arXiv subjects

Juan P. Garrahan

Publications and source records attributed to Juan P. Garrahan.

At least 163 records · Page 9Linked to original sources

arXiv2012

Dynamical phases and intermittency of the dissipative quantum Ising model

We employ the concept of a dynamical, activity order parameter to study the Ising model in a transverse magnetic field coupled to a Markovian bath. For a certain range of values of the spin-spin coupling, magnetic field and dissipation rate, we identify a first order dynamical phase transition between active and inactive {\em dynamical phases}. We demonstrate that dynamical phase-coexistence becomes manifest in an intermittent behavior of the bath quanta emission. Moreover, we establish the connection between the dynamical order parameter that quantifies the activity, and the longitudinal magnetization that serves as static order parameter. The system we consider can be implemented in current experiments with Rydberg atoms and trapped ions.

cond-mat.stat-mech↗

arXiv2012

Broken symmetry and the variation of critical properties in the phase behaviour of supramolecular rhombus tilings

The degree of randomness, or partial order, present in two-dimensional supramolecular arrays of isophthalate tetracarboxylic acids is shown to vary due to subtle chemical changes such as the choice of solvent or small differences in molecular dimensions. This variation may be quantified using an order parameter and reveals a novel phase behaviour including random tiling with varying critical properties as well as ordered phases dominated by either parallel or non-parallel alignment of neighbouring molecules, consistent with long-standing theoretical studies. The balance between order and randomness is driven by small differences in the intermolecular interaction energies, which we show, using numerical simulations, can be related to the measured order parameter. Significant variations occur even when the energy difference is much less than the thermal energy highlighting the delicate balance between entropic and energetic effects in complex self-assembly processes.

cond-mat.stat-mech↗

arXiv2011

Preparation and relaxation of very stable glassy states of a simulated liquid

We prepare metastable glassy states in a model glass-former made of Lennard-Jones particles by sampling biased ensembles of trajectories with low dynamical activity. These trajectories form an inactive dynamical phase whose `fast' vibrational degrees of freedom are maintained at thermal equilibrium by contact with a heat bath, while the `slow' structural degrees of freedom are located in deep valleys of the energy landscape. We examine the relaxation to equilibrium and the vibrational properties of these metastable states. The glassy states we prepare by our trajectory sampling method are very stable to thermal fluctuations and also more mechanically rigid than low-temperature equilibrated configurations.

cond-mat.stat-mech↗

arXiv2011

Quantum trajectory phase transitions in the micromaser

We study the dynamics of the single atom maser, or micromaser, by means of the recently introduced method of thermodynamics of quantum jump trajectories. We find that the dynamics of the micromaser displays multiple space-time phase transitions, i.e., phase transitions in ensembles of quantum jump trajectories. This rich dynamical phase structure becomes apparent when trajectories are classified by dynamical observables that quantify dynamical activity, such as the number of atoms that have changed state while traversing the cavity. The space-time transitions can be either first-order or continuous, and are controlled not just by standard parameters of the micromaser but also by non-equilibrium "counting" fields. We discuss how the dynamical phase behavior relates to the better known stationary state properties of the micromaser.

cond-mat.stat-mech↗

arXiv2010

Kinetically Constrained Models

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. We focus in particular on multipoint correlation functions and susceptibilities, and decoupling in the transport coefficients. Finally we discuss the recent view of KCMs as being at first order coexistence between an active and an inactive space-time phase.

cond-mat.stat-mech↗

arXiv2010

Corresponding States of Structural Glass Formers. II

The earlier paper of this same title demonstrated a collapse of relaxation data of fragile supercooled glass forming liquids [\textit{J. Phys. Chem. B} \textbf{113}, 5563-5567 (2009)]. For temperature $T$ below that of the onset to supercooled behavior, $T_{\mathrm{o}}$, the logarithm of structural relaxation time, $\log τ$, is given by the parabolic form $\log (τ/τ_{\mathrm{o}}) \, =\, J^2(1/T - 1/T_{\mathrm{o}})^{2}$, where $J$ and $τ_{\mathrm{o}}$ are temperature independent. This paper presents further applications of this formula. In particular, it is shown that the effects of attractive forces in numerical simulation of glass forming liquids can be logically organized in terms of $J$ and $T_{\mathrm{o}}$. Further, analysis of experimental data for several systems suggests that $J$ and $T_{\mathrm{o}}$ are material properties. In contrast, values of similar parameters for other fitting formulas are shown to depend not only upon the material but also upon the range of data used in fitting these formulas. Expressions demonstrated to fail in this way include the Vogel-Fulcher-Tammann formula, a double-exponential formula, and a fractional exponential formula.

cond-mat.stat-mech↗

arXiv2010

Entropically-stabilised growth of a two-dimensional random tiling

The assembly of molecular networks into structures such as random tilings and glasses has recently been demonstrated for a number of two-dimensional systems. These structures are dynamically-arrested on experimental timescales so the critical regime in their formation is that of initial growth. Here we identify a transition from energetic to entropic stabilisation in the nucleation and growth of a molecular rhombus tiling. Calculations based on a lattice gas model show that clustering of topological defects and the formation of faceted boundaries followed by a slow relaxation to equilibrium occurs under conditions of energetic stabilisation. We also identify an entropically-stabilised regime in which the system grows directly into an equilibrium configuration without the need for further relaxation. Our results provide a methodology for identifying equilibrium and non-equilibrium randomness in the growth of molecular tilings, and we demonstrate that equilibrium spatial statistics are compatible with exponentially slow dynamical behaviour.

cond-mat.stat-mech↗

arXiv2010

Thermalization in a coherently driven ensemble of two-level systems

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 particle number distribution. We investigate the evolution of the system into this thermal state and discuss how to determine the corresponding temperature. Our findings can be applied to understand thermalization in strongly interacting systems of laser-driven Rydberg atoms, ions or polar molecules.

cond-mat.stat-mech↗

arXiv2010

Space-time Phase Transitions in Driven Kinetically Constrained Lattice Models

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 corresponds to a singular change in ensembles of trajectories of the dynamics rather than ensembles of configurations. Here we extend these ideas to driven glassy systems by considering KCMs driven into non-equilibrium steady states through non-conservative forces. By classifying trajectories through their entropy production we prove that driven KCMs also display an analogous first-order space-time transition between dynamical phases of finite and vanishing entropy production. We also discuss how trajectories with rare values of entropy production can be realized as typical trajectories of a mapped system with modified forces.

cond-mat.stat-mech↗

arXiv2010

Finite-temperature critical point of a glass transition

We generalize the simplest kinetically constrained model of a glass-forming liquid by softening kinetic constraints, allowing them to be violated with a small finite rate. We demonstrate that this model supports a first-order dynamical (space-time) phase transition, similar to those observed with hard constraints. In addition, we find that the first-order phase boundary in this softened model ends in a finite-temperature dynamical critical point, which we expect to be present in natural systems. We discuss links between this critical point and quantum phase transitions, showing that dynamical phase transitions in $d$ dimensions map to quantum transitions in the same dimension, and hence to classical thermodynamic phase transitions in $d+1$ dimensions. We make these links explicit through exact mappings between master operators, transfer matrices, and Hamiltonians for quantum spin chains.

cond-mat.stat-mech↗

arXiv2009

Thermodynamics of Quantum Jump Trajectories

We apply the large-deviation method to study trajectories in dissipative quantum systems. We show that in the long time limit the statistics of quantum jumps can be understood from thermodynamic arguments by exploiting the analogy between large-deviation and free-energy functions. This approach is particularly useful for uncovering properties of rare dissipative trajectories. We also prove, via an explicit quantum mapping, that rare trajectories of one system can be realized as typical trajectories of an alternative system.

cond-mat.stat-mech↗

arXiv2009

Metastable states and space-time phase transitions in a spin-glass model

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 long-lived metastable states.

cond-mat.stat-mech↗

arXiv2009

Dynamics on the Way to Forming Glass: Bubbles in Space-time

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 with a newly discovered class of non-equilibrium phase transitions. Equilibrium properties have little if anything to do with it. The broken symmetries of these transitions are obscure or absent in spatial structures, but they are vivid in space-time (i.e., trajectory space). In our view, the glass transition is an example of this class of transitions. The basic ideas and principles we review were originally developed through the analysis of idealized and abstract models. Nevertheless, the central ideas are easily illustrated with reference to molecular dynamics of more realistic atomistic models, and we use that illustrative approach here.

cond-mat.soft↗

arXiv2009

Molecular random tilings as glasses

We have recently shown [Blunt et al., Science 322, 1077 (2008)] that p-terphenyl-3,5,3',5'-tetracarboxylic acid adsorbed on graphite self-assembles into a two-dimensional rhombus random tiling. This tiling is close to ideal, displaying long range correlations punctuated by sparse localised tiling defects. In this paper we explore the analogy between dynamic arrest in this type of random tilings and that of structural glasses. We show that the structural relaxation of these systems is via the propagation--reaction of tiling defects, giving rise to dynamic heterogeneity. We study the scaling properties of the dynamics, and discuss connections with kinetically constrained models of glasses.

cond-mat.stat-mech↗

arXiv2009

The limited role of non-native contacts in folding pathways of a lattice protein

Models of protein energetics which neglect interactions between amino acids that are not adjacent in the native state, such as the Go model, encode or underlie many influential ideas on protein folding. Implicit in this simplification is a crucial assumption that has never been critically evaluated in a broad context: Detailed mechanisms of protein folding are not biased by non-native contacts, typically imagined as a consequence of sequence design and/or topology. Here we present, using computer simulations of a well-studied lattice heteropolymer model, the first systematic test of this oft-assumed correspondence over the statistically significant range of hundreds of thousands of amino acid sequences, and a concomitantly diverse set of folding pathways. Enabled by a novel means of fingerprinting folding trajectories, our study reveals a profound insensitivity of the order in which native contacts accumulate to the omission of non-native interactions. Contrary to conventional thinking, this robustness does not arise from topological restrictions and does not depend on folding rate. We find instead that the crucial factor in discriminating among topological pathways is the heterogeneity of native contact energies. Our results challenge conventional thinking on the relationship between sequence design and free energy landscapes for protein folding, and help justify the widespread use of Go-like models to scrutinize detailed folding mechanisms of real proteins.

q-bio.BM↗

arXiv2008

Corresponding States of Structural Glass Formers

The variation with respect to temperature T of transport properties of 58 fragile structural glass forming liquids (68 data sets in total) are analyzed and shown to exhibit a remarkable degree of universality. In particular, super-Arrhenius behaviors of all super-cooled liquids appear to collapse to one parabola for which there is no singular behavior at any finite temperature. This behavior is bounded by an onset temperature To above which liquid transport has a much weaker temperature dependence. A similar collapse is also demonstrated, over the smaller available range, for existing numerical simulation data.

cond-mat.stat-mech↗

arXiv2008

Relationship between vibrations and dynamical heterogeneity in a model glass former: extended soft modes but local relaxation

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 propagate through the system; these localised excitations act as background disorder for the elastic network, giving rise to anomalous vibrational modes. Our results show that a correlation between spatially extended low frequency modes and high propensity regions does not imply that relaxational dynamics originates in extended soft modes. We consider other measures of elastic heterogeneity, such as non-affine displacement fields and mode localisation lengths, and discuss implications of our results to interpretations of dynamic heterogeneity more generally.

cond-mat.stat-mech↗

arXiv2008

Negative differential mobility of weakly driven particles in models of glass formers

We study the response of probe particles to weak constant driving in kinetically constrained models of glassy systems, and show that the probe's response can be non-monotonic and give rise to negative differential mobility: increasing the applied force can reduce the probe's drift velocity in the force direction. Oth er significant non-linear effects are also demonstrated, such as the enhancement with increasing force of the probe's fluctuations away from the average path, a phenomenon known in other contexts as giant diffusivity. We show that these res ults can be explained analytically by a continuous-time random walk approximatio n where there is decoupling between persistence and exchange times for local dis placements of the probe. This decoupling is due to dynamic heterogeneity in the glassy system, which also leads to bimodal distributions of probe particle disp lacements. We discuss the relevance of our results to experiments.

cond-mat.stat-mech↗