An official website of the United States government
Abstract The frequency scaling exponent of low-frequency excitations in microscopically small glasses, which do not allow for the existence of waves (phonons), has been in the focus of the recent literature. The density of statesg(ω) of these modes obeys anωsscaling, where the exponents, ranging between 2 and 5, depends on the quenching protocol. The orgin of these findings remains controversal. Here we show, using heterogeneous-elasticity theory, that in a marginally-stable glass sampleg(ω) follows a Debye-like scaling (s= 2), and the associated excitations (type-I) are of random-matrix type. Further, using a generalisation of the theory, we demonstrate that in more stable samples, other, (type-II) excitations prevail, which are non-irrotational oscillations, associated with local frozen-in stresses. The corresponding frequency scaling exponentsis governed by the statistics of small values of the stresses and, therefore, depends on the details of the interaction potential.
more »
« less
Scaling of the non-phononic spectrum of two-dimensional glasses
Low-frequency vibrational harmonic modes of glasses are frequently used to rationalize their universal low-temperature properties. One well studied feature is the excess low-frequency density of states over the Debye model prediction. Here, we examine the system size dependence of the density of states for two-dimensional glasses. For systems of fewer than 100 particles, the density of states scales with the system size as if all the modes were plane-wave-like. However, for systems greater than 100 particles, we find a different system-size scaling of the cumulative density of states below the first transverse sound mode frequency, which can be derived from the assumption that these modes are quasi-localized. Moreover, for systems greater than 100 particles, we find that the cumulative density of states scales with the frequency as a power law with the exponent that leads to the exponent β = 3.5 for the density of states. For systems whose sizes were investigated, we do not see a size-dependence of exponent β.
more »
« less
- Award ID(s):
- 2154241
- PAR ID:
- 10411778
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 158
- Issue:
- 12
- ISSN:
- 0021-9606
- Page Range / eLocation ID:
- 126101
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
We investigate the structural, vibrational, and mechanical properties of jammed packings of deformable particles with shape degrees of freedom in three dimensions (3D). Each 3D deformable particle is modeled as a surface-triangulated polyhedron, with spherical vertices whose positions are determined by a shape-energy function with terms that constrain the particle surface area, volume, and curvature, and prevent interparticle overlap. We show that jammed packings of deformable particles without bending energy possess low-frequency, quartic vibrational modes, whose number decreases with increasing asphericity and matches the number of missing contacts relative to the isostatic value. In contrast, jammed packings of deformable particles with non-zero bending energy are isostatic in 3D, with no quartic modes. We find that the contributions to the eigenmodes of the dynamical matrix from the shape degrees of freedom are significant over the full range of frequency and shape parameters for particles with zero bending energy. We further show that the ensemble-averaged shear modulus 〈 G 〉 scales with pressure P as 〈 G 〉 ∼ P β , with β ≈ 0.75 for jammed packings of deformable particles with zero bending energy. In contrast, β ≈ 0.5 for packings of deformable particles with non-zero bending energy, which matches the value for jammed packings of soft, spherical particles with fixed shape. These studies underscore the importance of incorporating particle deformability and shape change when modeling the properties of jammed soft materials.more » « less
-
Abstract Advancements in quantum system lifetimes and control have enabled the creation of increasingly complex quantum states, such as those on multiple bosonic cavity modes. When characterizing these states, traditional tomography scales exponentially with the number of modes in both computational and experimental measurement requirement, which becomes prohibitive as the system size increases. Here, we implement a state reconstruction method whose sampling requirement instead scales polynomially with system size, and thus mode number, for states that can be represented within such a polynomial subspace. We demonstrate this improved scaling with Wigner tomography of multimode entangled W states of up to 4 modes on a 3D circuit quantum electrodynamics (cQED) system. This approach performs similarly in efficiency to existing matrix inversion methods for 2 modes, and demonstrates a noticeable improvement for 3 and 4 modes, with even greater theoretical gains at higher mode numbers.more » « less
-
Due to their small size, measurements of the complex composition of atmospheric aerosol particles and their surfaces are analytically challenging. This is particularly true for microspectroscopic methods, where it can be difficult to optically identify individual particles smaller than the diffraction limit of visible light (∼350 nm) and measure their vibrational modes. Recently, surface enhanced Raman spectroscopy (SERS) has been applied to the study of aerosol particles, allowing for detection and characterization of previously undistinguishable vibrational modes. However, atmospheric particles analyzed via SERS have primarily been >1 μm to date, much larger than the diameter of the most abundant atmospheric aerosols (∼100 nm). To push SERS towards more relevant particle sizes, a simplified approach involving Ag foil substrates was developed. Both ambient particles and several laboratory-generated model aerosol systems (polystyrene latex spheres (PSLs), ammonium sulfate, and sodium nitrate) were investigated to determine SERS enhancements. SERS spectra of monodisperse, model aerosols between 400–800 nm were compared with non-SERS enhanced spectra, yielding average enhancement factors of 10 2 for both inorganic and organic vibrational modes. Additionally, SERS-enabled detection of 150 nm size-selected ambient particles represent the smallest individual aerosol particles analyzed by Raman microspectroscopy to date, and the first time atmospheric particles have been measured at sizes approaching the atmospheric number size distribution mode. SERS-enabled detection and identification of vibrational modes in smaller, more atmospherically-relevant particles has the potential to improve understanding of aerosol composition and surface properties, as well as their impact on heterogeneous and multiphase reactions involving aerosol surfaces.more » « less
-
null (Ed.)Simulations are used to find the zero temperature jamming threshold, ϕ j , for soft, bidisperse disks in the presence of small fixed particles, or “pins”, arranged in a lattice. The presence of pins leads, as one expects, to a decrease in ϕ j . Structural properties of the system near the jamming threshold are calculated as a function of the pin density. While the correlation length exponent remains ν = 1/2 at low pin densities, the system is mechanically stable with more bonds, yet fewer contacts than the Maxwell criterion implies in the absence of pins. In addition, as pin density increases, novel bond orientational order and long-range spatial order appear, which are correlated with the square symmetry of the pin lattice.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0139596
