On the rigidity of jamming systems at finite temperatures


Hajime Yoshino (Osaka University)


Usual solids including crystals as well as glasses at low enough temperatures can be regarded as harmonic systems. This is because the activity of plastic processes, which usually require some finite creation energy, can be safely neglected at low enough temperatures. We show that the situation is very different in repulsive contact systems which exhibit the jamming transition.

Using the cloned liquid approach which assumes the 1 step RSB (replica symmetry breaking) [1], we found that the shear-modulus of a class of jamming systems in the zero temperature limit is significantly smaller than and scales differently from the shear-modulus at zero temperature which can be obtained assuming the harmonicity.

By performing extensive MD simulations we actually found "two plateau modulus" in the shear-stress relaxation: the purely harmonic one at shorter time scales and much smaller one at longer time scales. Interestingly the latter one appears to be consistent with the 1RSB theory [1] and the experiments in emulsions [2]. Between the two plateaus, the dynamics exhibits strong aging effects and continuous variation of the effective temperature, apparently suggesting a 1+continuous RSB scenario. Closer inspections suggest that the transitions between the two plateaus are due to avalanche like processes.

[1] H. Yoshino, AIP Conf. Proc, 1518, 244-251 (2013), H. Yoshino and M. Mezard, PRL 105, 015504 (2010), H. Yoshino, JCP 136, 214108 (2012).
[2] T. G. Mason, J. Bibette and D. A. Weitz, PRL 75, 2051 (1995).

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