Journal
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
Volume -, Issue -, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/aab84f
Keywords
active matter; Brownian motion; diffusion
Categories
Funding
- S N Bhatt Memorial Excellence Fellowship Program at ICTS (DST, Government of India)
- INSPIRE-SHE (DST, Government of India)
- Max Planck partner group at ICTS
- Indo-French Centre for the promotion of advanced research (IFCPAR) [5604-2]
- large deviation theory program at ICTS [ICTS/Prog-ldt/2017/8]
- Simon foundation grant from ICTS
- Department of Biotechnology, India, through a Ramalingaswami reentry fellowship
- Max Planck Society
- Department of Science and Technology, India, through a Max Planck Partner Group at ICTS-TIFR
- National Science Foundation [DMR16-08211, DMR-1623243]
- ICTS for supporting his participation in the Bangalore school on statistical physics - VIII [ICTS/Prog-bssp/2017/06]
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [1608211] Funding Source: National Science Foundation
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We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite domain, this probability distribution approaches a Gaussian form in the long-time limit, as in the case of a regular Brownian particle. At intermediate times, this distribution exhibits unexpected multi-modal forms. In a finite domain, the probability distribution reaches a steady-state form with peaks at the boundaries, in contrast to a Brownian particle. We also study the relaxation to the steady-state analytically. Finally we compute the survival probability of the RTP in a semi-infinite domain with an absorbing boundary condition at the origin. In the finite interval, we compute the exit probability and the associated exit times. We provide numerical verification of our analytical results.
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