The nature of non-phononic excitations in disordered systems

Abstract

Using heterogeneous-elasticity theory (HET) and a generalisation of HET theory (GHET), obtained by applying a newly developed procedure for obtaining the continuum limit of the glass's Hessian, we investigate the nature of vibrational excitations, which are present in small systems, which do not allow for low-frequency phonons. We identify two types of such non-phononic excitations. In marginally stable systems, which can be prepared by quenching from a rather high parental temperature, the low-frequency regime is dominated by random-matrix vibrational wavefunctions (type-I) which in macroscopic samples gives rise to the boson peak. They show a density of states (DOS), which scales as $g(\omega )\sim {\omega }^2$. In more stable systems (reached by a somewhat lower parental temperature) a gap appears in the type-I spectrum. This gap is filled with other type-II non-phononic excitations, which are not described by the previous version of HET, and have a DOS, which scales as $g(\omega )\sim {\omega }^s$ with $3<s<5$. Using GHET we demonstrate that the type-II excitations are due to local non-irrotational oscillations associated with the stress field. The frequency scaling exponent $s$ turns out to be non-universal, depending on the details of the interaction potential. Specifically, we demonstrate that $s$ depends on the statistics of the small values of the local frozen-in stresses, which are, in turn, governed by the shape of the pair potential close to values where the potential or its first derivative vanishes. All these findings are verified by extensive numerical simulations of small soft-sphere glasses. Further, using level-distance statistics, we demonstrate that both types of non-phononic excitations obey the Gaussian-Orthogonal-Ensemble random-matrix statistics, which means that they are extended and not localized.

References in corpus (8)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Inhomogeneous elastic response of silica glass
• Rejuvenation and Memory Effects in a Structural Glass
• Universal non-Debye low-frequency vibrations in sheared amorphous solids
• Density of States below the First Sound Mode in 3D Glasses
• Microscopic observation of two-level systems in a metallic glass model
• Scaling of the Non-Phononic Spectrum of Two-Dimensional Glasses

Cited by in corpus (10)

• Unified percolation scenario for the $\alpha$ and $\beta$ processes in simple glass formers
• Yielding and plasticity in amorphous solids
• Testing the Heterogeneous-Elasticity Theory for low-energy excitations in structural glasses
• Two-level systems and harmonic excitations in a mean-field anharmonic quantum glass
• Soft modes in vector spin glass models on sparse random graphs
• A self-consistent current response theory of jamming and vibrational modes in low-temperature amorphous solids
• Computational Methods toward Ultrastable Glasses
• Further testing the validity of generalized heterogeneous-elasticity theory for low-frequency excitations in structural glasses
• Statistical mechanics of vector Hopfield network near and above saturation
• Particle pinning as a method to manipulate marginal stability