$A+ A \to \emptyset$ reaction for particles with a dynamic bias to move away from their nearest neighbour in one dimension

Roy, Reshmi; Sen, Parongama

doi:10.48550/arxiv.2004.01472

Cited by 2 publications

(4 citation statements)

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“…Here we study both the macroscopic dynamical features as well as the tagged particle dynamics. The results, as expected, reveal interesting differences when compared to those for asynchronous dynamics [4][5][6]. In particular.…”

Section: Introductionsupporting

confidence: 69%

“…Leading order time and ǫ dependence of several quantities in one dimensional A + A → ∅ model. Results for asynchronous dynamics are quoted from references [3,5,6]. Notation used: generic.…”

Section: Table Imentioning

confidence: 99%

“…The A + A → ∅ system has been studied in the recent past where the particles A move with a bias towards or away from their nearest neighbours [3][4][5][6][7][8][9]. The annihilation process is not directly affected by the bias which governs only the direction of motion but this extension leads to drastic changes in the dynamical properties.…”

Section: Introductionmentioning

confidence: 99%

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$A+ A \to \emptyset$ system in one dimension with particle motion determined by nearest neighbour distances: results for parallel updates

Roy,

Sen,

Ray

2020

Preprint

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A one dimensional A + A → ∅ system where the direction of motion of the particles is determined by the position of the nearest neighours is studied. The particles move with a probability 0.5 + ǫ towards their nearest neighbours with −0.5 ≤ ǫ ≤ 0.5. This implies a stochastic motion towards the nearest neighbour or away from it for positive and negative values of ǫ respectively, with ǫ = ± 0.5 the two deterministic limits. The position of the particles are updated in parallel. The macroscopic as well as tagged particle dynamics are studied which show drastic changes from the diffusive case ǫ = 0. The decay of particle density shows departure from the usual power law behaviour as found in ǫ = 0, on both sides of ǫ = 0 and a scaling regime is obtained for ǫ > 0. The ǫ = 0.5 point is characterized by the presence of dimers, which are isolated pairs of particles in adjacent sites that are never annihilated. The persistence probability is also calculated that decays in a stretched exponential manner for ǫ < 0 and switches over to power law behaviour for ǫ ≥ 0, with different exponents for ǫ = 0 and ǫ > 0. For the tagged particle, the probability distribution Π(x, t) that it is at position x at time t shows the existence of a scaling variable x/t ν where ν = 0.55 ± 0.05 for ǫ > 0 and varies with ǫ for ǫ < 0. Finally, a comparative analysis for the behaviour of all the relevant quantities for the system using parallel and asynchronous dynamics (studied recently) shows that there are significant differences for ǫ > 0 while the results are qualitatively similar for ǫ < 0.

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Section: Introductionsupporting

confidence: 69%

Section: Table Imentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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$A+ A \to \emptyset$ system in one dimension with particle motion determined by nearest neighbour distances: results for parallel updates

Roy,

Sen,

Ray

2020

Preprint

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“…We would like to comment on a recent numerical work [23] of the AWL for σ = 0 and positive ε, which claims that ρ(t) behaves as (ln t) −b with b to vary continuously, depending on ε. We think, however, the neglect of ln ln t correction [21] errorneously gives this conclusion.…”

Section: Modelmentioning

confidence: 99%

Branching annihilating random walk with long-range repulsion: logarithmic scaling, reentrant phase transitions, and crossover behaviors

Park¹

2020

Preprint

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We study absorbing phase transitions in the one-dimensional branching annihilating random walk with long-range repulsion. The repulsion is implemented as hopping bias in such a way that a particle is more likely to hop away from its closest particle. The bias strength due to long-range interaction has the form εx −σ , where x is the distance from a particle to its closest particle, 0 ≤ σ ≤ 1, and the sign of ε determines whether the interaction is repulsive (positive ε) or attractive (negative ε). A state without particles is the absorbing state. We find a threshold εs such that the absorbing state is dynamically stable for small branching rate q if ε < εs. The threshold differs significantly, depending on parity of the number ℓ of offspring. When ε > εs, the system with odd ℓ can exhibit reentrant phase transitions from the active phase with nonzero steady-state density to the absorbing phase, and back to the active phase. On the other hand, the system with even ℓ is in the active phase for nonzero q if ε > εs. Still, there are reentrant phase transitions for ℓ = 2. Unlike the case of odd ℓ, however, the reentrant phase transitions can occur only for σ = 1 and 0 < ε < εs. We also study the crossover behavior for ℓ = 2 when the interaction is attractive (negative ε), to find the crossover exponent φ = 1.123(13) for σ = 0.

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$A+ A \to \emptyset$ reaction for particles with a dynamic bias to move away from their nearest neighbour in one dimension

Cited by 2 publications

References 10 publications

$A+ A \to \emptyset$ system in one dimension with particle motion determined by nearest neighbour distances: results for parallel updates

$A+ A \to \emptyset$ system in one dimension with particle motion determined by nearest neighbour distances: results for parallel updates

Branching annihilating random walk with long-range repulsion: logarithmic scaling, reentrant phase transitions, and crossover behaviors

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