Approach to Hyperuniformity of Steady States of Facilitated Exchange Processes
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916110073331712 |
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| author | Goldstein, S. Lebowitz, J. L. Speer, E. R. |
| author_facet | Goldstein, S. Lebowitz, J. L. Speer, E. R. |
| contents | We consider the fluctuations in the number of particles in a box of size L^d in Z^d, 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 rho, these systems approach, as t goes to infinity, a "frozen" state for rho<=rho_c, with rho_c=1/2 for d=1 and rho_c<1/2 for d>=2. At rho=rho_c the limiting state is 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 as rho increases to rho_c. On the largest scale, L>>L_2, the fluctuations are normal (in fact the same as in the original product measure), while in a region L_1<<L<<L_2, with both L_1 and L_2 going to infinity as rho increases to rho_c, the variance grows faster than normal. For 1<<L<<L_1 the variance is the same as in the hyperuniform system. (All results discussed are rigorous for d=1 and based on simulations for d>=2.) |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16505 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approach to Hyperuniformity of Steady States of Facilitated Exchange Processes Goldstein, S. Lebowitz, J. L. Speer, E. R. Statistical Mechanics We consider the fluctuations in the number of particles in a box of size L^d in Z^d, 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 rho, these systems approach, as t goes to infinity, a "frozen" state for rho<=rho_c, with rho_c=1/2 for d=1 and rho_c<1/2 for d>=2. At rho=rho_c the limiting state is 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 as rho increases to rho_c. On the largest scale, L>>L_2, the fluctuations are normal (in fact the same as in the original product measure), while in a region L_1<<L<<L_2, with both L_1 and L_2 going to infinity as rho increases to rho_c, the variance grows faster than normal. For 1<<L<<L_1 the variance is the same as in the hyperuniform system. (All results discussed are rigorous for d=1 and based on simulations for d>=2.) |
| title | Approach to Hyperuniformity of Steady States of Facilitated Exchange Processes |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2401.16505 |