*Phys Rev E ; 106(1-1): 014128, 2022 Jul.*

##### RESUMO

The Fredkin spin chain serves as an interesting theoretical example of a quantum Hamiltonian whose ground state exhibits a phase transition between three distinct phases, one of which violates the area law. Here we consider a classical stochastic version of the Fredkin model, which can be thought of as a simple exclusion process subject to additional kinetic constraints, and study its classical stochastic dynamics. The ground-state phase transition of the quantum chain implies an equilibrium phase transition in the stochastic problem, whose properties we quantify in terms of numerical matrix product states (MPSs). The stochastic model displays slow dynamics, including power-law decaying autocorrelation functions and hierarchical relaxation processes due to exponential localization. Like in other kinetically constrained models, the Fredkin chain has a rich structure in its dynamical large deviations-which we compute accurately via numerical MPSs-including an active-inactive phase transition and a hierarchy of trajectory phases connected to particular equilibrium states of the model. We also propose, via its height field representation, a generalization of the Fredkin model to two dimensions in terms of constrained dimer coverings of the honeycomb lattice.

*Phys Rev E ; 105(4-1): 044121, 2022 Apr.*

##### RESUMO

We study in detail an open quantum generalization of a classical kinetically constrained model-the East model-known to exhibit slow glassy dynamics stemming from a complex hierarchy of metastable states with distinct lifetimes. Using the recently introduced theory of classical metastability for open quantum systems, we show that the driven open quantum East model features a hierarchy of classical metastabilities at low temperature and weak driving field. We find that the effective long-time description of its dynamics not only is classical, but shares many properties with the classical East model, such as obeying an effective detailed balance condition and lacking static interactions between excitations, but with this occurring within a modified set of metastable phases which are coherent, and with an effective temperature that is dependent on the coherent drive.

*Phys Rev E ; 105(3-1): 034124, 2022 Mar.*

##### RESUMO

We study the dynamics and statistics of the Rule 150 reversible cellular automaton (RCA). This is a one-dimensional lattice system of binary variables with synchronous (Floquet) dynamics that corresponds to a bulk deterministic and reversible discretized version of the kinetically constrained "exclusive one-spin facilitated" (XOR) Fredrickson-Andersen (FA) model, where the local dynamics is restricted: A site flips if and only if its adjacent sites are in different states from each other. Similar to other RCA that have been recently studied, such as Rule 54 and Rule 201, the Rule 150 RCA is integrable, however, in contrast is noninteracting: The emergent quasiparticles, which are identified by the domain walls, behave as free fermions. This property allows us to solve the model by means of matrix product ansatz. In particular, we find the exact equilibrium and nonequilibrium stationary states for systems with closed (periodic) and open (stochastic) boundaries, respectively, resolve the full spectrum of the time evolution operator and, therefore, gain access to the relaxation dynamics, and obtain the exact large deviation statistics of dynamical observables in the long-time limit.

*Phys Rev Lett ; 128(9): 090605, 2022 Mar 04.*

##### RESUMO

Recent work has shown the effectiveness of tensor network methods for computing large deviation functions in constrained stochastic models in the infinite time limit. Here we show that these methods can also be used to study the statistics of dynamical observables at arbitrary finite time. This is a harder problem because, in contrast to the infinite time case, where only the extremal eigenstate of a tilted Markov generator is relevant, for finite time the whole spectrum plays a role. We show that finite time dynamical partition sums can be computed efficiently and accurately in one dimension using matrix product states and describe how to use such results to generate rare event trajectories on demand. We apply our methods to the Fredrickson-Andersen and East kinetically constrained models and to the symmetric simple exclusion process, unveiling dynamical phase diagrams in terms of counting field and trajectory time. We also discuss extensions of this method to higher dimensions.

*Phys Rev E ; 104(1-1): 014108, 2021 Jul.*

##### RESUMO

We derive a general scheme to obtain quantum fluctuation relations for dynamical observables in open quantum systems. For concreteness, we consider Markovian nonunitary dynamics that is unraveled in terms of quantum jump trajectories and exploit techniques from the theory of large deviations like the tilted ensemble and the Doob transform. Our results here generalize to open quantum system fluctuation relations previously obtained for classical Markovian systems and add to the vast literature on fluctuation relations in the quantum domain, but without resorting to the standard two-point measurement scheme. We illustrate our findings with three examples to highlight and discuss the main features of our general result.

*Phys Rev E ; 103(6-1): 062144, 2021 Jun.*

##### RESUMO

The large deviation statistics of dynamical observables is encoded in the spectral properties of deformed Markov generators. Recent works have shown that tensor network methods are well suited to compute accurately the relevant leading eigenvalues and eigenvectors. However, the efficient generation of the corresponding rare trajectories is a harder task. Here, we show how to exploit the matrix product state approximation of the dominant eigenvector to implement an efficient sampling scheme which closely resembles the optimal (so-called "Doob") dynamics that realizes the rare events. We demonstrate our approach on three well-studied lattice models, the Fredrickson-Andersen and East kinetically constrained models, and the symmetric simple exclusion process. We discuss how to generalize our approach to higher dimensions.

*J Chem Phys ; 155(13): 134105, 2021 Oct 07.*

##### RESUMO

We present a method to probe rare molecular dynamics trajectories directly using reinforcement learning. We consider trajectories that are conditioned to transition between regions of configuration space in finite time, such as those relevant in the study of reactive events, and trajectories exhibiting rare fluctuations of time-integrated quantities in the long time limit, such as those relevant in the calculation of large deviation functions. In both cases, reinforcement learning techniques are used to optimize an added force that minimizes the Kullback-Leibler divergence between the conditioned trajectory ensemble and a driven one. Under the optimized added force, the system evolves the rare fluctuation as a typical one, affording a variational estimate of its likelihood in the original trajectory ensemble. Low variance gradients employing value functions are proposed to increase the convergence of the optimal force. The method we develop employing these gradients leads to efficient and accurate estimates of both the optimal force and the likelihood of the rare event for a variety of model systems.

*Phys Rev E ; 102(5-1): 052132, 2020 Nov.*

##### RESUMO

We study a one-dimensional classical stochastic kinetically constrained model (KCM) inspired by Rydberg atoms in their "facilitated" regime, where sites can flip only if a single of their nearest neighbors is excited. We call this model "XOR-FA" to distinguish it from the standard Fredrickson-Andersen (FA) model. We describe the dynamics of the XOR-FA model, including its relation to simple exclusion processes in its domain wall representation. The interesting relaxation dynamics of the XOR-FA is related to the prominence of large dynamical fluctuations that lead to phase transitions between active and inactive dynamical phases as in other KCMs. By means of numerical tensor network methods we study in detail such transitions in the dynamical large deviation regime.

*Phys Rev E ; 101(6-1): 062142, 2020 Jun.*

##### RESUMO

We extend previous work to describe a class of fluctuation relations (FRs) that emerge as a consequence of symmetries at the level of stochastic trajectories in Markov chains. We prove that given such a symmetry, and for a suitable dynamical observable, it is always possible to obtain a FR under a biased dynamics corresponding to the so-called generalized Doob transform. The general transformations of the dynamics that we consider go beyond time-reversal or spatial isometries, and an implication is the existence of FRs for observables irrespective of their behavior under time reversal, for example for time-symmetric observables rather than currents. We further show how to deduce in the long-time limit these FRs from the symmetry properties of the generator of the dynamics. We illustrate our results with four examples that highlight the novel features of our work.

*Phys Rev E ; 102(6-1): 062107, 2020 Dec.*

##### RESUMO

We study the dynamics of a bulk deterministic Floquet model, the Rule 201 synchronous one-dimensional reversible cellular automaton (RCA201). The system corresponds to a deterministic, reversible, and discrete version of the PXP model, whereby a site flips only if both its nearest neighbors are unexcited. We show that the RCA201 (Floquet-PXP) model exhibits ballistic propagation of interacting quasiparticles-or solitons-corresponding to the domain walls between nontrivial threefold vacuum states. Starting from the quasiparticle picture, we find the exact matrix product state form of the nonequilibrium stationary state for a range of boundary conditions, including both periodic and stochastic. We discuss further implications of the integrability of the model.

*Phys Rev Lett ; 123(20): 200601, 2019 Nov 15.*

##### RESUMO

Here we demonstrate that tensor network techniques-originally devised for the analysis of quantum many-body problems-are well suited for the detailed study of rare event statistics in kinetically constrained models (KCMs). As concrete examples, we consider the Fredrickson-Andersen and East models, two paradigmatic KCMs relevant to the modeling of glasses. We show how variational matrix product states allow us to numerically approximate-systematically and with high accuracy-the leading eigenstates of the tilted dynamical generators, which encode the large deviation statistics of the dynamics. Via this approach, we can study system sizes beyond what is possible with other methods, allowing us to characterize in detail the finite size scaling of the trajectory-space phase transition of these models, the behavior of spectral gaps, and the spatial structure and "entanglement" properties of dynamical phases. We discuss the broader implications of our results.

*Phys Rev Lett ; 123(10): 100602, 2019 Sep 06.*

##### RESUMO

We present a model for glassy dynamics in supercooled liquid mixtures. Given the relaxation behavior of individual supercooled liquids, the model predicts the relaxation times of their mixtures as temperature is decreased. The model is based on dynamical facilitation theory for glassy dynamics, which provides a physical basis for relaxation and vitrification of a supercooled liquid. This is in contrast to empirical linear interpolations such as the Gordon-Taylor equation typically used to predict glass transition temperatures of liquid mixtures. To understand the behavior of supercooled liquid mixtures we consider a multicomponent variant of the kinetically constrained East model in which components have a different energy scale and can also diffuse when locally mobile regions, i.e., excitations, are present. Using a variational approach we determine an effective single component model with a single effective energy scale that best approximates a mixture. When scaled by this single effective energy, we show that experimental relaxation times of many liquid mixtures all collapse onto the "parabolic law" predicted by dynamical facilitation theory. The model can be used to predict transport properties and glass transition temperatures of mixtures of glassy materials, with implications in atmospheric chemistry, biology, and pharmaceuticals.

*Phys Rev E ; 100(2-1): 020103, 2019 Aug.*

##### RESUMO

We study the statistical properties of the long-time dynamics of the rule 54 reversible cellular automaton (CA), driven stochastically at its boundaries. This CA can be considered as a discrete-time and deterministic version of the Fredrickson-Andersen kinetically constrained model (KCM). By means of a matrix product ansatz, we compute the exact large deviation cumulant generating functions for a wide range of time-extensive observables of the dynamics, together with their associated rate functions and conditioned long-time distributions over configurations. We show that for all instances of boundary driving the CA dynamics occurs at the point of phase coexistence between competing active and inactive dynamical phases, similar to what happens in more standard KCMs. We also find the exact finite size scaling behavior of these trajectory transitions, and provide the explicit "Doob-transformed" dynamics that optimally realizes rare dynamical events.

*Phys Rev E ; 100(1-1): 012110, 2019 Jul.*

##### RESUMO

Dense Rydberg gases are out-of-equilibrium systems where strong density-density interactions give rise to effective kinetic constraints. They cause dynamic arrest associated with highly constrained many-body configurations, leading to slow relaxation and glassy behavior. Multicomponent Rydberg gases feature additional long-range interactions such as excitation exchange. These are analogous to particle swaps used to artificially accelerate relaxation in simulations of atomistic models of classical glass formers. In Rydberg gases, however, swaps are real physical processes, which provide dynamical shortcuts to relaxation. They permit the accelerated approach to stationarity in experiment and at the same time have an impact on the nonequilibrium stationary state. In particular, their interplay with radiative decay processes amplifies irreversibility of the dynamics, an effect which we quantify via the entropy production at stationarity. Our work highlights an intriguing analogy between real dynamical processes in Rydberg gases and artificial dynamics underlying advanced Monte Carlo methods. Moreover, it delivers a quantitative characterization of the dramatic effect swaps have on the structure and dynamics of their stationary state.

*Nat Commun ; 10(1): 2932, 2019 Jul 03.*

##### RESUMO

The regular packing of atoms, molecules and nanoparticles provides the basis for the understanding of structural order within condensed phases of matter. Typically the constituent particles are considered to be rigid with a fixed shape. Here we show, through a combined experimental and numerical study of the adsorption of cyclic porphyrin polymers, nanorings, on a graphite surface, that flexible molecules can exhibit a rich and complex packing behaviour. Depending on the number of porphyrin sub-units within the nanoring we observe either a highly ordered hexagonal phase or frustrated packing driven by directional interactions which for some arrangements is combined with the internal deformation of the cyclic polymer. Frustration and deformation occur in arrays of polymers with ten sub-units since close packing and co-alignment of neighbouring groups cannot be simultaneously realised for nanorings with this internal symmetry.

*Phys Rev Lett ; 122(13): 130605, 2019 Apr 05.*

##### RESUMO

We analyze dynamical large deviations of quantum trajectories in Markovian open quantum systems in their full generality. We derive a quantum level-2.5 large deviation principle for these systems, which describes the joint fluctuations of time-averaged quantum jump rates and of the time-averaged quantum state for long times. Like its level-2.5 counterpart for classical continuous-time Markov chains (which it contains as a special case), this description is both explicit and complete, as the statistics of arbitrary time-extensive dynamical observables can be obtained by contraction from the explicit level-2.5 rate functional we derive. Our approach uses an unraveled representation of the quantum dynamics which allows these statistics to be obtained by analyzing a classical stochastic process in the space of pure states. For quantum reset processes we show that the unraveled dynamics is semi-Markovian and derive bounds on the asymptotic variance of the number of quantum jumps which generalize classical thermodynamic uncertainty relations. We finish by discussing how our level-2.5 approach can be used to study large deviations of nonlinear functions of the state, such as measures of entanglement.

*Phys Rev Lett ; 121(13): 130601, 2018 Sep 28.*

##### RESUMO

Thermodynamic uncertainty relations (TURs) are recently established relations between the relative uncertainty of time-integrated currents and entropy production in nonequilibrium systems. For small perturbations away from equilibrium, linear response (LR) theory provides the natural framework to study generic nonequilibrium processes. Here, we use LR to derive TURs in a straightforward and unified way. Our approach allows us to generalize TURs to systems without local time-reversal symmetry, including, e.g., ballistic transport and periodically driven classical and quantum systems. We find that, for broken time reversal, the bounds on the relative uncertainty are controlled both by dissipation and by a parameter encoding the asymmetry of the Onsager matrix. We illustrate our results with an example from mesoscopic physics. We also extend our approach beyond linear response: for Markovian dynamics, it reveals a connection between the TUR and current fluctuation theorems.

*Phys Rev E ; 98(2-1): 022129, 2018 Aug.*

##### RESUMO

We study the spectral properties of classical and quantum Markovian processes that are reset at random times to a specific configuration or state with a reset rate that is independent of the current state of the system. We demonstrate that this simple reset dynamics causes a uniform shift in the eigenvalues of the Markov generator, excluding the zero mode corresponding to the stationary state, which has the effect of accelerating or even inducing relaxation to a stationary state. Based on this result, we provide expressions for the stationary state and probability current of the reset process in terms of weighted sums over dynamical modes of the reset-free process. We also discuss the effect of resets on processes that display metastability. We illustrate our results with two classical stochastic processes, the totally asymmetric random walk and the one-dimensional Brownian motion, as well as two quantum models: a particle coherently hopping on a chain and the dissipative transverse field Ising model, known to exhibit metastability.

*Phys Rev Lett ; 121(4): 040603, 2018 Jul 27.*

##### RESUMO

One of the general mechanisms that give rise to the slow cooperative relaxation characteristic of classical glasses is the presence of kinetic constraints in the dynamics. Here we show that dynamical constraints can similarly lead to slow thermalization and metastability in translationally invariant quantum many-body systems. We illustrate this general idea by considering two simple models: (i) a one-dimensional quantum analogue to classical constrained lattice gases where excitation hopping is constrained by the state of neighboring sites, mimicking excluded-volume interactions of dense fluids; and (ii) fully packed quantum dimers on the square lattice. Both models have a Rokhsar-Kivelson (RK) point at which kinetic and potential energy constants are equal. To one side of the RK point, where kinetic energy dominates, thermalization is fast. To the other, where potential energy dominates, thermalization is slow, memory of initial conditions persists for long times, and separation of timescales leads to pronounced metastability before eventual thermalization. Furthermore, in analogy with what occurs in the relaxation of classical glasses, the slow-thermalization regime displays dynamical heterogeneity as manifested by spatially segregated growth of entanglement.

*Phys Rev Lett ; 120(26): 260602, 2018 Jun 29.*

##### RESUMO

We demonstrate pretransition effects in space-time in trajectories of systems in which the dynamics displays a first-order phase transition between distinct dynamical phases. These effects are analogous to those observed for thermodynamic first-order phase transitions, most notably the hydrophobic effect in water. Considering the (infinite temperature) East model as an elementary example, we study the properties of "space-time solvation" by examining trajectories where finite space-time regions are conditioned to be inactive in an otherwise active phase. We find that solvating an inactive region of space-time within an active trajectory shows two regimes in the dynamical equivalent of solvation free energy: an "entropic" small solute regime in which uncorrelated fluctuations are sufficient to evacuate activity from the solute, and an "energetic" large solute regime which involves the formation of a solute-induced inactive domain with an associated active-inactive interface bearing a dynamical interfacial tension. We also show that as a result of this dynamical interfacial tension there is a dynamical analog of the hydrophobic collapse that drives the assembly of large hydrophobes in water. We discuss the general relevance of these results to the properties of dynamical fluctuations in systems with slow collective relaxation such as glass formers.