Diffusion of two particles with a finite interaction potential in one dimension

Abstract

We investigate the dynamics of two interacting diffusing particles in an infinite effectively one dimensional system; the particles interact through a step-like potential of width b and height phi_0 and are allowed to pass one another. By solving the corresponding 2+1-variate Fokker-Planck equation an exact result for the two particle conditional probability density function (PDF) is obtained for arbitrary initial particle positions. From the two-particle PDF we obtain the overtake probability, i.e. the probability that the two particles has exchanged positions at time t compared to the initial configuration. In addition, we calculate the trapping probability, i.e. the probability that the two particles are trapped close to each other (within the barrier width b) at time t, which is mainly of interest for an attractive potential, phi_0<0. We also investigate the tagged particle PDF, relevant for describing the dynamics of one particle which is fluorescently labeled. Our analytic results are in excellent agreement with the results of stochastic simulations, which are performed using the Gillespie algorithm.

10 pages, 5 figures. Journal of Chemical Physics (in press)

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• Single-File diffusion in a Box
• Sequence sensitivity of breathing dynamics in heteropolymer DNA
• Nonequilibrium Dynamics in Low Dimensional Systems
• Stochastic approach to DNA breathing dynamics
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Cited by in corpus (6)

• Diffusion of Finite-Sized Hard-Core Interacting Particles In a One-Dimensional Box - Tagged Particle Dynamics
• Transition from single-file to two-dimensional diffusion of interacting particles in a quasi-one-dimensional channel
• Single-File Diffusion of Externally Driven Particles
• Order-preserving dynamics in one dimension -- single-file diffusion and caging from the perspective of dynamical density functional theory
• Single-file and normal diffusion of magnetic colloids in modulated channels
• Bubble merging in breathing DNA as a vicious walker problem in opposite potentials