Stress correlation function and linear response of Brownian particles

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The European Physical Journal E : Soft Matter and Biological Physics. Springer. 2020, 43, 70. ISSN 1292-8941. eISSN 1292-895X. Available under: doi: 10.1140/epje/i2020-11993-4
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Abstract.We determine the non-local stress autocorrelation tensor in an homogeneous and isotropic systemof interacting Brownian particles starting from the Smoluchowski equation of the configurational probabil-ity density. In order to relate stresses to particle displacements as appropriate in viscoelastic states, we gobeyond the usual hydrodynamic description obtained in the Zwanzig-Mori projection-operator formalismby introducing the proper irreducible dynamics following Cichocki and Hess, andKawasaki. Differentlyfrom these authors, we include transverse contributions as well. This recovers theexpression for the stressautocorrelation including the elastic terms in solid states as found for Newtonian and Langevin systems, incase that those are evaluated in the overdamped limit. Finally, we arguethat the found memory functionreduces to the shear and bulk viscosity in the hydrodynamic limit of smooth and slow fluctuations andderive the corresponding hydrodynamic equations.

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ISO 690VOGEL, Florian, Matthias FUCHS, 2020. Stress correlation function and linear response of Brownian particles. In: The European Physical Journal E : Soft Matter and Biological Physics. Springer. 2020, 43, 70. ISSN 1292-8941. eISSN 1292-895X. Available under: doi: 10.1140/epje/i2020-11993-4
BibTex
@article{Vogel2020Stres-51872,
  year={2020},
  doi={10.1140/epje/i2020-11993-4},
  title={Stress correlation function and linear response of Brownian particles},
  volume={43},
  issn={1292-8941},
  journal={The European Physical Journal E : Soft Matter and Biological Physics},
  author={Vogel, Florian and Fuchs, Matthias},
  note={Article Number: 70}
}
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