arXiv subjects

Walter Schirmacher

Publications and source records attributed to Walter Schirmacher.

At least 19 recordsLinked to original sources

arXiv2026

On non-phononic modes and glassy dynamics

The relationship between vibrational modes and glassy dynamics has been an important and controversial topic of study for many decades. We introduce a family of glass-forming model potentials that have identical molecular and swap dynamics but different low-frequency vibrational modes. In sufficiently small systems low frequency modes do not hybridize with phonons, and this enables us to study their statistical properties independently. We investigate i) the role of the optimization algorithm used to find a minimum; ii) that of the finite-size effects; iii) that of the truncation of the interaction potential; and, iv) that of the parent temperature. We find that models with identical supercooled liquid structure and dynamics can have dramatically different non-phononic vibrational modes at low frequency, based on how the potential is truncated. These findings challenge ideas relating the low-frequency non-phononic vibrational modes with the slow supercooled liquid relaxation.

cond-mat.dis-nn↗

arXiv2026

Classical versus quantum Anderson localization in disordered systems

We investigate Anderson localization in three-dimensional disordered systems by comparing scalar classical waves with mass and force-constant disorder to electronic tight-binding models with diagonal and off-diagonal disorder. We show that the commonly employed mapping between classical-wave localization and the electronic Anderson model with diagonal disorder is not mathematically justified. Instead, the correct modulus-type formulation reveals that classical-wave systems constitute a distinct constrained disorder class, in which the acoustic sum rule correlates diagonal and off-diagonal matrix elements and prevents any direct correspondence with the standard electronic disorder models. Within a unified eigenvalue framework, we determine localization phase diagrams for all four disorder classes using complementary spectral, eigenvector, and level-statistics diagnostics. We find that classical-wave systems share a key qualitative feature with electronic off-diagonal disorder: localized states occur only near a band edge, while extended states persist in the central part of the spectrum even at strong disorder. At the same time, the acoustic sum rule produces localization topologies that differ fundamentally from both diagonal- and off-diagonal-disorder electronic systems. In particular, for mass disorder we obtain a phase diagram that differs qualitatively from previous results based on the conventional potential-type approach and reveals an extended localized regime near the upper band edge. Our results establish a unified perspective on localization in quantum and classical wave systems and provide new insight into the conditions under which Anderson localization may occur in three-dimensional photonic and acoustic media.

cond-mat.dis-nn↗

arXiv2026

Further testing the validity of generalized heterogeneous-elasticity theory for low-frequency excitations in structural glasses

We summarize the salient features of our theory of non-phononic vibrational excitations in glasses [W. Schirmacher et al., Nature Comm. 15, 3107 (2024)]. Next, we provide further evidence of the non-universality of the $ω^4$ scaling of the non-phononic vibrational density of states (DoS), and the existence of an important class of non-phononic excitations in glasses, which we call defect states. These modes are induced by frozen-in stresses and can be classified as quasi-localized. Our results suggest that the commonly observed low-frequency $ω^4$ scaling of the non-phononic vibrational density of states is highly dependent on technical aspects of the molecular dynamics simulations employed to compute the DoS.

cond-mat.dis-nn↗

arXiv2025

Internal Stresses as Origin of the Anomalous Low-Temperature Specific Heat in Glasses

We apply a recently developed theory of the nonphononic vibrational density of states (DOS) in glasses to investigate the impact of local frozen-in stresses on the low-temperature specific heat. Using a completely harmonic description we show that the hybridization of the local nonphononic vibrational excitations with the waves leads to a low-frequency DOS, in excess to the Debye one, which varies linearly with frequency up to a certain crossover frequency, and then becomes constant. The actual value of the crossover depends of the ratio between the local stresses and the shear modulus. This excess DOS leads to a low-temperature specific heat with an apparent temperature exponent, which is between one and two, as observed experimentally. We discuss, how these findings may be utilized for the characterisation of glassy materials. We further compare our findings, which only rely on harmonic interactions, with the predictions of other theories, which invoke anharmonic interactions and tunneling for explaining the low-temperature behavior of the specific heat.

cond-mat.dis-nn↗

arXiv2023

The nature of non-phononic excitations in disordered systems

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 $g(ω)\sim ω^2$. 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 $g(ω)\simω^s$ 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.

cond-mat.dis-nn↗

arXiv2023

Diffusion of light in turbid media and Kubelka-Munk theory

We show that the Kubelka-Munk equations for the description of the intensity transfer of light in turbid media are equivalent to a one-dimensional diffusion equation, which is obtained by averaging the three-dimensional diffusion equation over the lateral directions. This enables us to identify uniquely the Kubelka-Munk parameters and derive expressions for diffuse reflection and transmission coefficients including the effect of internal reflections. Without internal reflections we recover the Kubelka-Munk formulas for these coefficients. We show that the Kubelka-Munk equations are the proper radiative-transfer equations for the one-dimensional diffusion problem and comment on previous attempts to derive the Kubelka-Munk equations.

cond-mat.dis-nn↗

arXiv2023

The electric and magnetic disordered Maxwell equations as eigenvalue problem

We consider Maxwell's equations in a 3-dimensional material, in which both, the electric permittivity, as well as the magnetic permeability, fluctuate in space. Differently from all previous treatments of the disordered electromagnetic problem, we transform Maxwell's equations and the electric and magnetic fields in such a way that the linear operator in the resulting secular equations is manifestly Hermitian, in order to deal with a proper eigenvalue problem. As an application of our general formalism, we use an appropriate version of the Coherent-Potential approximation (CPA) to calculate the photon density of states and scattering-mean-free path. Applying standard localization theory, we find that in the presence of both electric and magnetic disorder the spectral range of Anderson localization appears to be much larger than in the case of electric (or magnetic) disorder only. Our result could explain the absence of experimental evidence of 3D Anderson localization of light (all the existing experiments has been performed with electric disorder only) and pave the way towards a successful search of this, up to now, elusive phenomenon.

physics.optics↗

arXiv2023

Instantaneous normal modes in liquids: a heterogeneous-elastic-medium approach

The concept of vibrational density of states in glasses has been mirrored in liquids by the instantaneous-normal-mode spectrum. While in glasses instantaneous configurations correspond to minima of the potential-energy hypersurface and all eigenvalues of the associated Hessian matrix are therefore positive, in liquids this is no longer true, and modes corresponding to both positive and negative eigenvalues exist. The instantaneous-normal-mode spectrum has been numerically investigated in the past, and it has been demonstrated to bring important information on the liquid dynamics. A systematic deeper theoretical understanding is now needed. Heterogeneous-elasticity theory has proven to be successful in explaining many details of the low-frequency excitations in glasses, ranging from the thoroughly studied boson peak, down to the more elusive non-phononic excitations observed in numerical simulations at the lowest frequencies. Here we present an extension of heterogeneous-elasticity theory to the liquid state, and show that the outcome of the theory agrees well to the results of extensive molecular-dynamics simulations of a model liquid at different temperatures. We show that the spectral shape strongly depends on temperature, being symmetric at high temperatures and becoming rather asymmetric at low temperatures, close to the dynamical critical temperature. Most importantly, we demonstrate that the theory naturally reproduces a surprising phenomenon, a zero-energy spectral singularity with a cusp-like character developing in the vibrational spectra upon cooling. This feature, known from a few previous numerical studies, has been generally overlooked in the past due to a misleading representation of the data. We provide a thorough analysis of this issue, based on both very accurate predictions of our theory, and computational studies of model liquid systems with extended size.

cond-mat.dis-nn↗

arXiv2022

Terahertz Dynamics in the Glycerol-Water System

The model glass-former glycerol and its aqueous mixtures were investigated with terahertz-time domain spectroscopy (THz-TDS) in the frequency range of 0.3--3.0\,THz at temperatures from 80--305\,K. It was shown that the infrared absorption coefficient measured with THz-TDS can be theoretically related to the reduced Raman intensity ($\propto α/ω^2$) and the reduced density of states ($\propto α/ω^3$) and the agreement with experimental results confirms this. The data were further used to investigate the behaviour of model glasses in the harmonic (below the glass transition temperature $T_{\text{g}}$), anharmonic (above $T_{\text{g}}$), and liquid regime. The onset temperature of the molecular mobility as measured by the infrared active dipoles, $T_{\text{g}}$, was found to correlate with the onset of anharmonic effects, leading to an apparent shift of the boson peak and obscuring it at elevated temperatures. The influence of clustered and unclustered water on the dynamics, the boson peak, and the vibrational dynamics was also investigated. A change in structural dynamics was observed at a water concentration of approximately 5\,wt.\%, corresponding to a transition from isolated water molecules distributed homogeneously throughout the sample to the presence of small water clusters and an increased number of water-water hydrogen bonds which lower the barriers on the potential energy surface.

cond-mat.dis-nn↗

arXiv2022

Comment on "Explaining the specific heat of liquids based on instantaneous normal modes"

In a recent paper (Phys. Rev. E {\bf 104}, 014103 (2021) ) M. Baggioli and A. Zaccone formulate a theoretical description of the specific heat of liquids by using Debye's expression for the specific heat of solids and inserting a density of states (DOS) which they claim to represent the instantaneous-normal-mode (INM) spectrum of a liquid. However, the quantum-mechanical procedure of Debye cannot be used for a classical liquid and the authors' formula for the INM spectrum does not represent the known INM spectra of simple liquids. Furthermore, the derivation of this formula from their model equation of motion is mathematically in error. Finally experimental test of the teory for the specific heat of {\it liquids} is performed by fitting the data of {\it supercritical fluids}. \new{To our opinion,} these and a lot of other inconsistencies render this work not suitable for studying the specific heat of liquids.

cond-mat.dis-nn↗

arXiv2022

Comment on "Deformations, relaxation and broken symmetries in liquids, solids and glasses: a unified topological field theory"

We discuss a field-theoretical approach to liquids, solids and glasses, published recently [Phys.Rev.E {\bf105}, 034108 (2022)], which aims to describe these materials in a common quantum formalism. We argue that such quantum formalism is not applicable to classical liquids, and the results presented, which rely heavily on the concept of phase relaxation borrowed from quantum fluids, contradict the known hydrodynamic theory of classical liquids. In particular, the authors miss the important particle-number conservation law and the density fluctuations as hydrodynamic slow variable. Instead, the authors invoke Goldstone bosons as elementary hydrodynamic excitations. We point out that in a classical liquid there are no broken continuous symmetries and consequently no Goldstone bosons. The authors claim that the Goldstone bosons would be responsible for the existence of sound in liquids, instead of resulting from combined particle-number and momentum conservation, a fact well documented in fluid-mechanics textbooks.

cond-mat.dis-nn↗

arXiv2021

Disorder-induced vibrational anomalies from crystalline to amorphous solids

The origin of boson peak -- an excess of density of states over Debye's model in glassy solids -- is still under intense debate, among which some theories and experiments suggest that boson peak is related to van-Hove singularity. Here we show that boson peak and van-Hove singularity are well separated identities, by measuring the vibrational density of states of a two-dimensional granular system, where packings are tuned gradually from a crystalline, to polycrystals, and to an amorphous material. We observe a coexistence of well separated boson peak and van-Hove singularities in polycrystals, in which the van-Hove singularities gradually shift to higher frequency values while broadening their shapes and eventually disappear completely when the structural disorder $η$ becomes sufficiently high. By analyzing firstly the strongly disordered system ($η=1$) and the disordered granular crystals ($η=0$), and then systems of intermediate disorder with $η$ in between, we find that boson peak is associated with spatially uncorrelated random flucutations of shear modulus $δG/\langle G \rangle$ whereas the smearing of van-Hove singularities is associated with spatially correlated fluctuations of shear modulus $δG/\langle G \rangle$.

cond-mat.soft↗

arXiv2020

Heterogeneous Elasticity: The tale of the boson peak

The vibrational anomalies of glasses, in particular the boson peak, are addressed from the standpoint of heterogeneous elasticity, namely the spatial fluctuations of elastic constants caused by the structural disorder of the amorphous materials. In the first part of this review article a mathematical analogy between diffusive motion in a disordered environment and a scalar simplification of vibrational motion under the same condition is emploited. We demonstrate that the disorder-induced long-time tails of diffusion correspond to the Rayleigh scattering law in the vibrational system and that the cross-over from normal to anomalous diffusion corresponds to the boson peak. The anomalous motion arises as soon as the disorder-induced self-energy exceeds the frequency-independent diffusivity/elasticity. For this model a variational scheme is emploited for deriving two mean-field theories of disorder, the self-consistent Born approximation (SCBA) and coherent-potential approximation (CPA). The former applies if the fluctuations are weak and Gaussian, the latter applies for stronger and non-Gaussian fluctuations. In the second part the vectorial theory of heterogenous elasticity is presented and solved in SCBA and CPA, introduced for the scalar model. Both approaches predict and explain the boson-peak and the associated anomalies, namely a dip in the acoustic phase velocity and a characteristic strong increase of the acoustic attenuation below the boson peak. Explicit expressions for the density of states and the inelastic Raman, neutron and X-ray scattering laws are given. Recent conflicting ways of explaining the boson-peak anomalies are discussed.

cond-mat.dis-nn↗

arXiv2020

Level statistics and Anderson delocalization in two-dimensional granular materials

Contrary to the theoretical predictions that all waves in two-dimensional disordered materials are localized, Anderson localization is observed only for sufficiently high frequencies in an isotropically jammed two-dimensional disordered granular packing of photoelastic disks. More specifically, we have performed an experiment in analyzing the level statistics of normal mode vibrations. We observe delocalized modes in the low-frequency boson-peak regime and localized modes in the high frequency regime with the crossover frequency just below the Debye frequency. We find that the level-distance distribution obeys Gaussian-Orthogonal-Ensemble (GOE) statistics, i.e. Wigner-Dyson distribution, in the boson-peak regime, whereas those in the high-frequency regime Poisson statistics is observed. The scenario is found to coincide with that of harmonic vibrational excitations in three-dimensional disordered solids.

cond-mat.soft↗

arXiv2018

Disentangling boson peaks and Van Hove singularities in a model glass

Using the example of a two-dimensional macroscopic model glass in which the interparticle forces can be precisely measured, we obtain strong hints for resolving a controversy concerning the origin of the anomalous enhancement of the vibrational spectrum in glasses (boson peak). Whereas many authors attribute this anomaly to the structural disorder, some other authors claim that the short-range order, leading to washed-out Van Hove singularities, would cause the boson-peak anomaly. As in our model system, the disorder-induced and shortrange--order-induced features can be completely separated, we are able to discuss the controversy about the boson peak in real glasses in a new light. Our findings suggest that the interpretation of the boson peak in terms of short-range order only, might result from a coincidence of the two phenomena in the materials studied. In general, as we show, the two phenomena both exist, but are two completely separate entities.

cond-mat.soft↗

arXiv2017

What is the right theory for Anderson localization of light?

Anderson localization of light is traditionally described in analogy to electrons in a random potential. Within this description the disorder strength -- and hence the localization characteristics -- depends strongly on the wavelength of the incident light. In an alternative description in analogy to sound waves in a material with spatially fluctuating elastic moduli this is not the case. Here, we report on an experimentum crucis in order to investigate the validity of the two conflicting theories using transverse-localized optical devices. We do not find any dependence of the observed localization radii on the light wavelength. We conclude that the modulus-type description is the correct one and not the potential-type one. We corroborate this by showing that in the derivation of the traditional, potential-type theory a term in the wave equation has been tacititly neglected. In our new modulus-type theory the wave equation is exact. We check the consistency of the new theory with our data using a field-theoretical approach (nonlinear sigma model).

physics.optics↗

arXiv2015

Anomalous magneto-transport in disordered structures: classical edge-state percolation

By event-driven molecular dynamics simulations we investigate magneto-transport in a two-dimensional model with randomly distributed scatterers close to the field-induced localization transition. This transition is generated by percolating skipping orbits along the edges of obstacle clusters. The dynamic exponents differ significantly from those of the conventional transport problem on percolating systems, thus establishing a new dynamic universality class. This difference is tentatively attributed to a weak-link scenario, which emerges naturally due to barely overlapping edge trajectories. We make predictions for the frequency-dependent conductivity and discuss implications for active colloidal circle swimmers in a heterogeneous environment.

cond-mat.mes-hall↗

arXiv2015

Theory of heterogeneous viscoelasticity

We review a new theory of viscoelasticity of a glass-forming viscous liquid near and below the glass transition. In our model we assume that each point in the material has a specific viscosity, which varies randomly in space according to a fluctuating activation free energy. We include a Maxwellian elastic term and assume that the corresponding shear modulus fluctuates as well with the same distribution as that of the activation barriers. The model is solved in coherent-potential approximation (CPA), for which a derivation is given. The theory predicts an Arrhenius-type temperature dependence of the viscosity in the vanishing-frequency limit, independent of the distribution of the activation barriers. The theory implies that this activation energy is generally different from that of a diffusing particle with the same barrier-height distribution. If the distribution of activation barriers is assumed to have Gaussian form, the finite-frequency version of the theory describes well the typical low-temperature alpha relaxation peak of glasses. Beta relaxation can be included by adding another Gaussian with center at much lower energies than that responsible for the alpha relaxation. At high frequencies our theory reduces to the description of an elastic medium with spatially fluctuating elastic moduli (heterogeneous elasticity theory), which explains the occurrence of the boson-peak-related vibrational anomalies of glasses.

cond-mat.dis-nn↗