Velocity autocorrelation function in supercooled liquids: Long-time tails and anomalous shear-wave propagation

Abstract

Molecular dynamic simulations are performed to reveal the long-time behavior of the velocity autocorrelation function (VAF) by utilizing the finite-size effect in a Lennard-Jones binary mixture. Whereas in normal liquids the classical positive t −3/2 long-time tail is observed, we find in supercooled liquids a negative tail. It is strongly influenced by the transfer of the transverse current wave across the period boundary. The t −5/2 decay of the negative long-time tail is confirmed in the spectrum of VAF. Modeling the long-time transverse current within a generalized Maxwell model, we reproduce the negative long-time tail of the VAF, but with a slower algebraic t −2 decay. DOI: 10.1103/PhysRevE.94.060601 One of the simplest parameters for measuring liquid dynamics is the diffusion coefficient, which can be calculated from the mean-square displacement or from the single-particle velocity autocorrelation function (VAF) through the Green-Kubo relation [1,2]. In dilute fluids, where the correlation between binary collisions can be neglected, the time-dependent VAF decays exponentially. This has been validated by the kinetic theory for gases or granular media and Brownian dynamics [1,3]. It came as a surprise when Alder and Wainwright for the first time reported that the long-time tail of the VAF decays algebraically as t −d/2 , where d is the dimension of the system [4][5][6]. This long-lasting correlation is attributed to the well-known hydrodynamic vortex, or backflow, that supports the initial motion and develops a persistent long time tail [7,8].At high densities the initial direction of motion of an atom is, on average, soon reversed as the atom feels the surrounding neighbors, as a negative region. For the reversed velocity a t −5/2 decay has been reported for a hard-sphere fluid [9]. Interestingly, the same algebraic decay is observed in a Lorentz gas, where the long-time tail has been shown both theoretically [10] and by computer simulation (at low obstacle density) to decay as −t −d/2−1 [11]. A plausible conjecture is that they would have the same physical mechanism. Since the dynamic heterogeneity (both in space and time) manifests itself in the dynamics of high volume fraction of hard-sphere and of supercooled liquids [12][13][14], groups of immobile atoms might play the role of the fixed scatterers for mobile atoms as in the Lorentz gas. They then account for the negative long-time tail [9]. Actually frozen scatterers are not essential for the emergence of negative long-time tails. A more general approach using coarse graining has theoretically predicted a negative t −d/2−1 decay [15][16][17]. There are two mechanisms for the decay of the singleparticle momentum in atomic or molecular liquids: diffusion and sound propagation. By diffusion the momentum of a tagged atom is transferred into a region of typical length l = √ Dt (D is the diffusion coefficient) and the velocity decays * Corresponding author: hailong.peng@imr.tohoku.ac.jp, which is the classical long-time tail. In accordance with this mech...

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