arXiv subjects

Grzegorz Szamel

Publications and source records attributed to Grzegorz Szamel.

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

Theory of the $β$-Relaxation Beyond Mode-Coupling Theory: A Microscopic Treatment

We develop a systematic extension of mode-coupling theory (MCT) that incorporates critical dynamical fluctuations. Starting from a microscopic diagrammatic theory, we identify dominant classes of divergent diagrams near the mode-coupling transition and show that the corresponding asymptotic series dominates the mean-field below an upper critical dimension $d_c=8$. To resum these divergences, we construct a mapping to a stochastic dynamical process in which the order parameter evolves under random spatiotemporal fields. This reformulation provides a controlled, fully dynamical derivation of an effective theory for the $β$-relaxation which remarkably coincides with stochastic beta-relaxation theory [T. Rizzo, EPL 106, 56003 (2014)]. All coupling constants of the latter theory are expressed microscopically in terms of the liquid static structure factor and are computed for the paradigmatic hard-sphere system. The analysis demonstrates that fluctuations alone restore ergodicity and replace the putative mean-field transition by a smooth crossover. Our results establish a predictive framework for structural relaxation beyond mean-field.

cond-mat.stat-mech↗

arXiv2026

Microscopic Theory of a Fluctuation-Induced Dynamical Crossover in Supercooled Liquids

Mean-field theories of the glass transition predict a phase transition to a dynamically arrested state, yet no such transition is observed in experiments or simulations of finite-dimensional systems. We resolve this long-standing discrepancy by incorporating critical dynamical fluctuations into a microscopic mode-coupling framework. We show that these fluctuations round off the mean-field singularity and restore ergodicity at all finite densities (or temperatures) without invoking activated dynamics or facilitation. The resulting effective theory describes the order parameter as a stochastic process with self-induced, annealed disorder, determined self-consistently at the mean-field level. In the $β$-relaxation regime it reduces to stochastic beta-relaxation theory, thereby unifying mode-coupling and replica-based approaches beyond mean-field. All parameters of the stochastic $β$-relaxation theory are fixed by the static structure, enabling parameter-free predictions that extend mean-field theory into finite dimensions.

cond-mat.soft↗

arXiv2026

Scale-free correlations in extremely persistent active matter

Scale-free correlations are believed to be generic in out of equilibrium systems but their explicit derivations are rare and often involve approximations. Here we analyze a system of infinitely persistent active Brownian particles in the low density and small-swim-velocity limit. We show that both the density and swim velocity correlations decay algebraically as r^{-(d+1)} (with logarithmic corrections in d=2). In reciprocal space these correlations manifest themselves as cusps at k=0. The analytical predictions are confirmed by numerical simulations. The results were obtained through interaction with Claude (Opus 4.8 and 5, and Fable 5) and verified by the author.

cond-mat.soft↗

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↗

arXiv2026

Machine-learning-derived protocols for information-based work extraction from active particles

We propose and analyze a process that extracts useful work from a single active particle maintained at constant temperature in a harmonic potential by measuring the relative sign of the self-propulsion and the confining force and then adjusting the stiffness of the potential. First, we show analytically that useful work can be extracted by stepwise changes of the stiffness. Then, we use a machine learning procedure to find time-dependent stiffness change protocols. We find that these protocols involve discontinuous initial changes of the stiffness opposite to the expected direction, which resemble initial jumps analytically found by Garcia-Millan et al. [Phys. Rev. Lett. 135, 088301 (2025)] in a different information-based work extraction process. The learned protocols allow to extract significantly larger amounts of useful work. The work extracted exceeds that allowed by the conventional second law for feedback-controlled processes, which can be rationalized by the non-equilibrium character of the system considered.

cond-mat.stat-mech↗

arXiv2025

Sound Attenuation in Glasses

Comprehending sound damping is integral to understanding the anomalous low temperature properties of glasses. Despite decades of studies, the underlying mechanism of sound damping in glasses is still debated. In this perspective we review recent work on sound damping in amorphous solids. We focus on the role of defects, heterogeneous elasticity, and damping in model amorphous solids without defects. We review our definition of damping defects and show that they strongly influence sound damping. However, we also find another contribution to sound damping that cannot be attributed to damping defects. We confirm an earlier result of Kapteijns et al. [G. Kapteijns et al., J. Chem. Phys. 154, 081101 (2021)] that heterogeneous elasticity theory predicts relative changes of sound damping in model two-dimensional glasses if the configuration-to-configuration elastic constants fluctuations are used to quantify the heterogeneity. We extend this finding to similar three-dimensional glasses. We end by discussing the Euclidean Random Matrix model, which exhibits Rayleigh scaling of sound damping, but does not have quasi-localized excitations, and thus probably does not have sound damping defects. We propose that the mechanisms behind sound damping can be more fully understood by approaching the problem from two directions, one where the strong influence of defects is studied and another where sound damping is studied in defect free albeit disordered materials.

cond-mat.dis-nn↗

arXiv2025

Defects, Sound Damping, and the Boson Peak in Amorphous Solids

Two nearly universal and anomalous properties of glasses, the peak in the specific heat and plateau of the thermal conductivity, occur around the same temperature. This coincidence suggests that the two phenomena are related. Both effects can be rationalized by assuming Rayleigh scaling of sound attenuation and this scaling leads one to consider scattering from defects. Identifying defects in glasses, which are inherently disordered, is a long-standing problem that was approached in several ways. We examine candidates for defects in glasses that represent areas of strong sound damping. We show that some defects are associated with quasi-localized excitations, which may be associated with modes in excess of the Debye theory. We also examine generalized Debye relations, which relate sound damping and the speed of sound to excess modes. We derive a generalized Debye relation that does not resort to an approximation used by previous authors. We find that our relation and the relation given by previous authors are almost identical at small frequencies and also reproduce the independently determined density of states. However, the different generalized Debye relations do not agree around the boson peak. While generalized Debye relations accurately predict the boson peak in two-dimensional glasses, they under estimate the boson peak in three-dimensional glasses.

cond-mat.dis-nn↗

arXiv2025

The Origin of Sound Damping in Amorphous Solids: Defects and Beyond

Comprehending sound damping is integral to understanding the anomalous low temperature properties of glasses. After decades of theoretical and experimental studies, Rayleigh scattering scaling of the sound attenuation coefficient with frequency, $Γ\sim ω^{d+1}$, became generally accepted when quantum and finite temperature effects can be neglected. Rayleigh scaling invokes a picture of scattering from defects. However, it is unclear how to define glass defects, or even if defects are necessary for Rayleigh scaling. Here we determine a particle level contribution to sound damping in the Rayleigh scaling regime. We find that there are areas in the glass that contribute more to sound damping than other areas over a range of frequencies, which allows us to define defects. We show that over a range of glass stability, sound damping scales linearly with the fraction of particles in the defects. However, sound is still attenuated in ultra-stable glasses where no defects are identified. We show that sound damping in these glasses is due to nearly uniformly distributed non-affine, microscopic forces that arise after macroscopic deformations of non-centrosymetric structures. To fully understand sound attenuation in glasses one has to consider contributions from defects and a defect-free background, which represents a new paradigm of sound damping in glasses.

cond-mat.dis-nn↗

arXiv2024

Self-consistent theory for sound propagation in a simple model of a disordered, harmonic solid

We present a self-consistent theory for sound propagation in a simple model of a disordered solid. The solid is modeled as a collection of randomly distributed particles connected by harmonic springs with strengths that depend on the interparticle distances, i.e the Euclidean random matrix model of Mezard et al. [Nucl. Phys. 559B, 689 (1999)]. The derivation of the theory combines two exact projection operator steps and a factorization approximation. Within our approach the square of the speed of sound is non-negative. The unjamming transition manifests itself through vanishing of the speed of sound.

cond-mat.dis-nn↗

arXiv2024

Simple fluctuations in simple glass formers

Critical single-particle fluctuations associated with particle displacements are inherent to simple glass-forming liquids in the limit of large dimensions and leave a pseudo-critical trace across all finite dimensions. This characteristic could serve as a crucial test for distinguishing between theories of glass formation. We here examine these critical fluctuations, as captured by the well-established non-Gaussian parameter, within both mode-coupling theory (MCT) and dynamical mean-field theory (DMFT) across dimensions for hard sphere liquids and for the minimally structured Mari--Kurchan model. We establish general scaling laws relevant to any liquid dynamics theory in large dimensions and show that the dimensional scalings predicted by MCT are inconsistent with those from DMFT. Simulation results for hard spheres in moderately high dimensions align with the DMFT scenario, reinforcing the relevance of mean-field theory for capturing glass physics in finite dimensions. We identify potential adjustments to MCT to account for certain mean-field physics. Our findings also highlight that local structure and spatial dimensionality can affect single-particle critical fluctuations in non-trivial ways.

cond-mat.dis-nn↗

arXiv2024

Transverse forces and glassy liquids in infinite dimensions

We explore the dynamics of a simple liquid whose particles, in addition to standard potential-based interactions, are also subjected to transverse forces preserving the Boltzmann distribution. We derive the effective dynamics of one and two tracer particles in the infinite-dimensional limit. We determine the amount of acceleration of the dynamics caused by the transverse forces, in particular in the vicinity of the glass transition. We analyze the emergence and evolution of odd transport phenomena induced by the transverse forces.

cond-mat.soft↗

arXiv2024

Irreversible Boltzmann samplers in dense liquids: weak-coupling approximation and mode-coupling theory

Exerting a nonequilibrium drive on an otherwise equilibrium Langevin process brings the dynamics out of equilibrium but can also speedup the approach to the Boltzmann steady-state. Transverse forces are a minimal framework to achieve dynamical acceleration of the Boltzmann sampling. We consider a simple liquid in three space dimensions subjected to additional transverse pairwise forces, and quantify the extent to which transverse forces accelerate the dynamics. We first explore the dynamics of a tracer in a weak coupling regime describing high temperatures. The resulting acceleration is correlated with a monotonous increase of the magnitude of odd transport coefficients (mobility and diffusivity) with the amplitude of the transverse drive. We then develop a nonequilibrium version of the mode-coupling theory able to capture the effect of transverse forces, and more generally of forces created by additional degrees of freedom. Based on an analysis of transport coefficients, both odd and longitudinal, both for the collective modes and for a tracer particle, we find a systematic acceleration of the dynamics. Quantitatively, the gain, which is guaranteed throughout the ergodic phase, turns out to be a decreasing function of temperature beyond a temperature crossover, in particular as the glass transition is approached. Our theoretical results are in good agreement with available numerical results.

cond-mat.soft↗

arXiv2023

Sampling efficiency of transverse forces in dense liquids

Sampling the Boltzmann distribution using forces that violate detailed balance can be faster than with the equilibrium evolution, but the acceleration depends on the nature of the nonequilibrium drive and the physical situation. Here, we study the efficiency of forces transverse to energy gradients in dense liquids through a combination of techniques: Brownian dynamics simulations, exact infinite-dimensional calculation and a mode-coupling approximation. We find that the sampling speedup varies non-monotonically with temperature, and decreases as the system becomes more glassy. We characterize the interplay between the distance to equilibrium and the efficiency of transverse forces by means of odd transport coefficients.

cond-mat.soft↗

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

Are supercooled liquids Fickian yet non Gaussian?

Comment on `Fickian Non-Gaussian Diffusion in Glass-Forming Liquids', by Rusciano et al., Phys. Rev. Lett. 128, 168001 (2022). In a recent Letter, Rusciano et al. examined the statistics of individual particles displacements in two-dimensional glass-formers and concluded that the corresponding probability distribution is non-Gaussian in a time regime where the mean-squared displacement is Fickian. Here, we clarify that the multiple length scales and time scales reported in this work have either been characterized before, or are not well-defined. This leads us to dispute the conclusions that glass-formers display Fickian non-Gaussian behaviour and that this analogy fruitfully addresses the central questions regarding the nature of dynamic heterogeneity in these systems.

cond-mat.stat-mech↗

arXiv2023

Extremely Persistent Dense Active Fluids

We examine the dependence of the dynamics of three-dimensional active fluids on persistence time $τ_p$ and average self-propulsion force $f$. In the large persistence time limit many properties of these fluids become $τ_p$-independent. These properties include the mean squared velocity, the self-intermediate scattering function, the shear-stress correlation function and the low-shear-rate viscosity. We find that for a given $f$ in the large $τ_p$ limit the mean squared displacement is independent of the persistence time for times shorter than $τ_p$ and the long-time self-diffusion coefficient is proportional to the persistence time. For a large range of self-propulsion forces the large persistence time limits of many properties depend on $f$ as power laws.

cond-mat.soft↗

arXiv2023

On elastic constants of zero-temperature amorphous solids

Elastic constants of zero-temperature amorphous solids are given as the difference between the Born term, which results from a hypothetical affine deformation of an amorphous solid, and a correction term which originates from the fact that the deformation of an amorphous solid due to an applied stress is, at the microscopic level, non-affine. Both terms are non-negative and thus it is a priori not obvious that the resulting elastic constants are non-negative. In particular, theories that approximate the correction term may spuriously predict negative elastic constants and thus an instability of an amorphous solid. Here we derive alternative expressions for elastic constants of zero-temperature amorphous solids that are explicitly non-negative. These expressions provide a useful blueprint for approximate theories for elastic constants and sound damping in zero temperature amorphous solids.

cond-mat.stat-mech↗