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Publication# Thermal origin of quasilocalized excitations in glasses

Elisabeth Agoritsas, Thomas Willem Jan de Geus, Wencheng Ji, Marko Popovic, Matthieu Wyart

*AMER PHYSICAL SOC, *2020

Article

Article

Résumé

Key aspects of glasses are controlled by the presence of excitations in which a group of particles can rearrange. Surprisingly, recent observations indicate that their density is dramatically reduced and their size decreases as the temperature of the supercooled liquid is lowered. Some theories predict these excitations to cause a gap in the spectrum of quasilocalized modes of the Hessian that grows upon cooling, while others predict a pseudogap D-L (omega) similar to omega(alpha). To unify these views and observations, we generate glassy configurations of controlled gap magnitude w e at temperature T = 0, using so-called breathing particles, and study how such gapped states respond to thermal fluctuations. We find that (i) the gap always fills up at finite T with D-L (omega) approximate to A(4)(T) omega(4) and A(4) similar to exp(-E-a/T) at low T, (ii) E-a rapidly grows with omega(c), in reasonable agreement with a simple scaling prediction E-a similar to omega(4)(c) and (iii) at larger omega(c) excitations involve fewer particles, as we rationalize, and eventually become stringlike. We propose an interpretation of mean-field theories of the glass transition, in which the modes beyond the gap act as an excitation reservoir, from which a pseudogap distribution is populated with its magnitude rapidly decreasing at lower T. We discuss how this picture unifies the rarefaction as well as the decreasing size of excitations upon cooling, together with a stringlike relaxation occurring near the glass transition.

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Optical tweezers are commonly used and powerful tools to perform force measurements on the piconewton scale and to detect nanometer-scaled displacements. However, the precision of these instruments relies to a great extent on the accuracy of the calibration method. A well-known calibration procedure is to record the stochastic motion of the trapped particle and compare its statistical behavior with the theory of the Brownian motion in a harmonic potential. Here we present an interactive calibration software which allows for the simultaneous fitting of three different statistical observables (power spectral density, mean square displacement and velocity autocorrelation function) calculated from the trajectory of the probe to enhance fitting accuracy. The fitted theory involves the hydrodynamic interactions experimentally observable at high sampling rates. Furthermore, a qualitative extension is included in our model to handle the thermal fluctuations in the orientation of optically trapped asymmetric objects. The presented calibration methodology requires no prior knowledge of the bead size and can be applied to non-spherical probes as well. The software was validated on synthetic and experimental data. Program summary Program title: PFMCal Catalogue identifier: AEXH_v1_0 Program summary URL: http://cpc.cs.qub.ac.ukisummaries/AEXH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 206,399 No. of bytes in distributed program, including test data, etc.: 10,319,465 Distribution format: tar.gz Programming language: MatLab 2011a (Math Works Inc.). Computer: General computer running MatLab (MathWorks Inc.), using Statistics Toolbox. Operating system: Any which supports Matlab using Statistics Toolbox. RAM: 10 MB Classification: 3, 4.9, 18, 23. Nature of problem: Calibration of optical tweezers by measuring the Brownian motion of the trapped object. The voltage-to-displacement ratio of the detection system (the inverse of the sensitivity), the stiffness of the trap and the size of the bead are obtained via the simultaneous fitting of the power spectral density (PSD), mean square displacement (MSD) and velocity autocorrelation (VAF) functions calculated from the trajectory. The calibration can be performed for non-spherical probes as well. Solution method: Initialization points for all parameters are inferred from characteristic features of the statistical observables (PSD, MSD and VAF) based on the method developed by Grimm et al. in [1]. Theoretical functions for the PSD, the MSD and the VAF are calculated from the model of Brownian motion confined by a harmonic potential taking hydrodynamic interactions into consideration [2-4]. This calibration methodology has been successfully used in actual experiments with micro-spheres [5, 6]. Calculated functions are fitted to the measurement data via the Levenberg-Marquardt least square fitting routine available in the MatLab Optimalization Toolbox, using the nlinfit function. If the error to the measured data has been estimated, the corresponding data values can be weighted by the inverse of the standard error squared in order to eliminate bias introduced by heteroscedasticity. In order to increase robustness and avoid convergence to local minima, minimum search from multiple initial values in the vicinity of the first guess is possible. Additional comments: Input of the program is the experimental PSDexp, MSDexp, and VAF(exp) data points calculated from the measured x, y and z projections of the trajectory of the particle. The data may best be blocked and may optionally contain an error for each data point for better results. The data should be formatted into three columns: 1. independent variables (time or frequency array), 2. function values, 3. optionally, error values (e.g. standard error calculated from the binning) to improve fitting efficiency. In case error values were not estimated, the third column should be filled with zeros. The first row is reserved for a header, data is read from the second row. Data size should not be larger than a few hundreds of rows, otherwise, using larger blocks for binning is advised. In order to observe the short time behavior of the Brownian motion, influenced by hydrodynamic effects, the sampling rate should be typically higher than 100 kHz. Total sampling time is typically tens of seconds, to achieve a good resolution in the frequency range. The optical axis of the laser, the microscope and the detector system should be co-aligned to exclude artificial crosstalk between the x, y and z channels of the position detector. Running time: Seconds (C) 2015 Elsevier B.V. All rights reserved.

Amorphous solids are structurally disordered. They are very common and include glasses, colloids, and granular materials, but are far less understood than crystalline solids. Key aspects of these materials are controlled by the presence of excitations in which a group of particles rearranges. This motion can be triggered by (a) quantum fluctuations associated with two-level systems (TLS), which dominate the low temperature properties of conventional glasses and have practical importance on superconducting qubits; by (b) thermal fluctuations associated with activations, which are related to the famous and challenging

`glass transition'' problem; or by (c) exerting an external stress or strain associated with shear transformations, which control the plasticity. Hence, it is important to understand how temperature and system preparation determines the density and geometry of these excitations. The possible unification of these excitations into a common description is also a fundamental problem. These local excitations are thought to have a close relationship with `

Quasi-localised modes (QLMs)'' which are present in the low-frequency vibrational spectrum in amorphous solids. Understanding the properties of QLMs and clarifying the relation between QLMs and these local excitations are important to the study of the latter.
In this thesis: (1) we provide a theory for the QLMs, D_L(omega) ~ omega^alpha, that establishes the link between QLMs and shear transformations for systems under quasi-static loading. It predicts two regimes depending on the density of shear transformations P(x)~ x^theta (with x the additional stress needed to trigger a shear transformation). If theta>1/4, alpha=4 and a finite fraction of quasi-localised modes form shear transformations, whose amplitudes vanish at low frequencies. If thetaDense non-Brownian suspension flows of hard particles display mystifying properties: As the jamming threshold is approached, the viscosity diverges, as well as a length scale that can be identified from velocity correlations. To unravel the microscopic mechanism governing dissipation and its connection to the observed correlation length, we develop an analogy between suspension flows and the rigidity transition occurring when floppy networks are pulled, a transition believed to be associated with the stress stiffening of certain gels. After deriving the critical properties near the rigidity transition, we show numerically that suspension flows lie close to it. We find that this proximity causes a decoupling between viscosity and the correlation length of velocities ξ, which scales as the length lc characterizing the response to a local perturbation, previously predicted to follow lc∼1/zc-z∼p0.18, where p is the dimensionless particle pressure, z is the coordination of the contact network made by the particles, and zc is twice the spatial dimension. We confirm these predictions numerically and predict the existence of a larger length scale lr∼p with mild effects on velocity correlation and of a vanishing strain scale δγ∼1/p that characterizes decorrelation in flow. © 2014 American Physical Society.

2014