Using the non-interacting Anderson tight-binding model on the Bethe lattice as a toy model for the many-body quantum dynamics, we propose a novel and transparent theoretical explanation of the anomalously slow dynamics that emerges in the bad metal phase preceding the Many-Body Localization transition. By mapping the time-decorrelation of many-body wave-functions onto Directed Polymers in Random Media, we show the existence of a glass transition within the extended regime separating a metallic-like phase at small disorder, where delocalization occurs on an exponential number of paths, from a bad metal-like phase at intermediate disorder, where resonances are formed on rare, specific, disorder dependent site orbitals on very distant generations. The physical interpretation of subdiffusion and non-exponential relaxation emerging from this picture is complementary to the Griffiths one, although both scenarios rely on the presence of heavy-tailed distribution of the escape times. We relate the dynamical evolution in the glassy phase to the depinning transition of Directed Polymers, which results in macroscopic and abrupt jumps of the preferred delocalizing paths when a parameter like the energy is varied, and produce a singular behavior of the overlap correlation function between eigenstates at different energies. By comparing the quantum dynamics on loop-less Cayley trees and Random Regular Graphs we discuss the effect of loops, showing that in the latter slow dynamics and apparent power-laws extend on a very large time-window but are eventually cut-off on a time-scale that diverges at the MBL transition.
We study the stability of the glassy equilibrium state of a directed polymer in random media against weak perturbations including the intriguing problem of temperature-chaos. The statistical correlation of two real replica systems under perturbations, such as small difference of temperature, is studied using the mapping to a quantum problem of interacting bosons. Explicit replica symmetry breaking takes place being induced by the infinitesimally weak perturbations in the $n \to 0$ limit followed by the thermodynamic limit which leads to complete decorrelation of the two real replicas. The over…
The dynamics of many glassy systems are known to exhibit string-like hopping motions each consisting of a line of particles displacing one and other. By using molecular dynamics simulations of glassy polymers, we show that these motions become highly repetitive back-and-forth motions as temperature decreases and do not necessarily contribute to net displacements. Particle hops which constitute string-like motions are reversed with a high probability, reaching 73% and beyond at low temperature. Structural relaxation rate is then dictated not by a simple particle hopping rate but instead by the …
The temperature dependence of the non-ergodicity factor of vitreous GeO$_2$, $f_{q}(T)$, as deduced from elastic and quasi-elastic neutron scattering experiments, is analyzed. The data are collected in a wide range of temperatures from the glassy phase, up to the glass transition temperature, and well above into the undercooled liquid state. Notwithstanding the investigated system is classified as prototype of strong glass, it is found that the temperature- and the $q$-behavior of $f_{q}(T)$ follow some of the predictions of Mode Coupling Theory. The experimental data support the hypothesis of…
The glass transition is considered within two toys models, a mean field spin glass and a directed polymer in a correlated random potential. In the spin glass model there occurs a dynamical transition, where the system condenses in a state of lower entropy. The extensive entropy loss, called complexity or information entropy, is calculated by analysis of the metastable (TAP) states. This yields a well behaved thermodynamics of the dynamical transition. The multitude of glassy states also implies an extensive difference between the internal energy fluctuations and the specific heat. In the direc…
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.
We use the swap Monte Carlo algorithm to analyse the glassy behaviour of sticky spheres in equilibrium conditions at densities where conventional simulations and experiments fail to reach equilibrium, beyond predicted phase transitions and dynamic singularities. We demonstrate the existence of a unique ergodic region comprising all the distinct phases previously reported, except for a phase-separated region at strong adhesion. All structural and dynamic observables evolve gradually within this ergodic region, the physics evolving smoothly from well-known hard sphere glassy behaviour at small a…
We report results of molecular-dynamics simulations for a glassy polymer melt consisting of short, linear bead-spring chains. It was shown in previous work that this onset of the glassy slowing down is compatible with the predictions of the mode coupling theory. The physical process of `caging' of a monomer by its spatial neighbors leads to a distinct two step behavior in the particle mean square displacements. In this work we analyze the effects of this caging process on the Rouse description of the melt's dynamics. We show that the Rouse theory is applicable for length and time scales above …
The effects of the physical aging on the vibrational density of states (VDOS) of a polymeric glass is studied. The VDOS of a poly(methyl methacrylate) glass at low-energy (<15 meV), was determined from inelastic neutron scattering at low-temperature for two different physical thermodynamical states. One sample was annealed during a long time at temperature lower than Tg, and another was quenched from a temperature higher than Tg. It was found that the VDOS around the boson peak, relatively to the one at higher energy, decreases with the annealing at lower temperature than Tg, i.e., with the ph…
We have analyzed a non-randomly frustrated spin model which exhibits behavior remarkably similar to the phenomenology of structural glasses. The high-temperature disordered phase undergoes a strong first-order transition to a long-range ordered structure. Using Monte Carlo simulations, we have studied the behavior of the supercooled state by quenching to temperatures below this transition temperature. For a range of supercooling, the system remains ergodic and exhibits dynamics characteristic of supercooled liquids. Below a certain characteristic temperature, however, the system freezes into a…
Atomistic Framework for Glassy Polymer Viscoelasticity Across Twenty Frequency Decades
University of Milan（米兰大学）；University of Göttingen（哥廷根大学）；Graz University of Technology（格拉茨工业大学）；Polymer Competence Center Leoben GmbH（莱奥本聚合物能力中心有限公司）；US Army DEVCOM Army Research Laboratory（美国陆军DEVCOM陆军研究实验室）
A non-contact scanning-probe-microscopy method was used to probe local near-surface dielectric susceptibility and dielectric relaxation in poly-vinyl-acetate (PVAc) near the glass transition. Dielectric spectra were measured from 10-4 Hz to 102 Hz as a function of temperature. The measurements probed a 20 nm thick layer below the free-surface of a bulk film. A small (4 K) reduction in glass transition temperature and moderate narrowing of the distribution of relaxation times was found. In contrast to results for ultra-thin-films confined on or between metallic electrodes, no reduction in the d…
A directed polymer is considered on a flat substrate with randomly located parallel ridges. It prefers to lie inside wide regions between the ridges. When the transversel width $W=\exp(λL^{1/3})$ is exponential in the longitudinal length $L$, there can be a large number $\sim \exp L^{1/3}$ of available wide states. This ``complexity'' causes a phase transition from a high temperature phase where the polymer lies in the widest lane, to a glassy low temperature phase where it lies in one of many narrower lanes. Starting from a uniform initial distribution of independent polymers, equilibration u…
We report results of molecular-dynamics simulations of a model polymer melt consisting of short non-entangled chains in the supercooled state above the critical temperature of mode-coupling theory (MCT). To analyse the dynamics of the system we computed the incoherent, collective chain and melt intermediate scattering functions as well as the Van Hove correlation functions. We find good evidence for the space-time factorization theorem of MCT. From the critical amplitudes we could derive typical length scales of the beta-dyamics. In an extensive quantitative analysis the leading order descript…
The structure and vibrational density of states (VDOS) of polymer glasses are investigated using numerical simulations based on the classical Kremer-Grest bead-spring model. We focus on the roles of chain length and bending stiffness, the latter being set by imposing three-body angular potentials along chain backbones. Upon increasing the chain length and bending stiffness, structural reorganisation leads to volumetric expansion of the material and build-up of internal stresses. The VDOS has two dominant bands: a low frequency one corresponding to inter- and intra-chain non-bonding interaction…
I present the results of extensive numerical simulations which reveal the glassy properties of Anderson localization in dimension two at zero temperature: pinning, avalanches and chaos. I first show that strong localization confines quantum transport along paths which are pinned by disorder but can change abruptly and suddenly (avalanches) when the energy is varied. I determine the roughness exponent $ζ$ characterizing the transverse fluctuations of these paths and find that its value $ζ=2/3$ is the same as for the directed polymer problem. Finally, I characterize the chaos property, namely th…
We provide strong evidence that the effective spin-spin interaction in a multimodal confocal optical cavity gives rise to a self-induced glassy phase, which emerges exclusively from the peculiar euclidean correlations and is not related to the presence of disorder as in standard spin glasses. As recently shown, this spin-spin effective interaction is both non-local and non-translational invariant, and randomness in the atoms positions produces a spin glass phase. Here we consider the simplest feasible disorder-free setting where atoms form a one-dimensional regular chain and we study the therm…
We present simulation results for a model polymer melt, consisting of short, nonentangled chains, in the supercooled state. The analysis focuses on the monomer dynamics, which is monitored by the incoherent intermediate scattering function. The scattering function is recorded over six decades in time and for many different wave-vectors. The lowest temperatures studied are slightly above the critical temperature of mode-coupling theory (MCT), which was determined from a quantitative analysis of the beta- and alpha-relaxations. We find evidence for the space-time factorization theorem in the bet…
We analyze the unusual slow dynamics that emerges in the bad metal delocalized phase preceding the Many-Body Localization transition by using single-particle Anderson Localization on the Bethe lattice as a toy model of many-body dynamics in Fock space. We probe the dynamical evolution by measuring observables such as the imbalance and equilibrium correlation functions, which display slow dynamics and power-laws strikingly similar to the ones observed in recent simulations and experiments. We relate this unusual behavior to the non-ergodic spectral statistics found on Bethe lattices. We discuss…
We present a theory for the single-particle dynamics in binary mixtures with particle size swaps. The general structure of the theory follows that of the theory for the collective dynamics in binary mixtures with particle size swaps, which we developed previously [G. Szamel, Phys. Rev. E 98, 050601(R) (2018)]. Particle size swaps open up an additional relaxation channel, which speeds up both the collective dynamics and the single-particle dynamics. To make explicit predictions, we resort to a factorization approximation similar to that employed in the mode-coupling theory of glassy dynamics. W…
We propose a toy model with reversible mode coupling mechanism and with trivial Hamiltonian (and hence trivial statics). The model can be analyzed exactly without relying upon uncontrolled approximation such as the factorization approximation employed in the current MCT. We show that the model exhibits a kinetically driven transition from an ergodic phase to nonergodic phase. The nonergodic state is the nonequilibrium stationary solution of the Fokker-Planck equation for the distribution function of the model
It is shown that the limit $t-t'\to\infty$ of the equilibrium dynamic self-energy can be computed from the $n\to 1$ limit of the static self-energy of a $n$-times replicated system with one step replica symmetry breaking structure. It is also shown that the Dyson equation of the replicated system leads in the $n\to 1$ limit to the bifurcation equation for the glass ergodicity breaking parameter computed from dynamics. The equivalence of the replica formalism to the long time limit of the equilibrium relaxation dynamics is proved to all orders in perturbation for a scalar theory.
Whereas the first part of this paper dealt with the relaxation in the beta-regime, this part investigates the final (alpha) relaxation of a simulated polymer melt consisting of short non-entangled chains above the critical temperature Tc of mode-coupling theory (MCT). We monitor the intermediate incoherent as well as the coherent chain and coherent melt scattering functions over a wide range of wave numbers q. Upon approaching Tc the coherent alpha-relaxation time of the melt increases strongly close to the maximum of the static structure factor of the melt. At q corresponding to the radius of…
By making use of the Langevin dynamics and its generating functional (GF) formulation the influence of the long-range nature of the interaction on the tendency of the glass formation is systematically investigated. In doing so two types of models is considered: (i) the non-disordered model with a pure repulsive type of interaction and (ii) the model with a randomly distributed strength of interaction (a quenched disordered model). The long-ranged potential of interaction is scaled with a number of particles $N$ in such a way as to enable for GF the saddle-point treatment as well as the systema…
The Langevin dynamics of a self - interacting chain embedded in a quenched random medium is investigated by making use of the generating functional method and one - loop (Hartree) approximation. We have shown how this intrinsic disorder causes different dynamical regimes. Namely, within the Rouse characteristic time interval the anomalous diffusion shows up. The corresponding subdiffusional dynamical exponents have been explicitly calculated and thoroughly discussed. For the larger time interval the disorder drives the center of mass of the chain to a trap or frozen state provided that the Har…
By considering the quantum dynamics of a transverse field Ising spin glass on the Bethe lattice we find the existence of a many body localized region at small transverse field and low temperature. The region is located within the thermodynamic spin glass phase. Accordingly, we conjecture that quantum dynamics inside the glassy region is split in a small MBL and a large delocalized (but not necessarily ergodic) region. This has implications for the analysis of the performance of quantum adiabatic algorithms.
Motivated by recent experimental results on glassy polymer nanoparticles, we develop a minimal theoretical framework for the glass transition in spherical confinement. This is accomplished using our cooperative-string model for supercooled dynamics, that was successful at recovering the bulk phenomenology and describing the thin-film anomalies. In particular, we obtain predictions for the mobile-layer thickness as a function of temperature, and for the effective glass-transition temperature as a function of the radius of the spherical nanoparticle - including the existence of a critical partic…
We develop a new analytic approach for the study of lattice heteropolymers, and apply it to copolymers with correlated Markovian sequences. According to our analysis, heteropolymers present three different dense phases depending upon the temperature, the nature of the monomer interactions, and the sequence correlations: (i) a liquid phase, (ii) a ``soft glass'' phase, and (iii) a ``frozen glass'' phase. The presence of the new intermediate ``soft glass'' phase is predicted for instance in the case of polyampholytes with sequences that favor the alternation of monomers. Our approach is based on…
The complex dynamics of an increasing number of systems is attributed to the emergence of a rugged energy landscape with an exponential number of metastable states. To develop this picture into a predictive dynamical theory I discuss how to compute the exponentially small probability of a jump from one metastable state to another. This is expressed as a path integral that can be evaluated by saddle-point methods in mean-field models, leading to a boundary value problem. The resulting dynamical equations are solved numerically by means of a Newton-Krylov algorithm in the paradigmatic spherical …
We introduce a minimal theory of glass formation based on the ideas of molecular crowding and resultant string-like cooperative rearrangement, and address the effects of free interfaces. In the bulk case, we obtain a scaling expression for the number of particles taking part in cooperative strings, and we recover the Adam-Gibbs description of glassy dynamics. Then, by including thermal dilatation, the Vogel-Fulcher-Tammann relation is derived. Moreover, the random and string-like characters of the cooperative rearrangement allow us to predict a temperature-dependent expression for the cooperat…
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；School of Science, Constructor University（康斯坦茨大学理学院）；Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系）
A model of spinless interacting electrons in presence of randomness is examined using an extended dynamical mean-field formulation. When the interaction strength is large as compared to the Fermi energy, a low temperature glassy phase is identified, which in our formulation corresponds to a replica-symmetry breaking instability. The glassy phase is characterized by a pseudo-gap in the single particle density of states, reminiscent of the Coulomb gap of Efros and Shklovskii. Due to ergodicity breaking, the ``zero-field cooled'' compressibility of this electron glass vanishes at T=0, consistent …
We review several models of glassy systems where the randomness is self generated, i.e. already an infinitesimal amount of disorder is sufficient to cause a transition to a non-ergodic, glassy state. We discuss the application of the replica formalism developed for the spin glass systems to study the glass transition in uniformly frustrated many-body systems. Here a localization in configuration space emerges leading to an entropy crisis of the system. Using a combination of density functional theory and Landau theory of the glassy state, we first analyze the mean field glass transition within…
Magnetizations are introduced to the Generalized Random Energy Model (GREM) and numerical simulations on ac susceptibility is made for direct comparison with experiments in glassy materials. Prominent dynamical natures of spin glasses, {\it i.e.}, {\em memory} effect and {\em reinitialization}, are reproduced well in the GREM. The existence of many layers causing continuous transitions is very important for the two natures. Results of experiments in other glassy materials such as polymers, supercooled glycerol and orientational glasses, which are contrast to those in spin glasses, are interpre…
We introduce a lattice model of glass transition in polymer globules. This model exhibits a novel scenario of ergodicity breaking in which the disjoint regions of phase space do not arise uniformly, but as small chambers whose number increases exponentially with polymer density. Chamber sizes obey power law distribution, making phase space similar to a fractal foam. This clearly demonstrates the importance of the phase space geometry and topology in describing any glass-forming system, such as semicompact polymers during protein folding.
