Microscopic derivation of nonlinear fluctuating hydrodynamics for crystalline solid
arXiv:2303.17227 · doi:10.1103/PhysRevE.108.054101
Abstract
We present a microscopic derivation of the nonlinear fluctuating hydrodynamic equation for the homogeneous crystalline solid from the Hamiltonian description of a many-particle system. We propose a microscopic expression of the displacement field that correctly generates the nonlinear elastic properties of the solid and find the nonlinear mode-coupling terms in reversible currents which are consistent with the phenomenological equation. The derivation relies on the projection onto the coarse-grained fields including the displacement field, the long-wavelength expansion, and the stationarity condition of the Fokker-Planck equation.
arXiv comment11 pages
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