A structural approach to vibrational properties ranging from crystals to disordered systems

Abstract

Many scientists generally attribute the vibrational anomalies of disordered solids to the structural disorder, which, however, is still under intense debate.

Non-hyperuniform metastable states around a disordered hyperuniform state of densely packed spheres: stochastic density functional theory at strong coupling

“…In other words, isostaticity is a critical factor in mechanical marginal stability. 1,2,12,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][75][76][77][78][79][80][81][82][83] Recent simulation results have demonstrated that thermal fluctuations in the marginal states are accompanied by the intermittent rearrangements of particles. [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]…”

“…For instance, quasi-localized modes coupled to an elastic matrix create soft spots composed of tens to hundreds of particles undergoing displacements. [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] The low-frequency soft modes exhibit similar behaviors, and the common features of marginal states have been related to the emergence of many local minima in the free-energy landscape. 26,[84][85][86][87] The similarity in anharmonic vibrations suggests that the ensemble of configurations visited by the slow dynamics could reveal the characteristics of marginal stability associated with the free-energy landscape, even though possible configurations depend on a protocol adopted.…”

“…[19][20][21][22][76][77][78][79][80][81][82][83] The anomalous vibrational modes have been shown to exhibit strong anharmonicities that are accompanied by intermittent rearrangements of particles as follows: opening a weak contact of a buckler (i.e., buckling) yields a disordered core of a few particle scale with a power-law decay of displacements which are coupled to the elastic background of the contact network. [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][76][77][78][79][80][81][82][83] It is not the center of our concern whether or not the rattlers and/or bucklers significantly contribute to the quasicontacts to degrade the hyperuniformity. It is, however, illuminating to interpret eqn ( 86) and ( 87) in terms of quasi-localized soft modes.…”

Non-hyperuniform metastable states around a disordered hyperuniform state of densely packed spheres: stochastic density functional theory at strong coupling

“…The isostatic systems can be destabilized by cutting one particle contact unless disordered packings are strictly jammed. In other words, the isostaticity is a critical factor in the mechanical marginal stability [1,2,12,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][75][76][77][78][79][80][81][82][83].…”

“…Recent simulation results have demonstrated that thermal fluctuations in the marginal states are accompanied by intermittent rearrangements of particles [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. As a consequence, the marginal systems become responsive to have low-frequency soft modes that are nonphononic and anharmonic.…”