Mean First Passage Time in Single File Dynamics

Abstract

We derive the general scaling law of the mean first passage time (MFPT) in single file dynamics; the process where many real particles move in a channel of length L with absorbing boundaries, where the particles and the channel have about the same cross section. We derive the relation MFPT ∼ f(n)MFPTfree, here we compute the MFPT when the channel is free (all particles are absorbed, where the average is over many trajectories), n is the number of particles in the channel at initiation, f(n) is the many-particle effect and the quantity MFPTfree is the MFPT of the free particle. When at initiation the density is fixed in basic files f(n) ∼n and therefore e.g. MFPT ∼ L2.5 (basic stochastic dynamics). We also compute the MFPT in diverse files; for example, in a file with heterogeneous particles, in deterministic files, in slow files and in files with long-range interactions. When the particle density is not fixed yet scales with 1/length from the origin, f(n) < n; yet, interactions might increase (attractive) or decrease (repulsive) the many-particle effect relative to n. In slow files, MFPT ∼ L3 (in the number of jumps). We explain these valuable results with various methods and approaches, e.g., we derive a general mapping from the mean square displacement scaling law to the MFPT scaling law. We also connect the results with real life activities. Special Issue Comments: Mean first passage scaling law in single file dynamics and various particular results in files are derived in this project. The project is related to the Special Issue projects about heterogeneous files and slow files,27 expansions in files,26 files with force32 and the first passage time in files.23