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Jun 29, 2018
06/18
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Juan P. Garrahan
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Borrowing ideas from open quantum systems, we describe a formalism to encode ensembles of trajectories of classical stochastic dynamics in terms of continuous matrix product states (cMPSs). We show how to define in this approach "biased" or "conditioned" ensembles where the probability of trajectories is biased from that of the natural dynamics by some condition on trajectory observables. In particular, we show that the generalised Doob transform which maps a conditioned...
Topics: Statistical Mechanics, Condensed Matter
Source: http://arxiv.org/abs/1602.07966
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Sep 18, 2013
09/13
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Juan P. Garrahan
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I describe a class of spin models with short--range plaquette interactions whose static equilibrium properties are trivial but which display glassy dynamics at low temperatures. These models have a dual description in terms of free defects subject to effective kinetic constraints, and are thus an explicit realization of the constrained dynamics picture of glassy systems.
Source: http://arxiv.org/abs/cond-mat/0110151v1
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8.0
Jun 30, 2018
06/18
by
Juan P. Garrahan
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Recent large deviation results have provided general lower bounds for the fluctuations of time-integrated currents in the steady state of stochastic systems. A corollary are so-called thermodynamic uncertainty relations connecting precision of estimation to average dissipation. Here we consider this problem but for counting observables, i.e., trajectory observables which, in contrast to currents, are non-negative and non-decreasing in time (and possibly symmetric under time reversal). In the...
Topics: Statistical Mechanics, Condensed Matter
Source: http://arxiv.org/abs/1701.00539
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3.0
Jun 29, 2018
06/18
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Ricardo Gutierrez; Juan P. Garrahan
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Glasses prepared by physical vapour deposition have been shown to be remarkably more stable than those prepared by standard cooling protocols, with properties that appear to be similar to systems aged for extremely long times. When subjected to a rapid rise in temperature, ultrastable glasses anneal towards the liquid in a qualitatively different manner than ordinary glasses, with the seeming competition of different timescales and lengthscales. We numerically reproduce the phenomenology of...
Topics: Disordered Systems and Neural Networks, Soft Condensed Matter, Statistical Mechanics, Condensed...
Source: http://arxiv.org/abs/1604.03495
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Sep 22, 2013
09/13
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David Chandler; Juan P. Garrahan
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In recent papers, we have argued that kinetically constrained coarse grained models can be applied to understand dynamic properties of glass forming materials, and we have used this approach in various applications that appear to validate this view. In one such paper [J.P. Garrahan and D. Chandler, Proc. Nat. Acad. Sci. USA 100, 9710 (2003)], among other things we argued that this approach also explains why the heat capacity discontinuity at the glass transition is generally larger for fragile...
Source: http://arxiv.org/abs/cond-mat/0501544v2
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Sep 18, 2013
09/13
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Stephen Whitelam; Juan P. Garrahan
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Kinetically constrained models (KCMs) are models of glass formers based on the concept of dynamic facilitation. This concept accounts for many of the characteristics of the glass transition. KCMs usually display a combination of simple thermodynamics and complex glassy dynamics, the latter being a consequence of kinetic constraints. Here we show that KCMs can be regarded as systems whose configuration space is endowed with a simple energy surface but a complicated geometry. This geometry is...
Source: http://arxiv.org/abs/cond-mat/0401551v3
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Sep 18, 2013
09/13
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Juan P. Garrahan; David Chandler
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We show how dynamical heterogeneities in glass forming systems emerge as a consequence of the existence of dynamical constraints, and we offer an interpretation of the glass transition as an entropy crisis in trajectory space (space-time) rather than in configuration space. To illustrate our general ideas, we analyze the one dimensional (d=1) Fredrickson-Andersen and East models. Dynamics of such dynamically constrained systems are shown to be isomorphic to the statics of d+1 dimensional dense...
Source: http://arxiv.org/abs/cond-mat/0202392v2
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Sep 22, 2013
09/13
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David Chandler; Juan P. Garrahan
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We review a theoretical perspective of the dynamics of glass forming liquids and the glass transition. It is a perspective we have developed with our collaborators during this decade. It is based upon the structure of trajectory space. This structure emerges from spatial correlations of dynamics that appear in disordered systems as they approach non-ergodic or jammed states. It is characterized in terms of dynamical heterogeneity, facilitation and excitation lines. These features are associated...
Source: http://arxiv.org/abs/0908.0418v1
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Sep 22, 2013
09/13
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Thomas Speck; Juan P. Garrahan
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Kinetically constrained models (KCMs) have been used to study and understand the origin of glassy dynamics. Despite having trivial thermodynamic properties, their dynamics slows down dramatically at low temperatures while displaying dynamical heterogeneity as seen in glass forming supercooled liquids. This dynamics has its origin in an ergodic-nonergodic first-order phase transition between phases of distinct dynamical "activity". This is a "space-time" transition as it...
Source: http://arxiv.org/abs/1004.2698v1
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Sep 22, 2013
09/13
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Arnaud Buhot; Juan P. Garrahan
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We study the out-of-equilibrium fluctuation-dissipation (FD) relations in the low temperature, finite time, physical aging regime of two simple models with strong glass behaviour, the Fredrickson-Andersen model and the square-plaquette interaction model. We explicitly show the existence of unique, waiting-time independent dynamical FD relations. While in the Fredrickson-Andersen model the FD theorem is obeyed at all times, the plaquette model displays piecewise linear FD relations, similar to...
Source: http://arxiv.org/abs/cond-mat/0111035v2
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Sep 20, 2013
09/13
by
Stephen Whitelam; Juan P. Garrahan
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We use a real-space renormalization group (RSRG) to study the low temperature dynamics of kinetically constrained Ising chains (KCICs). We consider the cases of the Fredrickson-Andersen (FA) model, the East model, and the partially asymmetric KCIC. We show that the RSRG allows one to obtain in a unified manner the dynamical properties of these models near their zero-temperature critical points. These properties include the dynamic exponent, the growth of dynamical lengthscales, and the...
Source: http://arxiv.org/abs/cond-mat/0405647v2
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3.0
Jun 30, 2018
06/18
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Juan P. Garrahan; Igor Lesanovsky
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A recent paper [F. Radicchi and A. Arenas, Nature Phys. 9, 717 (2013)] presented the finding of an abrupt transition in the structure of interconnected networks. This transition was said to be generic and to occur even in networks of finite size. Furthermore, it was remarked that this singular behaviour could be understood in the spirit of a first-order phase transition. We show here that the generic singularity found in that paper is a trivial consequence of the reducibility of the...
Topics: Statistical Mechanics, Condensed Matter
Source: http://arxiv.org/abs/1406.4706
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Sep 18, 2013
09/13
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Ludovic Berthier; Juan P. Garrahan
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We show that the dynamics between inherent structures in glass forming systems can be understood in purely dynamical terms, without any reference to ``topographic'' features of the potential energy landscape. This ``non-topographic'' interpretation is based instead on the existence of dynamical heterogeneities and on their statistical properties. Our view is supported by the study of simple dynamically facilitated models of glass formers. These models also allow for the formulation of...
Source: http://arxiv.org/abs/cond-mat/0303451v1
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Sep 20, 2013
09/13
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Ludovic Berthier; Juan P. Garrahan
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We numerically study the three-dimensional generalization of the kinetically constrained East model, the North-or-East-or-Front (NEF) model. We characterize the equilibrium behaviour of the NEF model in detail, measuring the temperature dependence of several quantities: alpha-relaxation time, distributions of relaxation times, dynamic susceptibility, dynamic correlation length, and four-point susceptibility. We show that the NEF model describes quantitatively experimental observations over an...
Source: http://arxiv.org/abs/cond-mat/0410076v2
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Sep 20, 2013
09/13
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Juan P. Garrahan; David Chandler
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We introduce a coarse-grained model for atomic glass formers. Its elements are physically motivated local microscopic dynamical rules parameterized by observables. Results of the model are established and used to interpret the measured behaviors of supercooled fluids approaching glass transitions. The model predicts the presence of a crossover from hierarchical super-Arrhenius dynamics at short length scales to diffusive Arrhenius dynamics at large length scales. This prediction distinguishes...
Source: http://arxiv.org/abs/cond-mat/0301287v3
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Sep 21, 2013
09/13
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Arnaud Buhot; Juan P. Garrahan
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We show the existence of fragile-to-strong transitions in kinetically constrained systems by studying the equilibrium and out-of-equilibrium dynamics of a generic constrained Ising spin chain which interpolates between the symmetric and fully asymmetric cases. We find that for large but finite asymmetry the model displays a crossover from fragile to strong glassy behaviour at finite temperature, which is controlled by the asymmetry parameter. The relaxation in the fragile region presents...
Source: http://arxiv.org/abs/cond-mat/0104340v1
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Sep 18, 2013
09/13
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Ludovic Berthier; Juan P. Garrahan
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We show that the various crossovers between dynamical regimes observed in experiments and simulations of supercooled liquids can be explained in simple terms from the existence and statistical properties of dynamical heterogeneities. We confirm that dynamic heterogeneity is responsible for the slowing down of glass formers at temperatures well above the dynamic singularity T_c predicted by mode coupling theory. Our results imply that activated processes govern the long-time dynamics even in the...
Source: http://arxiv.org/abs/cond-mat/0306469v2
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Sep 23, 2013
09/13
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Giulio Biroli; Juan P. Garrahan
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We provide here a brief perspective on the glass transition field. It is an assessment, written from the point of view of theory, of where the field is and where it seems to be heading. We first give an overview of the main phenomenological characteristics, or "stylised facts", of the glass transition problem, i.e. the central observations that a theory of the physics of glass formation should aim to explain in a unified manner. We describe recent developments, with a particular focus...
Source: http://arxiv.org/abs/1303.3542v1
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2.0
Jun 30, 2018
06/18
by
Igor Lesanovsky; Juan P. Garrahan
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The non-equilibrium dynamics of a gas of cold atoms in which Rydberg states are off-resonantly excited is studied in the presence of noise. The interplay between interaction and off-resonant excitation leads to an initial dynamics where aggregates of excited Rydberg atoms slowly nucleate and grow, eventually reaching long-lived meta-stable arrangements which then relax further on much longer timescales. This growth dynamics is governed by an effective Master equation which permits a transparent...
Topics: Quantum Gases, Physics, Atomic Physics, Statistical Mechanics, Condensed Matter
Source: http://arxiv.org/abs/1402.2126
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Sep 18, 2013
09/13
by
Christian Flindt; Juan P. Garrahan
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We investigate Lee-Yang zeros of generating functions of dynamical observables and establish a general relation between phase transitions in ensembles of trajectories of stochastic many-body systems and the time evolution of high-order cumulants of such observables. This connects dynamical free-energies for full counting statistics in the long-time limit, which can be obtained via large-deviation methods and whose singularities indicate dynamical phase transitions, to observables that are...
Source: http://arxiv.org/abs/1209.2524v1
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Jun 30, 2018
06/18
by
Merlijn van Horssen; Juan P. Garrahan
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We consider an extension of classical stochastic reaction-diffusion (RD) dynamics to open quantum systems. We study a class of models of hard core particles on a one-dimensional lattice whose dynamics is generated by a quantum master operator and where particle hopping is coherent while reactions, such as pair annihilation or pair coalescence, are dissipative. These are quantum open generalisations of the $A+A \to \varnothing$ and $A+A \to A$ classical RD models. We characterise the relaxation...
Topics: Quantum Physics, Statistical Mechanics, Condensed Matter
Source: http://arxiv.org/abs/1411.7913
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Sep 19, 2013
09/13
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Lester O. Hedges; Juan P. Garrahan
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We apply the concept of dynamic propensity to a simple kinetically constrained model of glass formers, the two-vacancy assisted triangular lattice gas, or (2)-TLG. We find that the propensity field, defined in our case as the local root-mean square displacement averaged over the ensemble of trajectories with identical initial configurations, is a good measure of dynamical heterogeneity. This suggests a configurational origin for spatial fluctuations of the dynamics, but just as in the case of...
Source: http://arxiv.org/abs/cond-mat/0610635v2
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Sep 21, 2013
09/13
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Lester O. Hedges; Juan P. Garrahan
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Transitions between metabasins in supercooled liquids seem to occur through rapid "democratic" collective particle rearrangements. Here we show that this apparent homogeneous particle motion is a direct consequence of dynamic facilitation. We do so by studying metabasin transitions in facilitated spin models and constrained lattice gases. We find that metabasin transitions occur through a sequence of locally facilitated events taking place over a relatively short time frame. When...
Source: http://arxiv.org/abs/0706.0902v2
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Sep 19, 2013
09/13
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Robert L. Jack; Juan. P. Garrahan
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We consider two systems of Ising spins with plaquette interactions. They are simple models of glasses which have dual representations as kinetically constrained systems. These models allow an explicit analysis using the mosaic, or entropic droplet, approach of the random first-order transition theory of the glass transition. We show that the low temperature states of these systems resemble glassy mosaic states, despite the fact that excitations are localized and that there are no static...
Source: http://arxiv.org/abs/cond-mat/0507370v2
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Sep 21, 2013
09/13
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Douglas J. Ashton; Juan P. Garrahan
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We study the relation between short-time vibrational modes and long-time relaxational dynamics in a kinetically constrained lattice gas with harmonic interactions between neighbouring particles. We find a correlation between the location of the low (high) frequency vibrational modes and regions of high (low) propensity for motion. This is similar to what was observed in continuous force systems, but our interpretation is different: in our case relaxation is due to localised excitations which...
Source: http://arxiv.org/abs/0808.2412v1
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Sep 19, 2013
09/13
by
Robert L. Jack; Juan P. Garrahan
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We study large deviations of the dynamical activity in the random orthogonal model (ROM). This is a fully connected spin-glass model with one-step replica symmetry breaking behaviour, consistent with the random first-order transition scenario for structural glasses. We show that this model displays dynamical (space-time) phase-transitions between active and inactive phases, as demonstrated by singularities in large deviation functions. We argue that such transitions are generic in systems with...
Source: http://arxiv.org/abs/0910.1111v1
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Jun 28, 2018
06/18
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Robert L. Jack; Juan P. Garrahan
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We study a three-dimensional plaquette spin model whose low temperature dynamics is glassy, due to localised defects and effective kinetic constraints. While the thermodynamics of this system is smooth at all temperatures, we show that coupling it to a second system with a fixed (quenched) configuration can lead to a phase transition, at finite coupling. The order parameter is the overlap between the copies, and the transition is between phases of low and high overlap. We find critical points...
Topics: Statistical Mechanics, Condensed Matter
Source: http://arxiv.org/abs/1508.06470
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Sep 22, 2013
09/13
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Andrea Cavagna; Juan P. Garrahan; Irene Giardina
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We consider the p-spin spherical spin-glass model in the presence of an external magnetic field as a general example of a mean-field system where a one step replica symmetry breaking (1-RSB) occurs. In this context we compute the complexity of the Thouless-Anderson-Palmer states, performing a quenched computation. We find what is the general connection between this method and the standard static 1-RSB one, formulating a clear mapping between the parameters used in the two different...
Source: http://arxiv.org/abs/cond-mat/9807222v1
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Sep 22, 2013
09/13
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Ludovic Berthier; David Chandler; Juan P. Garrahan
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The interplay between self-diffusion and excitation lines in space-time was recently studied in kinetically constrained models to explain the breakdown of the Stokes-Einstein law in supercooled liquids. Here, we further examine this interplay and its manifestation in incoherent scattering functions. In particular, we establish a dynamic length scale below which Fickian diffusion breaks down, as is observed in experiments and simulations. We describe the temperature dependence of this length...
Source: http://arxiv.org/abs/cond-mat/0409428v3
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Jun 28, 2018
06/18
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Ricardo Gutiérrez; Juan P. Garrahan; Igor Lesanovsky
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The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power-law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic...
Topics: Physics, Statistical Mechanics, Atomic Physics, Quantum Gases, Condensed Matter
Source: http://arxiv.org/abs/1507.02652
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Sep 22, 2013
09/13
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Juan P. Garrahan; Esteban Moro; David Sherrington
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We study the continuous time dynamics of the Thermal Minority Game. We find that the dynamical equations of the model reduce to a set of stochastic differential equations for an interacting disordered system with non-trivial random diffusion. This is the simplest microscopic description which accounts for all the features of the system. Within this framework, we study the phase structure of the model and find that its macroscopic properties strongly depend on the initial conditions.
Source: http://arxiv.org/abs/cond-mat/0004277v2
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Jun 28, 2018
06/18
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Tom Oakes; Juan P. Garrahan; Stephen Powell
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We study the behavior of classical dimer coverings of the square lattice - a paradigmatic model for systems subject to constraints - evolving under local stochastic dynamics, by means of Monte Carlo simulations and theoretical arguments. We observe clear signatures of correlated dynamics in both global and local observables and over a broad range of time scales, indicating a breakdown of the simple continuum description that approximates well the statics. We show that this collective dynamics...
Topics: Statistical Mechanics, Condensed Matter
Source: http://arxiv.org/abs/1509.08476
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Jun 29, 2018
06/18
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Ricardo Gutierrez; Juan P. Garrahan; Igor Lesanovsky
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We study the out-of-equilibrium dynamics of dissipative gases of atoms excited to two or more high-lying Rydberg states. This situation bears interesting similarities to classical binary (in general $p$-ary) mixtures of particles. The effective forces between the components are determined by the inter-level and intra-level interactions of Rydberg atoms. These systems permit to explore new parameter regimes which are physically inaccessible in a classical setting, for example one in which the...
Topics: Atomic Physics, Statistical Mechanics, Condensed Matter, Quantum Gases, Physics
Source: http://arxiv.org/abs/1603.00828
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Sep 22, 2013
09/13
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Mauro Merolle; Juan P. Garrahan; David Chandler
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We consider the probability distribution for fluctuations in dynamical action and similar quantities related to dynamic heterogeneity. We argue that the so-called "glass transition" is a manifestation of low action tails in these distributions where the entropy of trajectory space is sub-extensive in time. These low action tails are a consequence of dynamic heterogeneity and an indication of phase coexistence in trajectory space. The glass transition, where the system falls out of...
Source: http://arxiv.org/abs/cond-mat/0501180v3
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Sep 19, 2013
09/13
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David Sherrington; Juan P. Garrahan; Esteban Moro
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Recent results and interpretations are presented for the thermal minority game, concentrating on deriving and justifying the fundamental stochastic differential equation for the microdynamics.
Source: http://arxiv.org/abs/cond-mat/0010455v1
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2.0
Jun 30, 2018
06/18
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Beatriz Olmos; Igor Lesanovsky; Juan P. Garrahan
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We explore the relaxation dynamics of quantum many-body systems that undergo purely dissipative dynamics through non-classical jump operators that can establish quantum coherence. Our goal is to shed light on the differences in the relaxation dynamics that arise in comparison to systems evolving via classical rate equations. In particular, we focus on a scenario where both quantum and classical dissipative evolution lead to a stationary state with the same values of diagonal or...
Topics: Quantum Physics, Quantum Gases, Atomic Physics, Physics, Condensed Matter
Source: http://arxiv.org/abs/1406.5485
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2.0
Jun 29, 2018
06/18
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Katherine Klymko; Juan P. Garrahan; Stephen Whitelam
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Models of bacterial growth tend to be `irreversible', allowing for the number of bacteria in a colony to increase but not to decrease. By contrast, models of molecular self-assembly are usually `reversible', allowing for addition and removal of particles to a structure. Such processes differ in a fundamental way because only reversible processes possess an equilibrium. Here we show at mean-field level that dynamic trajectories of reversible and irreversible growth processes are similar in that...
Topics: Soft Condensed Matter, Statistical Mechanics, Condensed Matter
Source: http://arxiv.org/abs/1603.06014
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Sep 22, 2013
09/13
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Igor Lesanovsky; Beatriz Olmos; Juan P. Garrahan
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We study the coherent quantum evolution of a closed and driven mesoscopic chain of two-level systems that interact via the van-der-Waals interaction in their excited state. The Hamiltonian consists of a part corresponding to a classical lattice gas and an off-diagonal driving term without classical counterpart. We show that in a certain parameter range the latter leads to a thermalization of the system with respect to observables of the classical lattice gas such as the interaction energy and...
Source: http://arxiv.org/abs/1004.3210v1
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Jun 30, 2018
06/18
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Sam Genway; Igor Lesanovsky; Juan P. Garrahan
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We study a two-dimensional tight-binding lattice for excitons with on-site disorder, coupled to a thermal environment at infinite temperature. The disorder acts to localise an exciton spatially, while the environment generates dynamics which enable exploration of the lattice. Although the steady state of the system is trivially uniform, we observe a rich dynamics and uncover a dynamical phase transition in the space of temporal trajectories. This transition is identified as a localisation in...
Topics: Statistical Mechanics, Condensed Matter
Source: http://arxiv.org/abs/1401.7280
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Sep 19, 2013
09/13
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Juan P. Garrahan; Peter Sollich; Cristina Toninelli
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In this chapter we summarize recent developments in the study of kinetically constrained models (KCMs) as models for glass formers. After recalling the definition of the KCMs which we cover we study the possible occurrence of ergodicity breaking transitions and discuss in some detail how, before any such transition occurs, relaxation timescales depend on the relevant control parameter (density or temperature). Then we turn to the main issue: the prediction of KCMs for dynamical heterogeneities....
Source: http://arxiv.org/abs/1009.6113v1
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Sep 22, 2013
09/13
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Stephen Whitelam; Ludovic Berthier; Juan P. Garrahan
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We propose that the dynamics of supercooled liquids and the formation of glasses can be understood from the existence of a zero temperature dynamical critical point. To support our proposal, we derive from simple physical assumptions a dynamic field theory for supercooled liquids, which we study using the renormalization group (RG). Its long time behaviour is dominated by a zero temperature critical point, which for dimensions d > 2 belongs to the directed percolation universality class....
Source: http://arxiv.org/abs/cond-mat/0310207v2
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Sep 18, 2013
09/13
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YounJoon Jung; Juan P. Garrahan; David Chandler
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We investigate statistics of dynamical exchange events in coarse--grained models of supercooled liquids in spatial dimensions $d=1$, 2, and 3. The models, based upon the concept of dynamical facilitation, capture generic features of statistics of exchange times and persistence times. Here, distributions for both times are related, and calculated for cases of strong and fragile glass formers over a range of temperatures. Exchange time distributions are shown to be particularly sensitive to the...
Source: http://arxiv.org/abs/cond-mat/0504535v3
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Jul 20, 2013
07/13
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Beatriz Olmos; Igor Lesanovsky; Juan P. Garrahan
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We introduce a class of dissipative quantum spin models with local interactions and without quenched disorder that show glassy behaviour. These models are the quantum analogs of the classical facilitated spin models. Just like their classical counterparts, quantum facilitated models display complex glassy dynamics despite the fact that their stationary state is essentially trivial. In these systems, dynamical arrest is a consequence of kinetic constraints and not of static ordering. These...
Source: http://arxiv.org/abs/1203.6585v1
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Sep 23, 2013
09/13
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Stephen Whitelam; Ludovic Berthier; Juan P. Garrahan
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We derive a dynamic field theory for a kinetically constrained model, based on the Fredrickson--Andersen model, which we expect to describe the properties of an Arrhenius (strong) supercooled liquid at the coarse-grained level. We study this field theory using the renormalization group. For mesoscopic length and time scales, and for space dimension d \geq 2, the behaviour of the model is governed by a zero-temperature dynamical critical point in the directed percolation universality class. We...
Source: http://arxiv.org/abs/cond-mat/0408694v1
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Sep 17, 2013
09/13
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Juan P. Garrahan; M. E. J. Newman
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We study the low temperature dynamics of a two dimensional short-range spin system with uniform ferromagnetic interactions, which displays glassiness at low temperatures despite the absence of disorder or frustration. The model has a dual description in terms of free defects subject to dynamical constraints, and is an explicit realization of the ``hierarchically constrained dynamics'' scenario for glassy systems. We give a number of exact results for the statics of the model, and study in...
Source: http://arxiv.org/abs/cond-mat/0007372v2
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Sep 21, 2013
09/13
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YounJoon Jung; Juan P. Garrahan; David Chandler
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By applying the concept of dynamical facilitation and analyzing the excitation lines that result from this facilitation, we investigate the origin of decoupling of transport coefficients in supercooled liquids. We illustrate our approach with two classes of models. One depicts diffusion in a strong glass former, and the other in a fragile glass former. At low temperatures, both models exhibit violation of the Stokes-Einstein relation, $D\sim\tau^{-1}$, where $D$ is the self diffusion constant...
Source: http://arxiv.org/abs/cond-mat/0311396v1
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Sep 19, 2013
09/13
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Arnaud Buhot; Juan P. Garrahan; David Sherrington
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We introduce simple models, inspired by previous models for froths and covalent glasses, with trivial equilibrium properties but dynamical behaviour characteristic of strong glass forming systems. These models are also a generalization of backgammon or urn models to a non--constant number of particles, where entropic barriers are replaced by energy barriers, allowing for the existence of activated processes. We formulate a mean--field version of the models, which keeps most of the features of...
Source: http://arxiv.org/abs/cond-mat/0209362v1
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Sep 19, 2013
09/13
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Andrea Cavagna; Juan P. Garrahan; Irene Giardina
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We study the energy distribution of maxima and minima of a simple one-dimensional disordered Hamiltonian. We find that in systems with short range correlated disorder there is energy separation between maxima and minima, such that at fixed energy only one kind of stationary points is dominant in number over the other. On the other hand, in the case of systems with long range correlated disorder maxima and minima are completely mixed.
Source: http://arxiv.org/abs/cond-mat/9812373v1
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Sep 21, 2013
09/13
by
Andrea Cavagna; Juan P. Garrahan; Irene Giardina
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We compute the distribution of the number of negative eigenvalues (the index) for an ensemble of Gaussian random matrices, by means of the replica method. This calculation has important applications in the context of statistical mechanics of disordered systems, where the second derivative of the potential energy (the Hessian) is a random matrix whose negative eigenvalues measure the degree of instability of the energy surface. An analysis of the probability distribution of the Hessian index is...
Source: http://arxiv.org/abs/cond-mat/9907296v1
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Jun 30, 2018
06/18
by
James M. Hickey; Sam Genway; Juan P. Garrahan
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We study a quantum spin system with local bilinear interactions and without quenched disorder which seems to display characteristic signatures of a many-body localisation (MBL) transition. From direct diagonalisation of small systems, we find a change in certain dynamical and spectral properties at a critical value of a coupling, from those characteristic of a thermalising phase to those characteristic of a MBL phase. The system we consider is known to have a quantum phase transition in its...
Topics: Statistical Mechanics, Condensed Matter
Source: http://arxiv.org/abs/1405.5780
