arXiv subjects

Shivam Mahajan

Publications and source records attributed to Shivam Mahajan.

8 recordsLinked to original sources

arXiv2026

A flat-band perspective on the boson peak in amorphous solids

The boson peak is a characteristic anomaly of amorphous solids broadly defined as a low-energy excess in the density of states and heat capacity compared to the textbook predictions of Debye theory. The origin of this anomaly has long been the subject of ongoing debate and remains a topic of active controversy. We propose that the boson peak may have a defining dynamical feature: the accumulation of vibrational spectral weight within a narrow frequency window that is only weakly dependent on wavevector. In this perspective, the boson peak reflects a flat or weakly dispersive band in the dynamical structure factor rather than a propagating excitation. We revisit both experimental and simulation data from the literature through this lens and conduct further simulations in 2D and 3D amorphous systems. Taken together, these analyses provide compelling converging evidence for this interpretation and sharply constrain the space of viable theoretical descriptions of the boson peak.

cond-mat.soft↗

arXiv2025

Revealing the Geometrical and Vibrational Properties of the Defects Driving the Boson Peak

In amorphous solids, the vibrational density of states shows an excess of modes over the Debye model, known as the boson peak, whose origin remains unclear. Studies suggest a link to quasi-localized nonphononic vibrations or 'defects,' but identifying them is challenging due to hybridization with phonons that renders methods based on localization properties, such as the participation ratio, unreliable. We introduce a practical method to separate hybridized phonons from localized vibrations and find that boson peak phonons hybridize with compact, two-dimensional defects exhibiting oscillatory pure shear deformations. These two-dimensional defects are also exposed by the procedure recently employed to identify stringlets (Nature Physics volume 18, pages 669-677 (2022)), suggesting that these may not be one-dimensional objects as speculated. Our work demonstrates the presence of localized defects at the boson peak frequency and provides a comprehensive characterization of their vibrational and geometric properties, resolving the tension between the concepts of quasi-localized quadrupolar defects and stringlets.

cond-mat.soft↗

arXiv2024

Heterogeneous attenuation of sound waves in three-dimensional amorphous solids

Sound waves are attenuated as they propagate in amorphous materials. We investigate the mechanism driving sound attenuation in the Rayleigh scattering regime by resolving the dynamics of an excited phonon in time and space via numerical simulations. We find sound attenuation is spatiotemporal heterogeneous. It starts in localised regions, which identify soft regions within the material and correlate with low-frequency vibrational modes. As time progresses, the regions where sound is primarily attenuated invade the system via an apparent diffusive process.

cond-mat.soft↗

arXiv2023

Quasi-localized vibrational modes, Boson peak and sound attenuation in model mass-spring networks

We introduce an algorithm that constructs disordered mass-spring networks whose elastic properties mimic that of glasses by tuning the fluctuations of the local elastic properties, keeping fixed connectivity and controlling the prestress. In two dimensions, the algorithm reproduces the dependence of gasses' vibrational properties, such as quasi-localised vibrational modes and Boson peak, on the degree of stability. The sound attenuation displays Rayleigh scattering and disorder-broadening regimes at different frequencies, and the attenuation rate increases with increased stability. Our results establish a strong connection between the vibrational features of disordered solids and the fluctuations of the local elastic properties and provide a new approach to investigating glasses' vibrational anomalies.

cond-mat.dis-nn↗

arXiv2021

Unifying description of the vibrational anomalies of amorphous materials

The vibrational density of states $D(ω)$ of solids controls their thermal and transport properties. In crystals, the low-frequency modes are extended phonons distributed in frequency according to Debye's law, $D(ω) \propto ω^2$. In amorphous solids, phonons are damped, and at low frequency $D(ω)$ comprises extended modes in excess over Debye's prediction, leading to the so-called boson peak in $D(ω)/ω^2$ at $ω_{\rm bp}$, and quasi-localized (QLMs) ones. Here we show that boson peak and phonon attenuation in the Rayleigh scattering regime are related, as suggested by correlated fluctuating elasticity theory (corr-FET), and that amorphous materials can be described as homogeneous isotropic elastic media punctuated by QLMs acting as elastic heterogeneities. Our numerical results resolve the conflict between theoretical approaches attributing amorphous solids' vibrational anomalies to elastic disorder and localized defects.

cond-mat.soft↗

arXiv2021

Emergence of linear isotropic elasticity in amorphous and polycrystalline materials

We investigate the emergence of isotropic linear elasticity in amorphous and polycrystalline solids, via extensive numerical simulations. We show that the elastic properties are correlated over a finite length scale $ξ_E$, so that the central limit theorem dictates the emergence of continuum linear isotropic elasticity on increasing the specimen size. The stiffness matrix of systems of finite size $L > ξ_E$ is obtained adding to that predicted by linear isotropic elasticity a random one of spectral norm $(L/ξ_E)^{-3/2}$, in three spatial dimensions. We further demonstrate that the elastic length scale corresponds to that of structural correlations, which in polycrystals reflect the typical size of the grain boundaries and length scales characterizing correlations in the stress field. We finally demonstrate that the elastic length scale affects the decay of the anisotropic long-ranged correlations of locally defined shear modulus and shear stress.

cond-mat.soft↗

arXiv2021

Designing Phononic Band Gaps with Sticky Potentials

Spectral gaps in the vibrational modes of disordered solids are key design elements in the synthesis and control of phononic metamaterials that exhibit a plethora of novel elastic and mechanical properties. However, reliably producing these gaps often require a high degree of network specificity through complex control optimization procedures. In this work, we present as an additional tool to the existing repertoire, a numerical scheme that rapidly generates sizeable spectral gaps in absence of any fine tuning of the network structure or elastic parameters. These gaps occur even in disordered polydisperse systems consisting of relatively few particles ($N \sim 10^2-10^3$). Our proposed procedure exploits sticky potentials that have recently been shown to suppress the formation of soft modes, thus effectively recovering the linear elastic regime where band structures appear, at much shorter length scales than in conventional models of disordered solids. Our approach is relevant to design and realization of gapped spectra in a variety of physical setups ranging from colloidal suspensions to 3D-printed elastic networks.

cond-mat.soft↗

arXiv2020

Reverse Janssen effect in narrow granular columns

When grains are added to a cylinder, the weight at the bottom is smaller than the total weight of the column, which is partially supported by the lateral walls through wall/grain frictional forces. This is known as the Janssen effect. Via a combined experimental and numerical investigation, here we demonstrate a reverse Jansen effect whereby the fraction of the weight supported by the base overcomes one. We characterize the dependence of this phenomenon on the various control parameters involved, rationalize the physical process responsible for the emergence of the compressional frictional forces responsible for the anomaly, and introduce a model to reproduce our findings. Contrary to prior assumptions, our results demonstrate that the constitutive relation on a material element can depend on the applied stress.

cond-mat.soft↗