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

Abstract : 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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Submitted on : Monday, August 21, 2017 - 8:34:59 AM
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Cédric Bernardin, Patricia Gonçalves, Milton Jara, Marielle Simon. Nonlinear Perturbation of a Noisy Hamiltonian Lattice Field Model: Universality Persistence. Communications in Mathematical Physics, Springer Verlag, 2018, 361 (2), pp.605-659. ⟨10.1007/s00220-018-3191-z⟩. ⟨hal-01491433v2⟩

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