Nonlinear Perturbation of a Noisy Hamiltonian Lattice Field Model: Universality Persistence

Creators: Bernardin, Cédric; Gonçalves, Patricia; Jara, Milton; Simon, Marielle

Others:: Laboratoire Jean Alexandre Dieudonné (JAD) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA); COMUE Université Côte d'Azur (2015-2019) (COMUE UCA); Department of Mathematics [Lisbonne] ; Instituto Superior Técnico, Universidade Técnica de Lisboa (IST); Instituto Nacional de Matemática Pura e Aplicada (IMPA); Méthodes quantitatives pour les modèles aléatoires de la physique (MEPHYSTO-POST) ; Inria Lille - Nord Europe ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria); ANR-14-CE25-0011,EDNHS,Diffusion de l'énergie dans des systèmes hamiltoniens bruitésés(2014); ANR-15-CE40-0020,LSD,Modèles stochastiques en grande dimension pour la physique statistique hors équilibre(2015); European Project: 715734,H2020,HyLEF(2016)

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In [2] it has been proved that a linear Hamiltonian lattice field perturbed by a conservative stochastic noise belongs to the 3/2-Lévy/Diffusive universality class in the nonlinear fluctuating theory terminology [15], i.e. energy superdiffuses like an asymmetric stable 3/2-Lévy process and volume like a Brownian motion. According to this theory this should remain valid at zero tension if the harmonic potential is replaced by an even potential. In this work we consider a quartic anharmonicity and show that the result obtained in the harmonic case persists up to some small critical value of the anharmonicity.

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Nonlinear Perturbation of a Noisy Hamiltonian Lattice Field Model: Universality Persistence

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