Absorbing State

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Ronald Dickman - One of the best experts on this subject based on the ideXlab platform.

  • traffic model with an Absorbing State phase transition
    Physical Review E, 2017
    Co-Authors: M L L Iannini, Ronald Dickman
    Abstract:

    We consider a modified Nagel-Schreckenberg (NS) model in which drivers do not decelerate if their speed is smaller than the headway (number of empty sites to the car ahead). (In the original NS model, such a reduction in speed occurs with probability $p$, independent of the headway, as long as the current speed is greater than zero.) In the modified model the free-flow State (with all vehicles traveling at the maximum speed, ${v}_{max}$) is Absorbing for densities $\ensuremath{\rho}$ smaller than a critical value ${\ensuremath{\rho}}_{c}=1/({v}_{max}+2)$. The phase diagram in the $\ensuremath{\rho}\ensuremath{-}p$ plane is reentrant: for densities in the range ${\ensuremath{\rho}}_{c,l}l\ensuremath{\rho}l{\ensuremath{\rho}}_{c}$, both small and large values of $p$ favor free flow, while for intermediate values, a nonzero fraction of vehicles have speeds $l{v}_{max}$. In addition to representing a more realistic description of driving behavior, this change leads to a better understanding of the phase transition in the original model. Our results suggest an unexpected connection between traffic models and stochastic sandpiles.

  • on the Absorbing State phase transition in the one dimensional triplet creation model
    Journal of Statistical Mechanics: Theory and Experiment, 2009
    Co-Authors: Geza Odor, Ronald Dickman
    Abstract:

    We study the lattice reaction–diffusion model , ('triplet creation') using numerical simulations and n-site approximations. The simulation results suggest that the phase transition is discontinuous at high diffusion rates. In this regime the order parameter appears to be a discontinuous function of the creation rate; no evidence of a stable interface between active and Absorbing phases is found. Based on an effective mapping to a modified compact directed percolation process, we shall nevertheless argue that the transition is continuous, despite the seemingly discontinuous phase transition suggested by studies of finite systems.

  • on the Absorbing State phase transition in the one dimensional triplet creation model
    arXiv: Statistical Mechanics, 2009
    Co-Authors: Geza Odor, Ronald Dickman
    Abstract:

    We study the lattice reaction diffusion model 3A -> 4A, A -> 0 (``triplet creation") using numerical simulations and n-site approximations. The simulation results provide evidence of a discontinuous phase transition at high diffusion rates. In this regime the order parameter appears to be a discontinuous function of the creation rate; no evidence of a stable interface between active and Absorbing phases is found. Based on an effective mapping to a modified compact directed percolation process, shall nevertheless argue that the transition is continuous, despite the seemingly discontinuous phase transition suggested by studies of finite systems.

  • the nature of the Absorbing State phase transition in the diffusive epidemic process
    Journal of Physics A, 2008
    Co-Authors: Ronald Dickman, Daniel Souza Maia
    Abstract:

    In the diffusive epidemic process (DEP), particles of two species (A and B) hop on a lattice and undergo reactions B ? A and A + B ? 2B; the B-free State is Absorbing. Renormalization group analysis predicts a continuous phase transition to the Absorbing State when the hopping rate of B particles, DB, is greater than or equal to that of A particles, and a discontinuous transition for DA > DB. Monte Carlo simulations of the one-dimensional DEP suggest that, on the contrary, the transition is continuous in all cases. Here we present strong evidence for a continuous transition for DA > DB in the two-dimensional model as well. Our results suggest that hysteresis is absent in both the one- and two-dimensional cases.

  • quasi stationary distributions for stochastic processes with an Absorbing State
    Journal of Physics A, 2002
    Co-Authors: Ronald Dickman, Ronaldo Vidigal
    Abstract:

    We study the long-time behaviour of stochastic models with an Absorbing State, conditioned on survival. For a large class of processes, in which saturation prevents unlimited growth, statistical properties of the surviving sample attain time-independent limiting values. We may then define a quasi-stationary probability distribution as one in which the ratios pn(t)/pm(t) (for any pair of non-Absorbing States n and m) are time-independent. This is not a true stationary distribution, since the overall normalization decays as probability flows irreversibly to the Absorbing State.We construct quasi-stationary solutions for the contact process on a complete graph, the Malthus–Verhulst process,

Igor Lesanovsky - One of the best experts on this subject based on the ideXlab platform.

  • numerical simulation of critical dissipative non equilibrium quantum systems with an Absorbing State
    New Journal of Physics, 2019
    Co-Authors: Edward Gillman, Federico Carollo, Igor Lesanovsky
    Abstract:

    The simulation of out-of-equilibrium dissipative quantum many body systems is a problem of fundamental interest to a number of fields in physics, ranging from condensed matter to cosmology. For unitary systems, tensor network methods have proved successful and extending these to open systems is a natural avenue for study. In particular, an important question concerns the possibility of approximating the critical dynamics of non-equilibrium systems with tensor networks. Here, we investigate this by performing numerical simulations of a paradigmatic quantum non-equilibrium system with an Absorbing State: the quantum contact process. We consider the application of matrix product States and the time-evolving block decimation algorithm to simulate the time-evolution of the quantum contact process at criticality. In the Lindblad formalism, we find that the Heisenberg picture can be used to improve the accuracy of simulations over the Schrodinger approach, which can be understood by considering the evolution of operator-space entanglement. Furthermore, we also consider a quantum trajectories approach, which we find can reproduce the expected universal behaviour of key observables for a significantly longer time than direct simulation of the average State. These improved results provide further evidence that the universality class of the quantum contact process is not directed percolation, which is the class of the classical contact process.

  • experimental signatures of an Absorbing State phase transition in an open driven many body quantum system
    European Quantum Electronics Conference, 2017
    Co-Authors: C Simonelli, Igor Lesanovsky, Matteo Archimi, Francesco Castellucci, E Arimondo, D Ciampini, Ricardo Gutierrez, Matteo Marcuzzi, O Morsch
    Abstract:

    Understanding and probing phase transitions in non-equilibrium systems is an ongoing challenge in physics. A particular instance are phase transitions that occur between a non-fluctuating Absorbing phase [1], e.g., an extinct population, and one in which the relevant order parameter, such as the population density, assumes a finite value. Here we report the observation of signatures of such a non-equilibrium phase transition in an open driven quantum system. In our experiment rubidium atoms in a quasi one-dimensional cold disordered gas are laser-excited to Rydberg States under so-called facilitation conditions [2]. This conditional excitation process competes with spontaneous decay (see Fig. 1a) and leads to a crossover between a stationary State with no excitations and one with a finite number of Rydberg excitations (see Fig. 1b, where the phase diagram is plotted as a function of the driving strength and detuning from resonance) [3]. We relate the underlying physics to that of an Absorbing State phase transition in the presence of a field which slightly offsets the system from criticality. We observe a characteristic power-law scaling of the Rydberg excitation density as well as increased fluctuations close to the transition point. Furthermore, we argue that the observed transition relies on the presence of atomic motion which introduces annealed disorder into the system and enables the formation of long-ranged correlations. Our study paves the road for future investigations into the largely unexplored physics of non-equilibrium phase transitions in open many-body quantum systems.

  • nonequilibrium effective field theory for Absorbing State phase transitions in driven open quantum spin systems
    Physical Review B, 2017
    Co-Authors: Michael Buchhold, Igor Lesanovsky, Matteo Marcuzzi, Benjamin Everest, Sebastian Diehl
    Abstract:

    Phase transitions to Absorbing States are among the simplest examples of critical phenomena out of equilibrium. The characteristic feature of these models is the presence of a fluctuationless configuration which the dynamics cannot leave, which has proved a rather stringent requirement in experiments. Recently, a proposal to seek such transitions in highly tuneable systems of cold atomic gases offers to probe this physics and, at the same time, to investigate the robustness of these transitions to quantum coherent effects. Here we specifically focus on the interplay between classical and quantum fluctuations in a simple driven open quantum model which, in the classical limit, reproduces a contact process, which is known to undergo a continuous transition in the "directed percolation" universality class. We derive an effective long-wavelength field theory for the present class of open spin systems and show that, due to quantum fluctuations, the nature of the transition changes from second to first order, passing through a bicritical point which appears to belong instead to the "tricritical directed percolation" class.

  • Absorbing State phase transition with competing quantum and classical fluctuations
    Physical Review Letters, 2016
    Co-Authors: Matteo Marcuzzi, Michael Buchhold, Sebastian Diehl, Igor Lesanovsky
    Abstract:

    Stochastic processes with Absorbing States feature examples of nonequilibrium universal phenomena. While the classical regime has been thoroughly investigated in the past, relatively little is known about the behavior of these nonequilibrium systems in the presence of quantum fluctuations. Here, we theoretically address such a scenario in an open quantum spin model which, in its classical limit, undergoes a directed percolation phase transition. By mapping the problem to a nonequilibrium field theory, we show that the introduction of quantum fluctuations stemming from coherent, rather than statistical, spin flips alters the nature of the transition such that it becomes first order. In the intermediate regime, where classical and quantum dynamics compete on equal terms, we highlight the presence of a bicritical point with universal features different from the directed percolation class in a low dimension. We finally propose how this physics could be explored within gases of interacting atoms excited to Rydberg States.

Kazumasa A Takeuchi - One of the best experts on this subject based on the ideXlab platform.

Romualdo Pastorsatorras - One of the best experts on this subject based on the ideXlab platform.

  • lifespan method as a tool to study criticality in Absorbing State phase transitions
    Physical Review E, 2015
    Co-Authors: Claudio Castellano, Angelica S Mata, Marian Boguna, Romualdo Pastorsatorras
    Abstract:

    In a recent work, a new numerical method (the lifespan method) has been introduced to study the critical properties of epidemic processes on complex networks [M. Boguna, C. Castellano, and R. Pastor-Satorras, Phys. Rev. Lett. 111, 068701 (2013)]. Here, we present a detailed analysis of the viability of this method for the study of the critical properties of generic Absorbing-State phase transitions in lattices. Focusing on the well-understood case of the contact process, we develop a finite-size scaling theory to measure the critical point and its associated critical exponents. We show the validity of the method by studying numerically the contact process on a one-dimensional lattice and comparing the findings of the lifespan method with the standard quasistationary method. We find that the lifespan method gives results that are perfectly compatible with those of quasistationary simulations and with analytical results. Our observations confirm that the lifespan method is a fully legitimate tool for the study of the critical properties of Absorbing phase transitions in regular lattices.

  • non mean field behavior of the contact process on scale free networks
    Physical Review Letters, 2006
    Co-Authors: Claudio Castellano, Romualdo Pastorsatorras
    Abstract:

    We present an analysis of the classical contact process on scale-free networks. A mean-field study, both for finite and infinite network sizes, yields an Absorbing-State phase transition at a finite critical value of the control parameter, characterized by a set of exponents depending on the network structure. Since finite size effects are large and the infinite network limit cannot be reached in practice, a numerical study of the transition requires the application of finite size scaling theory. Contrary to other critical phenomena studied previously, the contact process in scale-free networks exhibits a nontrivial critical behavior that cannot be quantitatively accounted for by mean-field theory.

  • sandpiles and Absorbing State phase transitions recent results and open problems
    arXiv: Condensed Matter, 2000
    Co-Authors: Miguel A Munoz, Romualdo Pastorsatorras, Ronald Dickman, Alessandro Vespignani, Stefano Zapperi
    Abstract:

    We review some recent results on the relations between sandpiles and a class of Absorbing State phase transitions. We use the concept of fixed energy sandpiles (FES), in which external driving and dissipation are absent. FES are shown to exhibit an Absorbing State transition with critical properties coinciding with those of the corresponding sandpile model. We propose a set of Langevin equations capturing the relevant features of this transition. These equations characterize the universality class of systems with an infinite number of Absorbing States and a static conserved field coupled to the order parameter. Different models in this class are identified, and strong evidence is presented showing that the Manna sandpile, as well as some other stochastic sandpiles, belong in this universality class. Finally some open problems and questions are discussed.

Carlo Vanderzande - One of the best experts on this subject based on the ideXlab platform.

  • Absorbing State phase transitions with quenched disorder
    Physical Review E, 2004
    Co-Authors: Jef Hooyberghs, Ferenc Igloi, Carlo Vanderzande
    Abstract:

    Quenched disorder---in the sense of the Harris criterion---is generally a relevant perturbation at an Absorbing State phase transition point. Here using a strong disorder renormalization group framework and effective numerical methods we study the properties of random fixed points for systems in the directed percolation universality class. For strong enough disorder the critical behavior is found to be controlled by a strong disorder fixed point, which is isomorph with the fixed point of random quantum Ising systems. In this fixed point dynamical correlations are logarithmically slow and the static critical exponents are conjecturedly exact for one-dimensional systems. The renormalization group scenario is confronted with numerical results on the random contact process in one and two dimensions and satisfactory agreement is found. For weaker disorder the numerical results indicate static critical exponents which vary with the strength of disorder, whereas the dynamical correlations are compatible with two possible scenarios. Either they follow a power-law decay with a varying dynamical exponent, like in random quantum systems, or the dynamical correlations are logarithmically slow even for a weak disorder. For models in the parity conserving universality class there is no strong disorder fixed point according to our renormalization group analysis.

  • strong disorder fixed point in Absorbing State phase transitions
    Physical Review Letters, 2003
    Co-Authors: Jef Hooyberghs, Ferenc Igloi, Carlo Vanderzande
    Abstract:

    The effect of quenched disorder on nonequilibrium phase transitions in the directed percolation universality class is studied by a strong disorder renormalization group approach and by density matrix renormalization group calculations. We show that for sufficiently strong disorder the critical behavior is controlled by a strong disorder fixed point and in one dimension the critical exponents are conjectured to be exact: $\ensuremath{\beta}=(3\ensuremath{-}\sqrt{5})/2$ and ${\ensuremath{\nu}}_{\ensuremath{\perp}}=2$. For disorder strengths outside the attractive region of this fixed point, disorder dependent critical exponents are detected. Existing numerical results in two dimensions can be interpreted within a similar scenario.