Symmetry and conservation laws alone yield nonlinear fluctuating hydrodynamics equations whose sound and heat modes both flow to a KPZ fixed point with dynamical exponent 3/2, confirmed by simulations matching the Prahofer-Spohn function.
De Dominicis, Dynamics as a substitute for replicas in systems with quenched random impurities, Physical Review B18, 4913 (1978)
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Symmetry-based nonlinear fluctuating hydrodynamics in one dimension
Symmetry and conservation laws alone yield nonlinear fluctuating hydrodynamics equations whose sound and heat modes both flow to a KPZ fixed point with dynamical exponent 3/2, confirmed by simulations matching the Prahofer-Spohn function.