Approach to hyperuniformity of steady states of facilitated exclusion processes.

Autor: Goldstein S; Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, United States of America., Lebowitz JL; Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, United States of America., Speer ER; Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, United States of America.
Jazyk: angličtina
Zdroj: Journal of physics. Condensed matter : an Institute of Physics journal [J Phys Condens Matter] 2024 May 31; Vol. 36 (34). Date of Electronic Publication: 2024 May 31.
DOI: 10.1088/1361-648X/ad4b83
Abstrakt: We consider the fluctuations in the number of particles in a box of size L d inZd,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 density ρ , these systems approach, ast→∞, a 'frozen' state forρ⩽ρc, withρc=1/2for d  = 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 than L d . We give a general description of how the variances at different scales of L behave asρ↗ρc. On the largest scale,L≫L2, the fluctuations are normal (in fact the same as in the original product measure), while in a regionL1≪L≪L2, with both L 1 and L 2 going to infinity asρ↗ρc, the variance grows faster than normal. For1≪L≪L1the variance is the same as in the hyperuniform system. (All results discussed are rigorous for d  = 1 and based on simulations ford⩾2.).
(Creative Commons Attribution license.)
Databáze: MEDLINE
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