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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Cited by in corpus (3)

• Equilibrium fluctuation for an anharmonic chain with boundary conditions in the Euler scaling limit
• Hyperbolic scaling limit of non-equilibrium fluctuations for a weakly anharmonic chain
• Non-equilibrium stationary properties of the boundary driven zero-range process with long jumps