Approach to hyperuniformity of steady states of facilitated exclusion processes.
J Phys Condens Matter
; 36(34)2024 May 31.
Article
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| ID: mdl-38744303
ABSTRACT
We consider the fluctuations in the number of particles in a box of sizeLdinZd,d⩾1, in the (infinite volume) translation invariant stationary states of the facilitated exclusion process, also called the conserved lattice gas model. When started in a Bernoulli (product) measure at densityρ, these systems approach, astâ∞, a 'frozen' state forρ⩽ρc, withρc=1/2ford = 1 andρc<1/2ford⩾2. Atρ=ρcthe limiting state is, as observed by Hexner and Levine, hyperuniform, that is, the variance of the number of particles in the box grows slower thanLd. We give a general description of how the variances at different scales ofLbehave asρâρc. On the largest scale,Lâ«L2, the fluctuations are normal (in fact the same as in the original product measure), while in a regionL1âªLâªL2, with bothL1andL2going to infinity asρâρc, the variance grows faster than normal. For1âªLâªL1the variance is the same as in the hyperuniform system. (All results discussed are rigorous ford = 1 and based on simulations ford⩾2.).
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MEDLINE
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En
Revista:
J Phys Condens Matter
Asunto de la revista:
BIOFISICA
Año:
2024
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Article
País de afiliación:
Estados Unidos