Elisabeth Agoritsas

The manuscript offers a critical perspective on the shear-induced solid-to-liquid transition in amorphous materials, synthesizing insights from the talks and informal discussions that unfolded during a week of vibrant exchange at the Lorentz Center.

Protocol-dependent states in structural glasses can encode a disordered, yet retrievable memory. While training such materials is typically done via a global drive, such as external shear, in dense active matter the driving is instead local and spatio-temporally correlated. Here we focus on the impact of such spatial correlation on memory formation. We investigate the mechanical response of a dense amorphous packing of athermal particles, subject to an oscillatory quasistatic driving with a tunable spatial correlation, akin to the instantaneous driving pattern in active matter. We find that the capacity to encode memory can be rendered comparable upon a proper rescaling on the spatial correlation, whereas the efficiency in memory formation increases with motion cooperativity.

Under an oscillating mechanical drive, an amorphous material progressively forgets its initial configuration and might eventually converge to a limit cycle. Beyond quasistatic drivings, how structurally disordered systems lose or record such memory remains theoretically challenging. Here we investigate these issues in a minimal model system -- with quenched disorder and memory encoded in a spatial pattern -- where the oscillating protocol can formally be replaced by finite positive-velocity driving. We consider an elastic line driven at zero temperature in a fixed disordered landscape, with bi-periodic boundary conditions and tunable system size. This setting allows us to control the area swept by the line at each cycle in a given disorder realisation, as would the amplitude of an oscillating drive. We find that the line converges to disorder-dependent limit cycles, jointly for its geometrical \emph{and} velocity profiles. Moreover, the way it forgets its initial condition is strongly coupled to the nature of the velocity dynamics it displays depending on system size. We conclude on the implications of these results for the response of amorphous materials under \emph{non}-quasistatic oscillating protocols.

Oscillatory-driven amorphous materials forget their initial configuration and converge to limit cycles. Here we investigate this memory loss under a nonquasistatic drive in a minimal model system, with quenched disorder and memory encoded in a spatial pattern, where oscillating protocols are formally replaced by a positive-velocity drive. We consider an elastic line driven athermally in a quenched disorder with biperiodic boundary conditions and tunable system size, thus controlling the area swept by the line per cycle as would the oscillation amplitude. The convergence to disorder-dependent limit cycle is strongly coupled to the nature of its velocity dynamics depending on system size. Based on the corresponding phase diagram, we propose a generic scenario for memory formation in disordered systems under finite driving rate.

Stochastic phenomena are often described by Langevin equations, which serve as a mesoscopic model for microscopic dynamics. It has been known since the work of Parisi and Sourlas that reversible (or equilibrium) dynamics present supersymmetries (SUSYs). These are revealed when the path-integral action is written as a function not only of the physical fields, but also of Grassmann fields representing a Jacobian arising from the noise distribution. SUSYs leave the action invariant upon a transformation of the fields that mixes the physical and the Grassmann ones. We show that contrary to common belief, it is possible to extend the known reversible construction to the case of arbitrary irreversible dynamics, for overdamped Langevin equations with additive white noise—provided their steady state is known. The construction is based on the fact that the Grassmann representation of the functional determinant is not unique, and can be chosen so as to present a generalization of the Parisi-Sourlas SUSY. We show how such SUSYs are related to time-reversal symmetries and allow one to derive modified fluctuation-dissipation relations valid in nonequilibrium. We give as a concrete example the results for the Kardar-Parisi-Zhang equation.

Self-affine rough interfaces are ubiquitous in experimental systems, and display characteristic scaling properties as a signature of the nature of disorder in their supporting medium, i.e. of the statistical features of its heterogeneities. Different methods have been used to extract roughness information from such self-affine structures, and in particular their scaling exponents and associated prefactors. Notably, for an experimental characterization of roughness features, it is of paramount importance to properly assess sample-to-sample fluctuations of roughness parameters. Here, by performing scaling analysis based on displacement correlation functions in real and reciprocal space, we compute statistical properties of the roughness parameters. As an ideal, artifact-free reference case study and particularly targeting finite-size systems, we consider three cases of numerically simulated one-dimensional interfaces: (i) elastic lines under thermal fluctuations and free of disorder, (ii) directed polymers in equilibrium with a disordered energy landscape, and (iii) elastic lines in the critical depinning state when the external applied driving force equals the depinning force set by disorder. Our results show that sample-to-sample fluctuations are rather large when measuring the roughness exponent. These fluctuations are also relevant for roughness amplitudes. Therefore a minimum of independent interface realizations (at least a few tens in our numerical simulations) should be used to guarantee sufficient statistical averaging, an issue often overlooked in experimental reports.

Significance: There is not yet a robust theoretical framework predicting the dynamics of dense active matter, where energy is injected at the scale of constituent particles. Previous work has shown that some features of dense active matter are similar to those in dense disordered materials that are sheared globally from the boundaries. Using analytic and computational tools, we show that there is a direct correspondence between active matter and applied shear strain, which can in turn be used to help predict the behavior of dense active matter.

In infinite dimensions, many-body systems of pairwise interacting particles provide exact analytical benchmarks for the features of amorphous materials, such as the stress–strain curve of glasses under quasistatic shear. Here, instead of global shear, we consider an alternative driving protocol, as recently introduced by Morse et al 2020 (arXiv: 2009.07706 ), which consists of randomly assigning a constant local displacement on each particle, with a finite spatial correlation length. We show that, in the infinite-dimensional limit, the mean-field dynamics under such a random forcing are strictly equivalent to those under global shear, upon a simple rescaling of the accumulated strain. Moreover, the scaling factor is essentially given by the variance of the relative local displacements of interacting pairs of particles, which encodes the presence of a finite spatial correlation. In this framework, global shear is simply a special case of a much broader family of local forcing, which can be explored by tuning its spatial correlations. We discuss the specific implications for the quasistatic driving of glasses—initially prepared at a replica-symmetric equilibrium—and how the corresponding ‘stress–strain’-like curves and elastic moduli can be rescaled onto their quasistatic-shear counterparts. These results hint at a unifying framework for establishing rigorous analogies, at the mean-field level, between different driven disordered systems.