Phase separation and disorder

 Interacting active particles (with or without attraction) can undergo

Motility Induced Phase separation (MIPS) M.E. Cates & J. Tailleur, Ann. Rev. Cond. Mat. 6, 219 (2015)

         

yellow ball Higher densities slow movement; density increases in regions of slow movement

instability and phase separation (ala jammed bumper cars!)

  What happens to this phase transition if active particles move on a random (short-range correlated, bounded) landscape?

yellow ball Simulations find that MIPS is destroyed by disorder: Sunghan Ro, Y. Kafri, M. Kardar, J. Tailleur, Phys. Rev. Lett. 126, 048003 (2021)

Quench with no disorder:

Quench with bulk disorder:

yellow ball Turning on bulk disorder in a phase separated state:

yellow ball Turning off bulk disorder:                                     

  Analogy from equilibrium: What happens to ordered magnets in the presence of (quaenched) random magnetic fields?

yellow ball Imry-Ma: Consider stability of an ordered domain of size  R  to flip to the oppositely ordered state;

The ordered phase is unstable to random field induced flips of large enough domains for

  MIPS: For non-interacting active particles, density variations are similar to those expected for an equilibrium system

in response to a spatially varying potential (magnetic field) with long-range correlations:

yellow ball   Comparison to   

suggests the following analogy to an equilibrium phase separating mixture:

Adapting the Imry-Ma argument to the long-range correlated random fields yields

The (MIPS) ordered phase is unstable to random pump induced flips at large enough scales for