Non-Gaussianity from Nonlinear Effective Field Theory

Abstract

We have studied nonlinear effect in an effective field theory model. Focusing on the nonlinear terms in the fluctuation field, we have established two stochastic formulations of the effective field theory, with the nonlinear terms manifested as multiple non-Gaussian noises in the Langevin equation and as higher order diffusive terms in the Fokker-Planck equation. The equivalence of the stochastic formulations with the original effective field theory have been checked, for arbitrary nonlinear parameters, with non-trivial examples. The stochastic formulations can be used to study nonequilibrium dynamics more effectively. Our results also suggest the nonlinearity in the fluctuation field is solvable and free of divergence.

Nonlinear response in diffusive systems

“…( 3) for these situations: Assuming that nonlinear static susceptibilities are finite 0.001 0.010 0.100 1) and ( 21), with no fitting parameters. Inset: dimensionless scaling function (7) g 3 ( (21). (Numerical parameters: δ = 0.9, L = 2 19 , 〈n〉 = 0.9, averaged over 5 realizations).…”

“…Certain general properties were also studied recently through the lens of the eigenstate thermalization hypothesis in [17,18]. Higher order correlation functions were computed in holographic models [19,20], models with relaxational dynamics [19,21], integrable systems [22,23] as well as more general ballistic regimes [24]. Nonlinear response is also related to higher cumulants (or full counting statistics) in out-of-equilibrium states (see, e.g., [25][26][27]).…”