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Long-time correlations in a binary mixture: analysis of the nonlinearities of fluctuating-hydrodynamic equations
The equations of fluctuating nonlinear hydrodynamics (FNH) following the proper conservation laws are considered for a binary mixture. We focus on the density ( ρ ) correlations’ renormalization due to the FNH equations’ nonlinearities. The consequence of density nonlinearities treated in simplest a...
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Published in: | Journal of statistical mechanics 2023-06, Vol.2023 (6), p.63301 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites |
Online Access: | Get full text |
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Summary: | The equations of fluctuating nonlinear hydrodynamics (FNH) following the proper conservation laws are considered for a binary mixture. We focus on the density (
ρ
) correlations’ renormalization due to the FNH equations’ nonlinearities. The consequence of density nonlinearities treated in simplest approximations gives rise to the well-studied form of the mode coupling theory (MCT) for a two-component system. The MCT predicts a sharp ergodicity–nonergodicity transition similar to the one-component fluid in this idealized form. In the first part of the present paper, we compare the predictions of the idealized MCT model with the computer simulation results for a hard sphere mixture. We show that there is clear disagreement in long-time dynamic behaviour. Next, we consider the full set of nonlinearities in the FNH equations using a Martin–Siggia–Rose field theory. From the time reversal properties of the correlation and response function of the associated field theory, a set of fluctuation–dissipation relations (FDR) are obtained. These FDRs impose constraints on the long-time behaviour of the correlation functions. Our non-perturbative analysis considers the viability of freezing the time correlations for the two-component fluid over the longest time scale. Due to the FDR constraints arising from the
1
/
ρ
nonlinearity in the FNH equations, a sharp ergodicity–nonergodicity transition for the binary mixture is not supported. If the
1
/
ρ
are replaced as
1
/
ρ
0
in terms of the average density
ρ
0
, ad hoc, while the density-nonlinearities in the pressure term of the corresponding FNH equations are kept, the ideal transition model of the simplified MCT is recovered. |
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ISSN: | 1742-5468 1742-5468 |
DOI: | 10.1088/1742-5468/acd696 |