Abstract
We study the role of the Jacobian arising from a constraint enforcing the nonlinear relationg=ρV, where ρ,g, andV are the mass density, the momentum density, and the local velocity field, respectively, in the field-theoretic formulation of the nonlinear fluctuating hydrodynamics of simple fluids. By investigating the Jacobian directly and by developing a field-theoretic formulation without the constraint, we find that no changes in dynamics result as compared to the previous formulation developed by Das and Mazenko (DM). In particular, the cutoff mechanism discovered by DM is shown to be a consequence of the 1/ρ nonlinearity in the problem, not of the constraint. The consequences of this result for the static properties of the system are also discussed.
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Mazenko, G.F., Yeo, J. Density nonlinearities and a field theory for the dynamics of simple fluids. J Stat Phys 74, 1017–1032 (1994). https://doi.org/10.1007/BF02188215
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DOI: https://doi.org/10.1007/BF02188215