Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/9806299

Asymptotic form of the approach to equilibrium in reversible recombination reactions

Pierre-Antoine Rey·John Cardy
View original source ↗Read source document ↗Export metadata ↓

Abstract

The reversible reactions A+A<=>C and A+B<=>C are investigated. From the exact Langevin equations describing our model, we set up a systematic approximation scheme to compute the approach of the density of C particles to its equilibrium value. We show that for sufficiently long time t, this approach takes the form of a power law At^(-d/2), for any dimension d. The amplitude A is also computed exactly, but is expected to be model dependent. For uncorrelated initial conditions, the C density turns out to be a monotonic time function. The cases of correlated initial conditions and unequal diffusion constants are investigated as well. In the former, correlations may break the monotonicity of the density or in some special cases they may change the long time behavior. For the latter, the power law remains valid, only the amplitude changes, even in the extreme case of immobile C particles. We also consider the case of segregated initial condition for which a reaction front is observed, and confirm that its width is governed by mean-field exponent in any dimension.

Explore related subjects

cond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Pierre-Antoine Rey, John Cardy. 1998-06-25. Asymptotic form of the approach to equilibrium in reversible recombination reactions. https://doi.org/10.1088/0305-4470%2F32%2F9%2F008

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Nonuniform asymmetric exclusion process: Stationary densities and domain walls

We compute the stationary densities in totally asymmetric exclusion processes (TASEP) with open boundary conditions and spatially nonuniform hopping rates. The stationary densities in the low and and high density phases can be discontinuous, only when the space-dependent hopping rate is spatially discontinuous. In contrast, the stationary density profile in the maximal current phase can be discontinuous, even when the space-dependent hopping rate is continuous. We further investigate the domain walls, which are delocalised with complex shapes. In striking contrast to a delocalised domain wall (DDW) in an open, uniform TASEP, these DDWs can also form at the transitions between the low or high density phases and maximal current phase, and can cover the entire TASEP channel or a part of it, depending upon the specific forms of the site-dependence of the hopping rates and the associated phase transitions. We calculate their envelopes, which are curved lines, revealing their dependence on the spatial nonuniformity of the hopping rates. The phase diagrams in the plane of the control parameters show universal topology. The associated phase transitions are explored, which can be different from their counterparts in an open uniform TASEP.

cond-mat.stat-mech↗
arXiv2026

Intermittency in Wind-Driven Fires

We construct a wind-driven forest-fire model in one dimension in which a fire can jump gaps between trees to ignite disjoint downwind forests. The size of a gap that a fire can jump depends on the fire intensity, which increases as the fire propagates through trees and diminishes as the fire jumps gaps. Trees grow on empty sites at rate $r$ and lightning strikes each site with rate $f$. When $f\ll r/L$, where $L$ is the system length, lightning is sufficiently rare that quasi-deterministic dynamics arises where all trees are consumed when a lightning-induced fire occurs. For $f\gg L^{-μ}$ with $μ\approx 0.8$, lightning is sufficiently frequent that a steady state is reached, but with unexpected behaviors for the forest- and gap-size distributions. Intermittency arises in between these regimes, with coexisting temporal domains of deterministic and chaotic dynamics.

cond-mat.stat-mech↗
arXiv2026

Uphill and downhill first passage of an active Brownian particle: Asymmetry and exact path reweighting

First passage processes in active systems combine stochastic transport with self-propulsion and orientational persistence, making motion along and against an external bias sensitive to the internal active dynamics. For passive biased diffusion, opposite exits can have different splitting probabilities while their conditional first passage time distributions remain identical. We study how this relation changes for an active Brownian particle driven by a constant external force between two absorbing boundaries. Self-propulsion breaks the equality of the uphill and downhill first passage time distributions and modifies the splitting probabilities. Nevertheless, the two directional path ensembles remain exactly related by spatial reflection, which pairs downhill and uphill first passage paths of the same duration while preserving their orientational history. The log-ratio of the probabilities of a path and its reflected partner defines a path-dependent asymmetry functional and provides an exact reweighting between the two ensembles. In the symmetric half-weighted representation, the uphill and downhill first passage time distributions coincide for arbitrary orientational persistence. The same path relation also allows rare uphill statistics to be reconstructed from the more frequently sampled downhill trajectories. Numerical simulations confirm the weighted equality across the explored bias and persistence regimes, while perturbative and asymptotic analyses clarify how orientational persistence produces the directional asymmetry of the unweighted statistics. The exact relation between the two directional path ensembles suggests that similar symmetry-based reconstruction protocols may be found in other nonequilibrium first-passage problems.

cond-mat.stat-mech↗