publication . Article . Preprint . 1994

Density nonlinearities and a field theory for the dynamics of simple fluids

Mazenko, Gene F.; Yeo, Joonhyun;
Open Access
  • Published: 04 Feb 1994 Journal: Journal of Statistical Physics, volume 74, pages 1,017-1,032 (issn: 0022-4715, eissn: 1572-9613, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
Abstract
We study the role of the Jacobian arising from a constraint enforcing the nonlinear relation: ${\bf g}=\rho{\bf V}$, where $\rho,\: {\bf g}$ and ${\bf V}$ 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 $1/\rho$ nonli...
Subjects
free text keywords: Mathematical Physics, Statistical and Nonlinear Physics, Vector field, Momentum, Statistical physics, Nonlinear system, Phase transition, Field theory (psychology), Cutoff, Jacobian matrix and determinant, symbols.namesake, symbols, Mathematics, Fluid dynamics, Classical mechanics, Condensed Matter
Related Organizations

[1] B. Kim and G. F. Mazenko, J. Stat. Phys. 64, 631 (1991).

[2] D. N. Zubarev and V. G. Morozov, Physica A 120, 411 (1983); V. G. Morozov, Physica A, 126, 443 (1984).

[3] S. P. Das and G. F. Mazenko, Phys. Rev. A 34, 2265 (1986)

[4] P. C. Martin, E. D. Siggia, and H. A. Rose, Phys. Rev. A 8, 423 (1973).

[5] U. Deker and F. Haake, Phys. Rev. A 11, 2043 (1975); 12, 1629 (1975). R. Bausch, H. J. Janssen, and H. Wagner, Z. Phys. B 24, 113 (1976); U. Deker, Phys. Rev. A 19, 846 (1979); C. De Dominicis and L. Peliti, Phys. Rev. B 18, 353 (1978); R. V. Jensen, J. Stat. Phys. 25, 183 (1981).

[6] E. Leutheusser, Phys. Rev. A 29, 2765 (1984).

[7] For a recent review of theoretical development, see W. Go¨tze in Liquids, Freezing and the Glass Transition, edited by D. Levesque, J. P. Hansen and J. Zinn-Justin (New York, Elsevier 1991); B. Kim and G. F. Mazenko, Phys. Rev. A 45, 2393 (1992).

[8] R. Schmitz, J. W. Dufty, and P. De, Broken Ergodicity and the Glass Transition, preprint

[9] F. A. Berezin, The Method of Second Quantization (Academic Press, New York 1966). G. Mun˜oz and W. S. Burgett, J. Stat. Phys. 56, 59 (1989); S. Chaturvedi, A. K. Kapoor and V. Srinivasan, Z. Phys. B 57, 249 (1984).

[10] S.-k. Ma and G. F. Mazenko, Phys. Rev. B 11, 4077 (1975). [12] G. F. Mazenko, S. Ramaswamy, and J. Toner, Phys. Rev. Lett. 49, 51 (1982); Phys. Rev. A 28, 1618 (1983). [OpenAIRE]

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publication . Article . Preprint . 1994

Density nonlinearities and a field theory for the dynamics of simple fluids

Mazenko, Gene F.; Yeo, Joonhyun;