Novel elastic instability of amorphous solids in finite spatial dimensions

Abstract

We study a disordered spring network to describe the low-frequency vibrational spectrum of amorphous solids.

Non-phononic density of states of two-dimensional glasses revealed by random pinning

“…Mean-field theories predict that glasses exhibit the non-Debye scaling law of g(ω) ∝ ω 2 at low frequencies by both the replica theory [8] and the effective medium theory [9], and numerical simulations of high-dimensional packings confirm this behavior [10,11]. Recently, replica theories of interacting anharmonic oscillators [12,13] and the effective medium theory [14][15][16] have also successfully derived the ω 4 scaling of glasses. Of these mean-field theories, the effective medium theory [9,[14][15][16] naturally deals with phonon modes together with non-phononic modes, whereas the other theories focus on non-phononic modes without particular attention on phonon modes.…”

“…Recently, replica theories of interacting anharmonic oscillators [12,13] and the effective medium theory [14][15][16] have also successfully derived the ω 4 scaling of glasses. Of these mean-field theories, the effective medium theory [9,[14][15][16] naturally deals with phonon modes together with non-phononic modes, whereas the other theories focus on non-phononic modes without particular attention on phonon modes.…”

Universal non-Debye low-frequency vibrations in sheared amorphous solids

“…Recently, a new vibrational characteristic of glass formers has been identified: a regime displaying a D (o) B o 4 scaling in the density of states. [12][13][14][15][16][17][18][19][20][21][22] Many theoretical models built around two-level systems, replica symmetry breaking, stress correlations, random matrices and other hypotheses have been proposed as the origin of this behaviour; 1,[23][24][25][26][27][28][29][30][31][32][33] however, the nature of the modes contributing to the o 4 behaviour is still a subject of active research. In this context, it is important to characterise new, deviant universal features and their connection to microscopic details.…”

Bose–Einstein-like condensation of deformed random matrix: a replica approach

“…• We speculate that the condition n > 1 for the existence of the localized phase is somehow universal. Recently, Shimada et al investigated the localization transition of a d -dimensional disordered lattice by using the effective medium theory [37][38][39]. They found that for the localized mode to exist, the distribution of the stiffness k should be P (k) ∼ k n with n > 1 for k ≪ 1.…”