Generalized discretization of the Kardar-Parisi-Zhang equation

Abstract

We introduce the generalized spatial discretization of the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. We solve exactly the steady state probability density function for the discrete heights of the interface, for any discretization scheme. We show that the discretization prescription is a consequence of each particular model. From the ballistic deposition model we derive the discretization prescription of the corresponding KPZ equation.

9 pages

References in corpus (3)

• A pseudo-spectral method for the Kardar-Parisi-Zhang equation
• Universal Behavior of the Coefficients of the Continuous Equation in Competitive Growth Models
• A pseudo-spectral approach to inverse problems in interface dynamics

Cited by in corpus (10)

• Discretization-related issues in the KPZ equation: Consistency, Galilean-invariance violation, and fluctuation--dissipation relation
• Characterisation of non-equilibrium growth through global two-time quantities
• Aging dynamics of non-linear elastic interfaces: the Kardar-Parisi-Zhang equation
• Numerical integration of KPZ equation with restrictions
• Feedback control of surface roughness in a one-dimensional KPZ growth process
• Revisiting random deposition with surface relaxation: approaches from growth rules to Edwards-Wilkinson equation
• Numerical Study of the Thermodynamic Uncertainty Relation for the KPZ-Equation
• Coarse grained approach for universality classification of discrete models
• Coarse grained approach for volume conserving models
• KPZ models: height-gradient fluctuations and the tilt method