2007/03/06 by Pratap Kumar Das, Pratap K. Das, Subinay Dasgupta +1 · 2 citations
Mathematics · Physics and Astronomy · #Domain (mathematical analysis) #Dynamics (music) #Function (biology) #Ising model #Probability density function #Quantum many-body systems #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Zero (linguistics) #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1088/1751-8113/40/23/001
published in Journal of Physics A Mathematical and Theoretical 40(23), 6013-6022 (Institute of Physics) · 6 pages, 7 figures
arxiv created 2007/03/06 · openalex publication_date 2007/05/22 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We have considered the persistence of unvisited sites of a lattice, i.e., the probability S ( t ) that a site remains unvisited till time t in the presence of mutually repulsive random walkers in one dimension. The dynamics of this system has direct correspondence to that of the domain walls in a certain system of Ising spins where the number of domain walls becomes fixed following a zero-temperature quench. Here we get the result that S ( t ) ∝ exp(−α t β ) where β is close to 0.5 and α a function of the density of the walkers ρ. The fraction of persistent sites in the presence of independent walkers of density ρ' is known to be . We show that a mapping of the interacting walkers' problem to the independent walkers' problem is possible with ρ' = ρ/(1 − ρ) provided ρ' and ρ are small. We also discuss some other intricate results obtained in the interacting walkers' case.