TIME BEHAVIOR OF A GENERATING FUNCTIONAL FOR THE KARDAR?PARISI?ZHANG (KPZ) EQUATIONTIME BEHAVIOR OF A GENERATING FUNCTIONAL FOR THE KARDAR?PARISI?ZHANG (KPZ) EQUATION

IZÚS, GONZALO G.; WIO, HORACIO S.; ALÉS, ALEJANDRO; DEZA, ROBERTO RAÚL; REVELLI, JORGE A.; RODRÍGUEZ, MIGUEL A.; GALLEGO, RAFAEL

Comodoro Rivadavia

Congreso; Matemática Aplicada, Computacional e Industrial; 2017

ASAMACI

In a previous MACI meeting, the KPZ equation for kinetic interface roughening was formulated as a stochastic gradient flow in a "nonequilibrium potential" (NEP) Φ[h], and a functional Taylor expansion of Φ[h] was performed around a reference configuration h0. This expansion - here denoted Φh0 [h] and argued before to yield an instantaneous landscape for the stochastic dynamics - is further interpreted in this work. In a finite-difference scheme, Φh0 [h] is a cubic polynomial in {hi}, shown to provide much intuition on the dynamics. Also, the time behavior of ⟨Φ[h]⟩t (the ensemble average of Φ[h] at t) is investigated. Finally, the asymptotically linear dependence of ⟨Φ[h]⟩t on t - i.e. effectively linear in h despite Φh0 [h] being cubic in {hi} - is explained on the basis of known facts.