathematics, The University of Edinburgh, James Clerk Maxwell Building, The King''s Buildings, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom;2. The Maxwell Institute for the Mathematical Sciences, James Clerk Maxwell Building, The King''s Buildings, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom;1. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria;2. Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8–10, 1040 Wien, Austria;3. Graduate School of Science and Technology, Niigata University, Niigata, 950-2181, Japan;1. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, Warsaw, Poland;2. Institute of Mathematics, University of Warsaw, Banacha 2, Warsaw, Poland |
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| Abstract: | We briefly discuss the state of the art on the anomalous dynamics of the Hamiltonian mean field (HMF) model. We stress the important role of the initial conditions for understanding the microscopic nature of the intriguing metastable quasi-stationary states (QSS) observed in the model and the connections to Tsallis statistics and glassy dynamics. We also present new results on the existence of metastable states in the Kuramoto model and discuss the similarities with those found in the HMF model. The existence of metastability seems to be quite a common phenomenon in fully coupled systems, whose origin could be also interpreted as a dynamical mechanism preventing or hindering synchronization. |
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