Continuum limit of amorphous elastic bodies (III): Three dimensional systems

Details Continuum limit of amorphous elastic bodies (III): Three dimensional systems Continuum limit of amorphous elastic bodies (III): Three dimensional systems

2005-05-25

arxiv.org/abs/cond-mat/0505610v1

Physics

Condensed Matter

Statistical Mechanics

27 pages, 11 figures, submitted to Phys. Rev. B

Scientific paper

10.1103/PhysRevB.72.224206

Extending recent numerical studies on two dimensional amorphous bodies, we characterize the approach of elastic continuum limit in three dimensional (weakly polydisperse) Lennard-Jones systems. While performing a systematic finite-size analysis (for two different quench protocols) we investigate the non-affine displacement field under external strain, the linear response to an external delta force and the low-frequency harmonic eigenmodes and their density distribution. Qualitatively similar behavior is found as in two dimensions. We demonstrate that the classical elasticity description breaks down below an intermediate length scale $\xi$, which in our system is approximately 23 molecular sizes. This length characterizes the correlations of the non-affine displacement field, the self-averaging of external noise with distance from the source and gives the lower wave length bound for the applicability of the classical eigenfrequency calculations. We trace back the "Boson-peak" of the density of eigenfrequencies (obtained from the velocity auto-correlation function) to the inhomogeneities on wave lengths smaller than $\xi$.

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