In this review, we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such ...as random walk and random acceleration problems, we progressively discuss the persistence properties in systems with many degrees of freedom. These systems include spin models undergoing phase-ordering dynamics, diffusion equation, fluctuating interfaces, etc. Persistence properties are nontrivial in these systems as the effective underlying stochastic process is non-Markovian. Several exact and approximate methods have been developed to compute the persistence of such non-Markov processes over the last two decades, as reviewed in this article. We also discuss various generalizations of the local site persistence probability. Persistence in systems with quenched disorder is discussed briefly. Although the main emphasis of this review is on the theoretical developments on persistence, we briefly touch upon various experimental systems as well.
We unravel the nonequilibrium correlated quantum quench dynamics of an impurity traveling through a harmonically confined Bose-Einstein condensate in one-dimension. For weak repulsive interspecies ...interactions the impurity oscillates within the bosonic gas. At strong repulsions and depending on its prequench position the impurity moves towards an edge of the bosonic medium and subsequently equilibrates. This equilibration being present independently of the initial velocity, the position and the mass of the impurity is inherently related to the generation of entanglement in the many-body system. Focusing on attractive interactions the impurity performs a damped oscillatory motion within the bosonic bath, a behavior that becomes more evident for stronger attractions. To elucidate our understanding of the dynamics an effective potential picture is constructed. The effective mass of the emergent quasiparticle is measured and found to be generically larger than the bare one, especially for strong attractions. In all cases, a transfer of energy from the impurity to the bosonic medium takes place. Finally, by averaging over a sample of simulated in situ single-shot images we expose how the single-particle density distributions and the two-body interspecies correlations can be probed.
Kibble–Zurek mechanism in colloidal monolayers Deutschländer, Sven; Dillmann, Patrick; Maret, Georg ...
Proceedings of the National Academy of Sciences - PNAS,
06/2015, Volume:
112, Issue:
22
Journal Article
Peer reviewed
Open access
Significance Spontaneous symmetry breaking describes a variety of transformations from high- to low-temperature phases and applies to cosmological concepts as well as atomic systems. T. W. B. Kibble ...suggested defect structures (domain walls, strings, and monopoles) to appear during the expansion and cooling of the early universe. The lack of such defects within the visible horizon of the universe mainly motivated inflationary Big Bang theories. W. H. Zurek pointed out that the same principles are relevant within the laboratory when a system obeying a second-order phase transition is cooled at finite rates into the low symmetry phase. Using a colloidal system, we visualize the Kibble–Zurek mechanism on single particle level and clarify its nature in the background of an established microscopic melting formalism.
The Kibble–Zurek mechanism describes the evolution of topological defect structures like domain walls, strings, and monopoles when a system is driven through a second-order phase transition. The model is used on very different scales like the Higgs field in the early universe or quantum fluids in condensed matter systems. A defect structure naturally arises during cooling if separated regions are too far apart to communicate (e.g., about their orientation or phase) due to finite signal velocity. This lack of causality results in separated domains with different (degenerated) locally broken symmetry. Within this picture, we investigate the nonequilibrium dynamics in a condensed matter analog, a 2D ensemble of colloidal particles. In equilibrium, it obeys the so-called Kosterlitz–Thouless–Halperin–Nelson–Young (KTHNY) melting scenario with continuous (second order-like) phase transitions. The ensemble is exposed to a set of finite cooling rates covering roughly three orders of magnitude. Along this process, we analyze the defect and domain structure quantitatively via video microscopy and determine the scaling of the corresponding length scales as a function of the cooling rate. We indeed observe the scaling predicted by the Kibble–Zurek mechanism for the KTHNY universality class.
Dynamic Gardner cross-over in a simple glass Liao, Qinyi; Berthier, Ludovic; Zhou, Hai-Jun ...
Proceedings of the National Academy of Sciences - PNAS,
06/2023, Volume:
120, Issue:
26
Journal Article
Peer reviewed
Open access
The criticality of the jamming transition responsible for amorphous solidification has been theoretically linked to the marginal stability of a thermodynamic Gardner phase. While the critical ...exponents of jamming appear independent of the preparation history, the pertinence of Gardner physics far from equilibrium is an open question. To fill this gap, we numerically study the nonequilibrium dynamics of hard disks compressed toward the jamming transition using a broad variety of protocols. We show that dynamic signatures of Gardner physics can be disentangled from the aging relaxation dynamics. We thus define a generic dynamic Gardner cross-over regardless of the history. Our results show that the jamming transition is always accessed by exploring increasingly complex landscape, resulting in anomalous microscopic relaxation dynamics that remains to be understood theoretically.
In this paper, we present a novel operator theoretic framework for optimal placement of actuators and sensors in nonlinear systems. The problem is motivated by its application to control of ...nonequilibrium dynamics in the form of temperature in building systems and control of oil spill in oceanographic flow. The controlled evolution of a passive scalar field, modeling the temperature distribution or density of oil dispersant, is governed by a linear advection partial differential equation (PDE) with spatially located actuators and sensors. Spatial locations of actuators and sensors are optimized to maximize the controllability and observability regions of the linear advection PDE. Linear transfer Perron–Frobenius and Koopman operators, associated with the advective velocity field, are used to provide an analytical characterization for the controllable and observable spaces of the advection PDE. Set-oriented numerical methods are proposed for the finite dimensional approximation of the linear transfer operators. The finite dimensional approximation is shown to introduce weaker notion of controllability and observability, referred to as coarse controllability and observability. The finite dimensional approximation is used to formulate the optimization problem for the optimal placement of sensors and actuators. The optimal placement problem is a combinatorial optimization problem. However, the positivity property of the linear transfer operator is exploited to provide an exact solution to the optimal placement problem using greedy algorithm. Application of the framework is demonstrated for the placement of sensors in a building system for the detection of contaminants and for optimal release of dispersant location for control of contaminant in a Double Gyre velocity field. Simulation results reveal interesting connections between the optimal location of actuators and sensors, maximizing the controllability and observability regions respectively, and the coherent structures in the fluid flow.
Understanding the ultrafast electron transfer (ET) processes involving various vibronic excitation in biological systems remains challenging and requires well-defined model proteins for in-depth ...studies. In this work, we selected three types of mutants with different ET lifetimes in flavodoxin to explore the excitation dependence of the photo-induced ET dynamics. For the ultrafast ET processes within the time window of intramolecular vibrational relaxation, with increasing excitation energies, we observed no change of ET lifetimes but with higher vibrational excitation in products, both of which can be attributed to the unique nature of ultrafast ET. For the slower ET, we did not find any dependence of product vibration excitation relative to the initial different excitation due to the complete vibrational relaxation. These results strongly indicate the vibrational energy can be propagated to the subsequent reactions during ultrafast ET processes.
Single molecule force spectroscopy probes the strength, lifetime, and energetic details of intermolecular interactions in a simple experiment. A growing number of these studies have reported ...distinctly nonlinear trends in rupture force with loading rate that are typically explained in conventional models by invoking complex escape pathways. Recent analyses suggested that these trends should be expected even for simple barriers based on the basic assumptions of bond rupture dynamics and thus may represent the norm rather than the exception. Here we explore how these nonlinear trends reflect the two fundamental regimes of bond rupture: (i) a near-equilibrium regime, produced either by bond reforming in the case of a single bond or by asynchronized rupture of multiple individual bonds, and (ii) a kinetic regime produced by fast, non-equilibrium bond rupture. We analyze both single-and multibonded cases, describe the full evolution of the system as it transitions between near-and far-from-equilibrium loading regimes, and show that both interpretations produce essentially identical force spectra. Data from 10 different molecular systems show that this model provides a comprehensive description of force spectra for a diverse suite of bonds over experimentally relevant loading rates, removes the inconsistencies of previous interpretations of transition state distances, and gives ready access to both kinetic and thermodynamic information about the interaction. These results imply that single-molecule binding free energies for a vast number of bonds have already been measured.
We study a model of competition between two types evolving as branching random walks on Z(d). The two types are represented by red and blue balls, respectively, with the rule that balls of different ...colour annihilate upon contact. We consider initial configurations in which the sites of Z(d) contain one ball each which are independently coloured red with probability p and blue otherwise. We address the question of fixation, referring to the sites and eventually settling for a given colour or not. Under a mild moment condition on the branching rule, we prove that the process will fixate almost surely for p not equal 1/2 and that every site will change colour infinitely often almost surely for the balanced initial condition p = 1/2.
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