Glassy systems are disordered systems characterized by extremely slow dynamics. Examples are supercooled liquids, whose dynamics slow down under cooling. The specific pattern of slowing-down depends on the material considered. This dependence is poorly understood, in particular, it remains generally unclear which aspects of the microscopic structures control the dynamics and other macroscopic properties. Attacking this question is one of the two main aspects of this dissertation. We have introduced a new class of models of supercooled liquids, which captures the central aspects of the correspondence between structure and elasticity on the one hand, the correlation of structure and thermodynamic and dynamic properties on the other. Our results shed new light on the temperature-dependence of the topology of covalent networks, in particular, on the rigidity transition that occurs when the valence is increased.
Other questions appear in glassy systems at zero temperature. In that situation, a glassy system can flow if an external driving force is imposed above some threshold. The first example we will consider is the erosion of a riverbed. Experiments support the existence of a threshold forcing, below which no erosion flux is observed. In this dissertation, we present a novel microscopic model to describe the erosion near threshold. This model makes new quantitative predictions for the spatial reparation of the flux. To study further the self-organization of driven glassy systems, we investigate the athermal dynamics of mean-field spin glasses. The spin glass self-organizes into the configurations that are stable, but barely so. Such marginal stability appears with the presence of a pseudogap in soft excitations. We show that the emergence of a pseudogap is deeply related to very strong anti-correlations emerging among soft excitations.
In this report, I will review some of the most used models in theoretical ecology along with appealing reformulations and recent results in terms of diversity, stability, and functioning of large well-mixed ecological communities.
Dynamics of structural models with a long-range interaction: glassy versus non-glassy behavior
利用Langevin动力学及其生成泛函（GF）公式，系统地研究了相互作用的长程性质对玻璃形成趋势的影响。在这样做时，考虑两种类型的模型：（i）具有纯排斥型相互作用的非无序模型和（ii）具有随机分布的相互作用强度的模型（淬火无序模型）。长程相互作用势与粒子数$N$成比例，使得GF的鞍点处理以及系统的1/N - expansion around it. We表明，非无序模型没有玻璃化转变，这与模耦合理论（MCT）预测的平均场极限一致。另一方面，具有长程相互作用的模型，其上具有淬火无序，导致MC -方程，其对于$p$ -自旋玻璃模型和随机介质中的聚合物歧管是通用的。
We describe a series of surface levelling experiments in glassy polystyrene (PS) of varying molecular weight. The evolution through a mobile surface layer is described by the glassy thin film equation that was introduced and used in a previous work. Excellent agreement with the data is achieved, with surface mobility as the single free parameter. Different molecular-weight dependencies in mobility are then observed above and below the glass transition. The results are discussed in terms of surface-chain anchoring in the bulk matrix, and the length scale for surface mobility.
Particle swaps can drastically accelerate dynamics in glass. The mechanism is expected to be vital for a fundamental understanding of glassy dynamics. To extract defining features, we propose a partial swappability with a fraction {ϕ_s} of swap-initiating particles, which can only swap locally with each other or with regular particles. We focus on the swap-dominating regime. At all temperatures studied, particle diffusion coefficients scale with {ϕ_s} in unexpected power laws with temperature-dependent exponents, consistent with the kinetic picture of glass transition. At small {ϕ_s}, swap-ini…
Diverse processes -- e.g., environmental pollution, groundwater remediation, oil recovery, filtration, and drug delivery -- involve the transport of colloidal particles in porous media. Using confocal microscopy, we directly visualize this process in situ and thereby identify the fundamental mechanisms by which particles are distributed throughout a medium. At high injection pressures, hydrodynamic stresses cause particles to be continually deposited on and eroded from the solid matrix -- notably, forcing them to be distributed throughout the entire medium. By contrast, at low injection pressu…
We numerically study out-of-equilibrium dynamics in a family of Heisenberg models with $1/r^6$ power-law interactions and positional disorder. Using the semi-classical discrete truncated Wigner approximation (dTWA) method, we investigate the time evolution of the magnetization and ensemble-averaged single-spin purity for a strongly disordered system after initializing the system in an out-of-equilibrium state. We find that both quantities display robust glassy behavior for almost any value of the anisotropy parameter of the Heisenberg Hamiltonian. Furthermore, a systematic analysis allows us t…
Columbia University（哥伦比亚大学）；Université Paris Saclay（巴黎萨克雷大学）；CEA（法国原子能和替代能源委员会）；CNRS（法国国家科学研究中心）；EPFL（洛桑联邦理工学院）；New York University（纽约大学）；King’s College London（伦敦国王学院）；Facebook Inc.（脸书公司）；École Normale Supérieure（巴黎高等师范学院）；PSL Research University（巴黎文理研究大学）；Sorbonne Universités（索邦大学）
We analyze numerically the training dynamics of deep neural networks (DNN) by using methods developed in statistical physics of glassy systems. The two main issues we address are (1) the complexity of the loss landscape and of the dynamics within it, and (2) to what extent DNNs share similarities with glassy systems. Our findings, obtained for different architectures and datasets, suggest that during the training process the dynamics slows down because of an increasingly large number of flat directions. At large times, when the loss is approaching zero, the system diffuses at the bottom of the…
We study the out-of-equilibrium dynamics in the quantum Ising model with power-law interactions and positional disorder. For arbitrary dimension $d$ and interaction range $α\geq d$ we analytically find a stretched exponential decay of the global magnetization and ensemble-averaged single-spin purity with a stretch-power $β= d/α$ in the thermodynamic limit. Numerically, we confirm that glassy behavior persists for finite system sizes and sufficiently strong disorder. We identify dephasing between disordered coherent pairs as the main mechanism leading to a relaxation of global magnetization, wh…
We have performed a thorough examination of the reorientational relaxation dynamics and the ionic charge transport of three typical deep eutectic solvents, ethaline, glyceline and reline by broadband dielectric spectroscopy. Our experiments cover a broad temperature range from the low-viscosity liquid down to the deeply supercooled state, allowing to investigate the significant influence of glassy freezing on the ionic charge transport in these systems. In addition, we provide evidence for a close coupling of the ionic conductivity in these materials to reorientational dipolar motions which sh…
Understanding the dynamics of strongly interacting disordered quantum systems is one of the most challenging problems in modern science, due to features such as the breakdown of thermalization and the emergence of glassy phases of matter. We report on the observation of anomalous relaxation dynamics in an isolated XXZ quantum spin system realized by an ultracold gas of atoms initially prepared in a superposition of two-different Rydberg states. The total magnetization is found to exhibit sub-exponential relaxation analogous to classical glassy dynamics, but in the quantum case this relaxation …
Amorphous materials exhibit structural heterogeneities that relax only on long timescales. Using machine learning techniques, we construct a Markov state model (MSM) for model glass formers that coarse-grains the dynamics into a low-dimensional space, in which transitions occur with rates corresponding to the slowest modes of the system. The transition timescale between states is more than an order of magnitude larger than the conventional alpha-relaxation time, and reveals a fragile to strong crossover at the glass transition. The learned map of states assigned to the particles exhibits corre…
