Transport properties of diffusive particles conditioned to survive in trapping environments

Abstract

We consider a one-dimensional Brownian motion with diffusion coefficient $D$ in the presence of $n$ partially absorbing traps with intensity $\beta$, separated by a distance $L$ and evenly spaced around the initial position of the particle. We study the transport properties of the process conditioned to survive up to time $t$. We find that the surviving particle first diffuses normally, before it encounters the traps, then undergoes a period of transient anomalous diffusion, after which it reaches a final diffusive regime. The asymptotic regime is governed by an effective diffusion coefficient $D_{\text{eff}}$, which is induced by the trapping environment and is typically different from the original one. We show that when the number of traps is \emph{finite}, the environment enhances diffusion and induces an effective diffusion coefficient that is systematically equal to $D_{\text{eff}}=2D$, independently of the number of the traps, the trapping intensity $\beta$ and the distance $L$. On the contrary, when the number of traps is \emph{infinite}, we find that the environment inhibits diffusion with an effective diffusion coefficient that depends on the traps intensity $\beta$ and the distance $L$ through a non-trivial scaling function $D_{\text{eff}}=D\mathcal{F}(\beta L/D)$, for which we obtain a closed-form. Moreover, we provide a rejection-free algorithm to generate surviving trajectories by deriving an effective Langevin equation with an effective repulsive potential induced by the traps. Finally, we extend our results to other trapping environments.

arXiv comment28 pages, 10 figures

References in corpus (37)

• Direct evaluation of large-deviation functions
• Nonequilibrium Markov processes conditioned on large deviations
• Simulating rare events in dynamical processes
• Length scale for the onset of Fickian diffusion in supercooled liquids
• Leaking Chaotic Systems
• First-passage times for random walks in bounded domains
• Aspects of non-equilibrium in classical and quantum systems: slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics
• Chaos-assisted directional light emission from microcavity lasers
• Exact Asymptotics for One-Dimensional Diffusion with Mobile Traps
• Fractal Weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering
• Trapping Reactions with Randomly Moving Traps: Exact Asymptotic Results for Compact Exploration
• Survival probability of a diffusing particle in the presence of Poisson-distributed mobile traps
• Survival probability of a particle in a sea of mobile traps: A tale of tails
• Generating Transition Paths by Langevin Bridges
• Rare behavior of growth processes via umbrella sampling of trajectories
• Survival of classical and quantum particles in the presence of traps
• A reinforcement learning approach to rare trajectory sampling
• Formal Solution of a Class of Reaction-Diffusion Models: Reduction to a Single-Particle Problem
• Constraint Ornstein-Uhlenbeck bridges
• Resonance distribution in open quantum chaotic systems
• Non-intersecting Brownian bridges in the flat-to-flat geometry
• Effective Hamiltonians and Lagrangians for conditioned Markov processes at large volume
• Sinai model in presence of dilute absorbers
• Chaotic Systems with Absorption
• Diffusion in normal and critical transient chaos
• One-dimensional disordered quantum mechanics and Sinai diffusion with random absorbers
• Quantum Poincare Recurrences for Hydrogen Atom in a Microwave Field
• One-dimensional classical diffusion in a random force field with weakly concentrated absorbers
• Generating discrete-time constrained random walks and Lévy flights
• Survival Probability of a Ballistic Tracer Particle in the Presence of Diffusing Traps
• Generating stochastic trajectories with global dynamical constraints
• Perturbation theory for the one-dimensional trapping reaction
• Generating constrained run-and-tumble trajectories
• How to generate the tip of branching random walks evolved to large times
• Microcanonical conditioning of Markov processes on time-additive observables
• Transient subdiffusion from an Ising environment
• Winding statistics of a Brownian particle on a ring

Cited by in corpus (1)

• Run-and-tumble motion in trapping environments