Derivation of the nonlinear fluctuating hydrodynamic equation from underdamped Langevin equation

Details Derivation of the nonlinear fluctuating hydrodynamic equation from underdamped Langevin equation Derivation of the nonlinear fluctuating hydrodynamic equation from underdamped Langevin equation

2008-07-30

arxiv.org/abs/0807.4768v1

2009 J. Phys. A: Math. Theor. 42 065001 (15pp)

Physics

Condensed Matter

Statistical Mechanics

16 pages

Scientific paper

10.1088/1751-8113/42/6/065001

We derive the fluctuating hydrodynamic equation for the number and momentum densities exactly from the underdamped Langevin equation. This derivation is an extension of the Kawasaki-Dean formula in underdamped case. The steady state probability distribution of the number and momentum densities field can be expressed by the kinetic and potential energies. In the massless limit, the obtained fluctuating hydrodynamic equation reduces to the Kawasaki-Dean equation. Moreover, the derived equation corresponds to the field equation derived from the canonical equation when the friction coefficient is zero.

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