Superdiffusivity of the 1D lattice Kardar-Parisi-Zhang equation

Abstract

The continuum Kardar-Parisi-Zhang equation in one dimension is lattice discretized in such a way that the drift part is divergence free. This allows to determine explicitly the stationary measures. We map the lattice KPZ equation to a bosonic field theory which has a cubic anti-hermitian nonlinearity. Thereby it is established that the stationary two-point function spreads superdiffusively.

21 pages

References in corpus (4)

• Exact scaling functions for one-dimensional stationary KPZ growth
• Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals
• Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques
• Superdiffusivity of Asymmetric Energy Model in Dimension One and Two

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• Anomalous fluctuations for a perturbed Hamiltonian system with exponential interactions
• Approximating rough stochastic PDEs
• Anomalous ballistic scaling in the tensionless or inviscid Kardar-Parisi-Zhang equation
• ASEP(q,j) converges to the KPZ equation
• The derivative of the Kardar-Parisi-Zhang equation is not in the KPZ universality class
• Diffusivity of lattice gases
• Numerical Study of the Thermodynamic Uncertainty Relation for the KPZ-Equation