Superdiffusivity of the 1D lattice Kardar-Parisi-Zhang equation
classification
🧮 math-ph
cond-mat.stat-mechmath.MP
keywords
equationlatticekardar-parisi-zhangstationaryallowsanti-hermitianbosoniccontinuum
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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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