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Atsushi Ikeda

Publications and source records attributed to Atsushi Ikeda.

At least 55 records · Page 3Linked to original sources
arXiv2019

Anharmonic properties of vibrational excitations in amorphous solids

Understanding the vibrational and thermal properties of amorphous solids is one of the most discussed and long-standing issues in condensed matter physics. Recent works have made significant steps towards understanding harmonic vibrational states. In particular, it has been established that quasi-localized vibrational modes emerge in addition to phonon-like vibrational modes. In this work, we study the anharmonic properties of these vibrational modes. We find that vibrational modes exhibit anharmonicities that induce particle rearrangements and cause transitions to different states. These anharmonicities are distinct from those in crystals, where particle rearrangements never occur. Remarkably, for both the phonon modes and quasi-localized modes, the vibrational modes exhibit strong anharmonicities, and the induced particle rearrangements are always localized in space and are composed of 1 to 1000 particles. Our findings contribute to the understanding of low-temperature thermal properties, for which anharmonic vibrations are crucial.

cond-mat.soft↗
arXiv2019

Low-frequency vibrations of jammed packings in large spatial dimensions

Amorphous packings prepared in the vicinity of the jamming transition play a central role in theoretical studies of the vibrational spectrum of glasses. Two mean-field theories predict that the vibrational density of states $g(ω)$ obeys a characteristic power law, $g(ω)\simω^2$, called the non-Debye scaling in the low-frequency region. Numerical studies have however reported that this scaling breaks down at low frequencies, due to finite dimensional effects. In this study, we prepare amorphous packings of up to $128000$ particles in spatial dimensions from $d=3$ to $d=9$ to characterise the range of validity of the non-Debye scaling. Our numerical results suggest that the non-Debye scaling is obeyed down to a frequency that gradually decreases as $d$ increases, and possibly vanishes for large $d$, in agreement with mean-field predictions. We also show that the prestress is an efficient control parameter to quantitatively compare packings across different spatial dimensions.

cond-mat.soft↗
arXiv2019

Stress relaxation above and below the jamming transition

We numerically investigate stress relaxation in soft athermal disks to reveal critical slowing down when the system approaches the jamming point. The exponents describing the divergence of the relaxation time differ dramatically depending on whether the transition is approached from the jammed or unjammed phase. This contrasts sharply with conventional dynamic critical scaling scenarios, where a single exponent characterizes both sides. We explain this surprising difference in terms of the vibrational density of states (vDOS), which is a key ingredient of linear viscoelastic theory. The vDOS exhibits an extra slow mode that emerges below jamming, which we utilize to demonstrate the anomalous exponent below jamming.

cond-mat.soft↗
arXiv2019

Vibrational spectrum derived from the local mechanical response in disordered solids

The low-frequency vibrations of glasses are markedly different from those of crystals. These vibrations have recently been categorized into two types: spatially extended vibrations, whose vibrational density of states (vDOS) follows a non-Debye quadratic law, and quasilocalized vibrations (QLVs), whose vDOS follows a quartic law. The former are explained by elasticity theory with quenched disorder and microscopic replica theory as being a consequence of elastic instability, but the origin of the latter is still debated. Here, we show that the latter can also be directly derived from elasticity theory with quenched disorder. We find another elastic instability that the theory encompasses but that has been overlooked so far, namely, the instability of the system against a local dipolar force. This instability gives rise to an additional contribution to the vDOS, and the spatial structure and energetics of the mode originating from this instability are consistent with those of the QLVs. Finally, we construct a model in which the additional contribution to the vDOS follows a quartic law.

cond-mat.soft↗
arXiv2019

Vibrational properties of two-dimensional dimer packings near the jamming transition

Jammed particulate systems composed of various shapes of particles undergo the jamming transition as they are compressed or decompressed. To date, sphere packings have been extensively studied in many previous works, where isostaticity at the transition and scaling laws with the pressure of various quantities, including the contact number and the vibrational density of states, have been established. Additionally, much attention has been paid to nonspherical packings, and particularly recent work has made progress in understanding ellipsoidal packings. In the present work, we study the dimer packings in two dimensions, which have been much less understood than systems of spheres and ellipsoids. We first study the contact number of dimers near the jamming transition. It turns out that packings of dimers have "rotational rattlers", each of which still has a free rotational motion. After correcting this effect, we show that dimers become isostatic at the jamming, and the excess contact number obeys the same critical law and finite size scaling law as those of spheres. We next study the vibrational properties of dimers near the transition. We find that the vibrational density of states of dimers exhibits two characteristic plateaus that are separated by a peak. The high-frequency plateau is dominated by the translational degree of freedom, while the low-frequency plateau is dominated by the rotational degree of freedom. We establish the critical scaling laws of the characteristic frequencies of the plateaus and the peak near the transition. In addition, we present detailed characterizations of the real space displacement fields of vibrational modes in the translational and rotational plateaus.

cond-mat.soft↗
arXiv2019

Universal relaxation dynamics of sphere packings below jamming

We show that non-Brownian suspensions of repulsive spheres below jamming display a slow relaxational dynamics with a characteristic time scale that diverges at jamming. This slow time scale is fully encoded in the structure of the unjammed packing and can be readily measured via the vibrational density of states. We show that the corresponding dynamic critical exponent is the same for randomly generated and sheared packings. Our results show that a wide variety of physical situations, from suspension rheology to algorithmic studies of the jamming transition are controlled by a unique diverging timescale, with a universal critical exponent.

cond-mat.soft↗
arXiv2019

Glassy dynamics of a model of bacterial cytoplasm with metabolic activities

Recent experiments have revealed that cytoplasms become glassy when their metabolism is suppressed, while they maintain fluidity in a living state. The mechanism of this active fluidization is not clear, especially for bacterial cytoplasms, since they lack traditional motor proteins, which can cause directed motions. We introduce a model of bacterial cytoplasm focusing on the impact of conformational change in proteins due to metabolism. In the model, proteins are treated as particles under thermal agitation, and conformation changes are treated as changes in particle volume. Simulations revealed that a small change in volume fluidizes the glassy state, accompanied by a change in fragility, as observed experimentally.

cond-mat.soft↗
arXiv2018

Phonon transport and vibrational excitations in amorphous solids

One of the long-standing issues concerning the thermal properties of amorphous solids is the complex pattern of phonon transport. Recent advances in experiments and computer simulations have indicated a crossover from Rayleigh scattering to viscous damping. A number of theories have been proposed, yet critical tests are missing and the validity of these theories is unclear. In particular, the precise location of the crossover frequency remains controversial, and more critically, even the validity of the Rayleigh scattering itself has been seriously questioned. The present work settles these issues by using information on the underlying vibrational eigenmodes. Vibrational eigenmodes were recently clarified over a wide frequency regime: a mixture of phonon modes and soft localized modes in the continuum limit and disordered and extended modes in the boson peak regime. Here, we demonstrate that Rayleigh scattering occurs in the continuum limit and viscous damping occurs in the boson peak regime, and these behaviors are therefore linked to the underlying eigenmodes in the corresponding frequency regimes. Our results unambiguously determine the crossover frequency. Furthermore, we establish characteristic scaling laws of phonon transport, which are consistent with the prediction of the mean-field theory at higher frequencies but inconsistent in the low-frequency, Rayleigh scattering regime. Our results therefore reveal crucial issues to be solved with regard to the current theory.

cond-mat.soft↗
arXiv2018

Ideal glass states are not purely vibrational: Insight from randomly pinned glasses

We use computer simulations to probe the thermodynamic and dynamic properties of a glass-former that undergoes an ideal glass-transition because of the presence of randomly pinned particles. We find that even deep in the equilibrium glass state the system relaxes to some extent because of the presence of localized excitations that allow the system to access different inherent structures, giving thus rise to a non-trivial contribution to the entropy. By calculating with high accuracy the vibrational part of the entropy, we show that also in the equilibrium glass state thermodynamics and dynamics give a coherent picture and that glasses should not be seen as a disordered solid in which the particles undergo just vibrational motion but instead as a system with a highly nonlinear internal dynamics.

cond-mat.dis-nn↗
arXiv2018

Spatial structure of quasi-localized vibrations in nearly jammed amorphous solids

The low-temperature properties of amorphous solids are widely believed to be controlled by low-frequency quasi-localized modes. What governs their spatial structure and density is however debated. We study these questions numerically in very large systems as the jamming transition is approached and the pressure p vanishes. We find that these modes consist of an unstable core in which particles undergo the buckling motions and decrease the energy, and a stable far-field component which increases the energy and prevents the buckling of the core. The size of the core diverges as $p^{-1/4}$ and its characteristic volume as $p^{-1/2}$ These features are precisely those of the anomalous modes known to cause the Boson peak in the vibrational spectrum of weakly-coordinated materials. From this correspondence we deduce that the density of quasi-localized modes must go as $g_{\mathrm{loc}}(ω) \sim ω^4/p^2$ , in agreement with previous observations. Our analysis thus unravels the nature of quasi-localized modes in a class of amorphous materials.

cond-mat.dis-nn↗
arXiv2017

Mean field theory of the swap Monte Carlo algorithm

The swap Monte Carlo algorithm combines the translational motion with the exchange of particle species, and is unprecedentedly efficient for some models of glass former. In order to clarify the physics underlying this acceleration, we study the problem within the mean field replica liquid theory. We extend the Gaussian ansatz so as to take into account the exchange of particles of different species, and we calculate analytically the dynamical transition points corresponding to the swap and standard Monte Carlo algorithms. We show that the system evolved with the standard Monte Carlo algorithm exhibits the dynamical transition before that of the swap Monte Carlo algorithm. We also test the result by performing numerical simulations of a binary mixture of the Mari-Kurchan model, both with standard and swap Monte Carlo. This scenario provides a possible explanation for the efficiency of the swap Monte Carlo algorithm. Finally, we discuss how the thermodynamic theory of the glass transition should be modified based on our results.

cond-mat.dis-nn↗
arXiv2017

Anomalous vibrational properties in the continuum limit of glasses

The low-temperature thermal properties of glasses are anomalous with respect to those of crystals. These thermal anomalies indicate that the low-frequency vibrational properties of glasses differ from those of crystals. Recent studies revealed that, in the simplest model of glasses, i.e., the harmonic potential system, phonon modes coexist with soft localized modes in the low-frequency (continuum) limit. However, the nature of low-frequency vibrational modes of more realistic models is still controversial. In the present work, we study the Lennard-Jones (LJ) system using large-scale molecular-dynamics (MD) simulation and establish that the vibrational property of the LJ glass converges to coexistence of the phonon modes and the soft localized modes in the continuum limit as in the case of the harmonic potential system. Importantly, we find that the low-frequency vibrations are rather sensitive to the numerical scheme of potential truncation which is usually implemented in the MD simulation, and this is the reason why contradictory arguments have been reported by previous works. We also discuss the physical origin of this sensitiveness by means of a linear stability analysis.

cond-mat.soft↗
arXiv2017

Large-scale structure of randomly jammed particles

We numerically analyse the density field of three-dimensional randomly jammed packings of monodisperse soft frictionles spherical particles, paying special attention to fluctuations occurring at large lengthscales. We study in detail the two-point static structure factor at low wavevectors in Fourier space. We also analyse the nature of the density field in real space by studying the large-distance behavior of the two-point pair correlation function, of density fluctuations in subsystems of increasing sizes, and of the direct correlation function. We show that such real space analysis can be greatly improved by introducing a coarse-grained density field to disentangle genuine large-scale correlations from purely local effects. Our results confirm that both Fourier and real space signatures of vanishing density fluctuations at large scale are absent, indicating that randomly jammed packings are not hyperuniform. In addition, we establish that the pair correlation function displays a surprisingly complex structure at large distances, which is however not compatible with the long-range negative correlation of hyperuniform systems but fully compatible with an analytic form for the structure factor. This implies that the direct correlation function is short-ranged, as we also demonstrate directly. Our results reveal that density fluctuations in jammed packings do not follow the behavior expected for random hyperuniform materials, but display instead a more complex behavior.

cond-mat.stat-mech↗
arXiv2017

Continuum limit of the vibrational properties of amorphous solids

The low-frequency vibrational and low-temperature thermal properties of amorphous solids are markedly different from those of crystalline solids. This situation is counter-intuitive because any solid material is expected to behave as a homogeneous elastic body in the continuum limit, in which vibrational modes are phonons following the Debye law. A number of phenomenological explanations have been proposed, which assume elastic heterogeneities, soft localized vibrations, and so on. Recently, the microscopic mean-field theories have been developed to predict the universal non-Debye scaling law. Considering these theoretical arguments, it is absolutely necessary to directly observe the nature of the low-frequency vibrations of amorphous solids and determine the laws that such vibrations obey. Here, we perform an extremely large-scale vibrational mode analysis of a model amorphous solid. We find that the scaling law predicted by the mean-field theory is violated at low frequency, and in the continuum limit, the vibrational modes converge to a mixture of phonon modes following the Debye law and soft localized modes following another universal non-Debye scaling law.

cond-mat.soft↗
arXiv2017

Bielliptic curves of genus three and the Torelli problem for certain elliptic surfaces

We study the Hodge structure of elliptic surfaces which are canonically defined from bielliptic curves of genus three. We prove that the period map for the second cohomology has one dimensional fibers, and the period map for the total cohomology is of degree twelve, and moreover, by adding the information of the Hodge structure of the canonical divisor, we prove a generic Torelli theorem for these elliptic surfaces. Finally, we give explicit examples of the pair of non-isomorphic elliptic surfaces which have the same Hodge structure on themselves and the same Hodge structure on their canonical divisors.

math.AG↗
arXiv2016

Note: A replica liquid theory of binary mixtures

It has been known that the binary replica liquid theory (RLT) is inconsistent with its one-component counterpart; In the limit that all atoms are identical, the configurational entropy and thus the glass transition point calculated by the binary RLT differ from those obtained by the one-component RLT. More specifically, an extra composition-dependent term, or the mixing entropy, remains finite in the configurational entropy computed by the binary RLT. In this Short Note, we reformulate the RLT in order to resolve this problem.

cond-mat.soft↗
arXiv2016

The decoupling of the glass transitions in the two-component $p$-spin spherical model

Binary mixtures of large and small particles with disparate size ratio exhibit a rich phenomenology at their glass transition points. In order to gain insights on such systems, we introduce and study a two-component version of the $p$-spin spherical spin glass model. We employ the replica method to calculate the free energy and the phase diagram. We show that when the strengths of the interactions of each component are not widely separated, the model has only one glass phase characterized by the conventional one-step replica symmetry breaking. However when the strengths of the interactions are well separated, the model has three glass phases depending on temperature and component ratio. One is the "single" glass phase in which only the spins of one component are frozen while the spins of the other component remain mobile. This phase is characterized by the one-step replica symmetry breaking. The second is the "double" glass phase obtained by cooling further the single glass phase, in which the spins of the remaining mobile component are also frozen. This phase is characterized by the two-step replica symmetry breaking. The third is also the "double" glass phase, which however is formed by the simultaneous freezing of the spins of both components at the same temperatures and is characterized by the one-step replica symmetry breaking. We discuss the implications of these results for the glass transitions of binary mixtures.

cond-mat.dis-nn↗