Superdiffusivity of the 1D lattice Kardar-Parisi-Zhang equation
Tomohiro Sasamoto, Herbert Spohn
TL;DR
This paper investigates the one-dimensional lattice KPZ equation, demonstrating that its stationary two-point function exhibits superdiffusive spreading, by discretizing the equation and mapping it to a bosonic field theory.
Contribution
It introduces a divergence-free discretization of the lattice KPZ equation and explicitly determines its stationary measures, revealing superdiffusive behavior through a bosonic field theory mapping.
Findings
Stationary measures are explicitly determined.
Stationary two-point function spreads superdiffusively.
Mapping to a bosonic field theory elucidates superdiffusivity.
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.
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