A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales

A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales is proposed. The ansatz is based on an effective summation of the infinite continued fraction at a reasonable assumption about convergence of relaxation times of the higher order memory functions, w...

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Bibliographic Details
Published in:Condensed matter physics 2018-01, Vol.21 (1), p.13001
Main Authors: Ignatyuk, V V, Mryglod, I M, Bryk, T
Format: Article
Language:English
Subjects:
Autocorrelation functions
classical fluids
Langevin equation
Markov processes
Markovian processes
nonequilibrium statistical mechanics
Singularities
statistical hydrodynamics
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Summary:A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales is proposed. The ansatz is based on an effective summation of the infinite continued fraction at a reasonable assumption about convergence of relaxation times of the higher order memory functions, which have a purely kinetic origin. The VAFs obtained within our approach are compared with the results of the Markovian approximation for memory kernels. It is shown that although in the "overdamped" regime both approaches agree to a large extent at the initial and intermediate times of the system evolution, our formalism yields power law relaxation of the VAFs which is not observed at the description with a finite number of the collective modes. Explicit expressions for the transition times from kinetic to hydrodynamic regimes are obtained from the analysis of the singularities of spectral functions in the complex frequency plane.
ISSN:1607-324X
2224-9079
DOI:10.5488/CMP.21.13001