2017/11/10 by Joachim Krug, Robert Axel Neiss, Robert A. Neiss +2 · 6 citations
Mathematics · Physics and Astronomy · #Anisotropy #Correlation function (quantum field theory) #Coupling (piping) #Exponent #Lattice (music) #Logarithm #Materials science #Mathematical analysis #Mathematics #Mode coupling #Physics #Quantum mechanics #Random Matrices and Applications #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1007/s10955-018-1995-z
published in Journal of Statistical Physics 172(2), 493-504 (Springer Science+Business Media) · 14 pages, 4 figures
arxiv created 2017/11/10 · openalex publication_date 2018/03/01 · arxiv updated 2018/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The spreading of density fluctuations in two-dimensional driven diffusive systems is marginally anomalous. Mode coupling theory predicts that the diffusivity in the direction of the drive diverges with time as (ln t)2/3 with a prefactor depending on the macroscopic current-density relation and the diffusion tensor of the fluctuating hydrodynamic field equation. Here we present the first numerical verification of this behavior for a particular version of the two-dimensional asymmetric exclusion process. Particles jump strictly asymmetrically along one of the lattice directions and symmetrically along the other, and an anisotropy parameter p governs the ratio between the two rates. Using a novel massively parallel coupling algorithm that strongly reduces the fluctuations in the numerical estimate of the two-point correlation function, we are able to accurately determine the exponent of the logarithmic correction. In addition, the variation of the prefactor with p provides a stringent test of mode coupling theory.