Relaxation properties of (1 + 1)-dimensional driven interfaces in disordered media

Abstract

We use the Kardar–Parisi–Zhang equation with quenched noise in order to study the relaxation properties of driven interfaces in disordered media. For λ ≠ 0 this equation belongs to the directed percolation depinning universality class and for λ = 0 it belongs to the quenched Edwards–Wilkinson universality class. We study the Fourier transform of the two-time autocorrelation function of the interface height Ck(t', t). These functions depend on the difference of times t − t' in the steady-state regime. We find a two-step relaxation decay in this regime for both universality classes. The long time tail can be fitted by a stretched exponential function, where the exponent β depends on the universality class. The relaxation time and the wavelength of the Fourier transform, where the two-step relaxation is lost, are related to the length of the pinned regions. The stretched exponential relaxation is caused by the existence of pinned regions which is a direct consequence of the quenched noise.