arXiv subjects

Juan P. Garrahan

Publications and source records attributed to Juan P. Garrahan.

At least 127 records · Page 7Linked to original sources

arXiv2015

Dynamics of many-body localisation in a translation invariant quantum glass model

We study the real-time dynamics of a translationally invariant quantum spin chain, based on the East kinetically constrained glass model, in search for evidence of many-body localisation in the absence of disorder. Numerical simulations indicate a change, controlled by a coupling parameter, from a regime of fast relaxation---corresponding to thermalisation---to a regime of very slow relaxation. This slowly relaxing regime is characterised by dynamical features usually associated with non-ergodicity and many-body localisation (MBL): memory of initial conditions, logarithmic growth of entanglement entropy, and non-exponential decay of time-correlators. We show that slow relaxation is a consequence of sensitivity to spatial fluctuations in the initial state. While numerics indicate that certain relaxation timescales grow markedly with size, our finite size results are consistent both with an MBL transition, expected to only occur in disordered systems, or with a pronounced quasi-MBL crossover.

cond-mat.stat-mech↗

arXiv2015

Overlap and activity glass transitions in plaquette spin models with hierarchical dynamics

We consider thermodynamic and dynamic phase transitions in plaquette spin models of glasses. The thermodynamic transitions involve coupled (annealed) replicas of the model. We map these coupled-replica systems to a single replica in a magnetic field, which allows us to analyse the resulting phase transitions in detail. For the triangular plaquette model (TPM), we find for the coupled-replica system a phase transition between high- and low-overlap phases, occuring at a coupling eps*(T), which vanishes in the low-temperature limit. Using computational path sampling techniques, we show that a single TPM also displays space-time transitions between active and inactive dynamical phases. These first-order dynamical transitions occur at a critical counting field s_c(T)>=0 that appears to vanish at zero temperature, in a manner reminiscent of the thermodynamic overlap transition. In order to extend the ideas to three dimensions we introduce the square pyramid model which also displays both overlap and activity transitions. We discuss a possible common origin of these various phase transitions, based on long-lived (metastable) glassy states.

cond-mat.stat-mech↗

arXiv2015

Equivalence of matrix product ensembles of trajectories in open quantum systems

The equivalence of thermodynamic ensembles is at the heart of statistical mechanics and central to our understanding of equilibrium states of matter. Recently, it has been shown that there is a formal connection between the dynamics of open quantum systems and the statistical mechanics in an extra dimension. This is established through the fact that an open system dynamics generates a Matrix Product state (MPS) which encodes the set of all possible quantum jump trajectories and permits the construction of generating functions in the spirit of thermodynamic partition functions. In the case of continuous-time Markovian evolution, such as that generated by a Lindblad master equation, the corresponding MPS is a so-called continuous MPS which encodes the set of continuous measurement records terminated at some fixed total observation time. Here we show that if one instead terminates trajectories after a fixed total number of quantum jumps, e.g. emission events into the environment, the associated MPS is discrete. This establishes an interesting analogy: The continuous and discrete MPS correspond to different ensembles of quantum trajectories, one characterised by total time the other by total number of quantum jumps. Hence they give rise to quantum versions of different thermodynamic ensembles, akin to "grand-canonical" and "isobaric", but for trajectories. Here we prove that these trajectory ensembles are equivalent in a suitable limit of long time or large number of jumps. This is in direct analogy to equilibrium statistical mechanics where equivalence between ensembles is only strictly established in the thermodynamic limit. An intrinsic quantum feature is that the equivalence holds only for all observables that commute with the number of quantum jumps.

quant-ph↗

arXiv2015

A generic map from non-Lindblad to Lindblad master equations

Many current problems of interest in quantum non-equilibrium are described by time-local master equations (TLMEs) for the density matrix that are not of the Lindblad form, that is, that are not strictly probability conserving and/or Markovian. Here we describe an generic approach by which the system of interest that obeys the TLME is coupled to an ancilla, such that the dynamics of the combined system-plus-ancilla is Markovian and thus described by a Lindblad equation. This in turn allows us to recover the properties of the original TLME dynamics from a physical unravelling of this associated Lindblad dynamics. We discuss applications of this generic mapping in two areas of current interest. The first one is that of "thermodynamics of trajectories", where non-Lindblad master equations encode the large-deviation properties of the dynamics, and we show that the relevant large-deviation functions (i.e. dynamical free-energies) can be recovered from appropriate observables of the ancilla. The second one is that of quantum filters, where we show tracking a quantum system undergoing a continuous homodyne measurement with another quantum system of the same size will inherently be inefficient in our framework.

quant-ph↗

arXiv2015

Dynamical symmetries and crossovers in a three-spin system with collective dissipation

We consider the non-equilibrium dynamics of a simple system consisting of interacting spin-$1/2$ particles subjected to a collective damping. The model is close to situations that can be engineered in hybrid electro/opto-mechanical settings. Making use of large-deviation theory, we find a Gallavotti-Cohen symmetry in the dynamics of the system as well as evidence for the coexistence of two dynamical phases with different activity levels. We show that additional damping processes smoothen out this behavior. Our analytical results are backed up by Monte Carlo simulations that reveal the nature of the trajectories contributing to the different dynamical phases.

quant-ph↗

arXiv2015

Intermittency and dynamical Lee-Yang zeros of open quantum systems

We use high-order cumulants to investigate the Lee-Yang zeros of generating functions of dynamical observables in open quantum systems. At long times the generating functions take on a large deviation form with singularities of the associated cumulant generating functions - or dynamical free energies - signifying phase transitions in the ensemble of dynamical trajectories. We consider a driven three-level system as well as the dissipative Ising model. Both systems exhibit dynamical intermittency in the statistics of quantum jumps. From the short-time behavior of the dynamical Lee-Yang zeros we identify critical values of the counting field which we attribute to the observed intermittency and dynamical phase co-existence. Furthermore, for the dissipative Ising model we construct a trajectory phase diagram and estimate the value of the transverse field where the stationary state changes from being ferromagnetic (inactive) to being paramagnetic (active).

cond-mat.mes-hall↗

arXiv2014

Open quantum reaction-diffusion dynamics: absorbing states and relaxation

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 of the state towards the stationary regime via a decomposition of the system Hilbert space into transient and recurrent subspaces. We provide a complete classification of the structure of the recurrent subspace (and the non-equilibrium steady states) in terms of the dark states associated to the quantum master operator and its general spectral properties. We also show that, in one dimension, relaxation towards these absorbing dark states is slower than that predicted by a mean-field analysis due to fluctuation effects, in analogy with what occurs in classical RD systems. Numerical simulations of small systems suggest that the decay of the density in one dimension, in both the open quantum $A+A \to \varnothing$ and $A+A \to A$ cases, may go asymptotically as $t^{-b}$ with $1/2 < b < 1$.

cond-mat.stat-mech↗

arXiv2014

Dynamical phase transitions as a resource for quantum enhanced metrology

We consider the general problem of estimating an unknown control parameter of an open quantum system. We establish a direct relation between the evolution of both system and environment and the precision with which the parameter can be estimated. We show that when the open quantum system undergoes a first-order dynamical phase transition the quantum Fisher information (QFI), which gives the upper bound on the achievable precision of any measurement of the system and environment, becomes quadratic in observation time (cf. "Heisenberg scaling"). In fact, the QFI is identical to the variance of the dynamical observable that characterises the phases that coexist at the transition, and enhanced scaling is a consequence of the divergence of the variance of this observable at the transition point. This identification allows to establish the finite time scaling of the QFI. Near the transition the QFI is quadratic in time for times shorter than the correlation time of the dynamics. In the regime of enhanced scaling the optimal measurement whose precision is given by the QFI involves measuring both system and output. As a particular realisation of these ideas, we describe a theoretical scheme for quantum enhanced phase estimation using the photons being emitted from a quantum system near the coexistence of dynamical phases with distinct photon emission rates.

quant-ph↗

arXiv2014

Emergent rhombus tilings from molecular interactions with $M$-fold rotational symmetry

We show that model molecules with particular rotational symmetries can self-assemble into network structures equivalent to rhombus tilings. This assembly happens in an emergent way, in the sense that molecules spontaneously select irregular 4-fold local coordination from a larger set of possible local binding geometries. The existence of such networks can be rationalized by simple geometrical arguments, but the same arguments do not guarantee networks' spontaneous self-assembly. This class of structures must in certain regimes of parameter space be able to reconfigure into networks equivalent to triangular tilings.

cond-mat.stat-mech↗

arXiv2014

Out-of-equilibrium evolution of kinetically constrained many-body quantum systems under purely dissipative dynamics

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 "classical" observables. As a basis for illustrating our ideas we use spin systems whose dynamics becomes correlated and complex due to dynamical constraints, inspired by kinetically constrained models (KCMs) of classical glasses. We show that in the quantum case the relaxation can be orders of magnitude slower than the classical one due to the presence of quantum coherences. Aspects of these idealized quantum KCMs become manifest in a strongly interacting Rydberg gas under electromagnetically induced transparency (EIT) conditions in an appropriate limit. Beyond revealing a link between this Rydberg gas and the rather abstract dissipative KCMs of quantum glassy systems, our study sheds light on the limitations of the use of classical rate equations for capturing the non-equilibrium behavior of this many-body system.

quant-ph↗

arXiv2014

Comment on "Abrupt transition in the structural formation of interconnected networks", F. Radicchi and A. Arenas, Nature Phys. 9, 717 (2013)

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 "supra-Laplacian" operator studied. The singular changes observed are therefore not related to any collective abrupt structural transformation in the interconnected networks.

cond-mat.stat-mech↗

arXiv2014

Meta-work and the analogous Jarzynski relation in ensembles of dynamical trajectories

Recently there has been growing interest in extending the thermodynamic method from static configurations to dynamical trajectories. In this approach, ensembles of trajectories are treated in an analogous manner to ensembles of configurations in equilibrium statistical mechanics: generating functions of dynamical observables are interpreted as partition sums, and the statistical properties of trajectory ensembles are encoded in free-energy functions that can be obtained through large-deviation methods in a suitable large time limit. This establishes what one can call a 'thermodynamics of trajectories'. In this paper we go a step further, and make a first connection to fluctuation theorems by generalising them to this dynamical context. We show that an effective 'meta-dynamics' in the space of trajectories gives rise to the celebrated Jarzynski relation connecting an appropriately defined 'meta-work' with changes in dynamical generating functions. We demonstrate the potential applicability of this result to computer simulations for two open quantum systems, a two-level system and the micromaser. We finally discuss the behavior of the Jarzynski relation across a first-order trajectory phase transition.

cond-mat.stat-mech↗

arXiv2014

Excitations are localized and relaxation is hierarchical in glass-forming liquids

For several atomistic models of glass formers, at conditions below their glassy dynamics onset temperatures, ${T_\mathrm{o}}$, we use importance sampling of trajectory space to study the structure, statistics and dynamics of excitations responsible for structural relaxation. Excitations are detected in terms of persistent particle displacements of length $a$. At supercooled conditions, for $a$ of the order of or smaller than a particle diameter, we find that excitations are associated with correlated particle motions that are sparse and localized, occupying a volume with an average radius that is temperature independent and no larger than a few particle diameters. We show that the statistics and dynamics of these excitations are facilitated and hierarchical. Excitation energy scales grow logarithmically with $a$. Excitations at one point in space facilitate the birth and death of excitations at neighboring locations, and space-time excitation structures are microcosms of heterogeneous dynamics at larger scales. This nature of dynamics becomes increasingly dominant as temperature $T$ is lowered. We show that slowing of dynamics upon decreasing temperature below $T_\mathrm{o}$ is the result of a decreasing concentration of excitations and concomitant growing hierarchical length scales, and further that the structural relaxation time $τ$ follows the parabolic law, $\log(τ/ τ_\mathrm{o}) = J^2(1/T - 1/T_\mathrm{o})^2$, for $T<T_\mathrm{o}$, where $J$, $τ_\mathrm{o}$ and $T_\mathrm{o}$ can be predicted quantitatively from dynamics at short time scales. Particle motion is facilitated and directional, and we show this becomes more apparent with decreasing $T$. We show that stringlike motion is a natural consequence of facilitated, hierarchical dynamics.

cond-mat.stat-mech↗

arXiv2014

Using the s-Ensemble to Probe Glasses Formed by Cooling and Aging

From length scale distributions characterizing frozen amorphous domains, we relate the s-ensemble method with standard cooling and aging protocols for forming glass. We show that in a general class of models, where space-time scaling is in harmony with that of experiment, the domain size distributions obtained with the s-ensemble are identical to those obtained through cooling or aging, but the computational effort for applying the s-ensemble is generally many orders of magnitude smaller than that of straightforward numerical simulation of cooling or aging.

cond-mat.stat-mech↗

arXiv2014

Common physical framework explains phase behavior and dynamics of atomic, molecular and polymeric network-formers

We show that the self-assembly of a diverse collection of building blocks can be understood within a common physical framework. These building blocks, which form periodic honeycomb networks and nonperiodic variants thereof, range in size from atoms to micron-scale polymers, and interact through mechanisms as different as hydrogen bonds and covalent forces. A combination of statistical mechanics and quantum mechanics shows that one can capture the physics that governs assembly of these networks by resolving only the geometry and strength of building block interactions. The resulting framework reproduces a broad range of phenomena seen experimentally, including periodic and nonperiodic networks in thermal equilibrium, and nonperiodic supercooled and glassy networks away from equilibrium. Our results show how simple `design criteria' control assembly of a wide variety of networks, and suggest that kinetic trapping can be a useful way of making functional assemblies.

cond-mat.stat-mech↗

arXiv2014

Cumulants of time-integrated observables of closed quantum systems and PT-symmetry, with an application to the quantum Ising chain

We study the connection between the cumulants of a time-integrated observable of a quantum system and the PT-symmetry properties of the non-Hermitian deformation of the Hamiltonian from which the generating function of these cumulants is obtained. This non-Hermitian Hamiltonian can display regimes of broken and of unbroken PT-symmetry, depending on the parameters of the problem and on the counting field that sets the strength of the non-Hermitian perturbation. This in turn determines the analytic structure of the long-time cumulant generating function (CGF) for the time-integrated observable. We consider in particular the case of the time-integrated (longitudinal) magnetisation in the one-dimensional Ising model in a transverse field. We show that its long-time CGF is singular on a curve in the magnetic field/counting field plane that delimits a regime where PT-symmetry is spontaneously broken (which includes the static ferromagnetic phase), from one where it is preserved (which includes the static paramagnetic phase). In the paramagnetic phase, conservation of PT -symmetry implies that all cumulants are sub-linear in time, a behaviour usually associated to the absence of decorrelation.

cond-mat.stat-mech↗

arXiv2014

Out-of-equilibrium structures in strongly interacting Rydberg gases with dissipation

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 and largely analytical understanding of the underlying physics. By means of extensive numerical simulations we study the many-body dynamics and the correlations of the resulting non-equilibrium states in various dimensions. Our results provide insight into the dynamical richness of strongly interacting Rydberg gases in noisy environments, and highlight the usefulness of these kind of systems for the exploration of soft-matter-type collective behaviour.

cond-mat.quant-gas↗

arXiv2014

Localisation in space and time in disordered-lattice open quantum dynamics

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 the dynamics generated by the bath. We explore spatial features in the dynamics and employ a generalisation of the inverse participation ratio to deduce an ergodic timescale for the lattice.

cond-mat.stat-mech↗