2008/01/26 by Masaharu Isobe · 2 citations
Materials Science · Mathematics · Physics and Astronomy · #Autocorrelation #Combinatorics #Dimension (graph theory) #Divergence (linguistics) #Event (particle physics) #Exponent #Function (biology) #Limit (mathematics) #Logarithm #Material Dynamics and Properties #Mathematical analysis #Mathematical physics #Mathematics #Physics #Power function #Quantum mechanics #Quantum, superfluid, helium dynamics #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.77.021201
published as Phys. Rev. E 77, 021201 (2008) · 5 pages, 5 figures, to appear in Phys. Rev. E
arxiv created 2008/01/26 · openalex publication_date 2008/02/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Alder and Wainwright discovered the slow power decay ~t(-d/2) (d is dimension) of the velocity autocorrelation function in moderately dense hard-sphere fluids using the event-driven molecular dynamics simulations. In the two-dimensional (2D) case, the diffusion coefficient derived using the time correlation expression in linear response theory shows logarithmic divergence, which is called the "2D long-time-tail problem." We reexamined this problem to perform a large-scale, long-time simulation with 1x10(6) hard disks using a modern efficient algorithm and found that the decay of the long tail in moderately dense fluids is slightly faster than the power decay (~1/t) . We also compared our numerical data with the prediction of the self-consistent mode-coupling theory in the long-time limit [~1/(t sqrt[ln t])] .