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

TL;DR

This paper introduces a simple ansatz for analyzing velocity autocorrelation functions in fluids across different timescales, emphasizing a novel summation approach and power law relaxation behavior.

Contribution

It proposes a new ansatz based on an effective summation of continued fractions, providing explicit transition times between kinetic and hydrodynamic regimes.

Findings

VAFs show power law relaxation not captured by finite mode models

The approach aligns with Markovian approximation in overdamped regimes

Explicit transition times are derived from spectral function analysis

Abstract

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.