TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.14.6.165
TI  - Nonexistence of motility induced phase separation transition in one dimension
PY  - 2023/06/21
UR  - https://www.scipost.org/SciPostPhys.14.6.165
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 14
IS  - 6
SP  - 165
A1  - Mukherjee, Indranil
AU  - Raghu, Adarsh
AU  - Mohanty, Pradeep Kumar
AB  - We introduce and  study a model of hardcore particles  obeying  run-and-tumble dynamics  on a one-dimensional lattice, where  particles run  in  either $+$ve or $-$ve $x$-direction with   an effective speed $v$  and  tumble  (change their direction of  motion)  with  a constant rate $\omega$ when assisted by another particle  from right.   We show that the coarse-grained dynamics of the system  can be mapped  to a beads-in-urn  model called misanthrope process  where  particles  are identified as urns and vacancies as  beads  that hop to a neighbouring urn situated in the direction  opposite to the  current. The hop rate  is  same as  the magnitude of the  particle current; we calculate  it  analytically  for a two-particle system and show  that it  does  not satisfy  the  criteria   required  for a  phase separation  transition.  Nonexistence of phase separation in this model,  where  tumbling dynamics is  rather restricted, necessarily  imply that  motility  induced  phase separation transition  can not occur  in  other models  in  one dimension with unconditional tumbling.
ER  -

@Article{10.21468/SciPostPhys.14.6.165,
	title={{Nonexistence of motility induced phase separation transition in one dimension}},
	author={Indranil Mukherjee and Adarsh Raghu and Pradeep Kumar Mohanty},
	journal={SciPost Phys.},
	volume={14},
	pages={165},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.14.6.165},
	url={https://scipost.org/10.21468/SciPostPhys.14.6.165},
}