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A hallmark of structural glasses and other disordered solids is the emergence of excess low-frequency vibrations, on top of the Debye spectrum $D_{\rm Debye}(\omega)$ of phonons ($\omega$ denotes the vibrational frequency), which exist in…

It has been recently established that the low-frequency spectrum of simple computer glass models is populated by soft, quasilocalized nonphononic vibrational modes whose frequencies $\omega$ follow a gapless, universal distribution ${\cal…

The relaxation dynamics of glass-forming systems shows a multitude of features that are absent in normal liquids, such as non-exponential relaxation and a strong temperature-dependence of the relaxation time. Connecting these dynamic…

Active systems are comprised of constituents with interactions that are generically non-reciprocal in nature. Such non-reciprocity often gives rise to situations where conflicting objectives exist, such as in the case of a predator pursuing…

The quantum excitations in glasses have long presented a set of puzzles for condensed matter physicists. A common view is that they are largely disordered analogs of elementary excitations in crystals, supplemented by two level systems…

In glasses, atomic disorder combined with atomic connectivity makes understanding of the nature of the vibrations much more complex than in crystals or molecules. With a simple model, however, it is possible to show how disorder generates…

Structural glasses formed by quenching a melt possess a population of soft quasilocalized excitations --- often called `soft spots' --- that are believed to play a key role in various thermodynamic, transport and mechanical phenomena. Under…

We study a recently introduced and exactly solvable mean-field model for the density of vibrational states $\mathcal{D}(\omega)$ of a structurally disordered system. The model is formulated as a collection of disordered anharmonic…

Marginal stability is the notion that stability is achieved, but only barely so. This property constrains the ensemble of configurations explored at low temperature in a variety of systems, including spin, electron and structural glasses. A…

Using large-scale molecular dynamics simulations for a system of $10^6$ particles, the response of a dense amorphous solid to the continuous expansion of its volume is investigated. We find that the spatially uniform glassy state becomes…

We study in this paper the effect of weak, short-ranged interaction on disordered metals. Through analysing the interaction matrix elements between different eigenstates of the non-interacting and corresponding Hartree-Fock single-particle…

Understanding the statistical mechanics of low-energy excitations in structural glasses has been the focus of extensive research efforts in the past decades due to their key roles in determining the low-temperature mechanical and transport…

The nature of defects in amorphous materials, analogous to vacancies and dislocations in crystals, remains elusive. Here we explore their nature in a three-dimensional microscopic model glass-former which describes granular, colloidal,…

Plastically deforming crystals exhibit scale-free fluctuations that are similar to those observed in driven disordered elastic systems close to depinning, but the nature of the yielding critical point is still debated. Here, we study the…

Glass phases can be stabilized by quenched disorders, as in most spin-glass materials, or self-generated through kinetic freezing in disorder-free systems. A canonical example of the latter is structural glasses, which have been extensively…

We study energy minimized configurations of amorphous solids with a simple shear degree of freedom. We show that the low-frequency regime of the vibrational density of states of structural glass formers is crucially sensitive to the…

It is a persistent problem in condensed matter physics that glasses exhibit vibrational and thermal properties that are markedly different from those of crystals. While recent works have advanced our understanding of vibrational excitations…

We consider the contribution to the density of vibrational states and the distribution of energy barrier heights of incipient instabilities in a glass modeled by a jammed packing of spheres. On approaching an instability, the frequency of a…

The universal form of the density of nonphononic, quasilocalized vibrational modes of frequency $\omega$ in structural glasses, ${\cal D}(\omega)$, was predicted theoretically decades ago, but only recently revealed in numerical…

Quest for new states of matter near an ordered phase is a promising route for making modern physics forward. By probing thermal properties of a ferroelectric (FE) crystal Ba1-xSrxAl2O4, we have clarified that low-energy excitation of…