2004/01/22 by David S. Dean, D. S. Dean, Alexandre Lefèvre +1 · 17 citations
Materials Science · Physics and Astronomy · #Anomalous diffusion #Constant (computer programming) #Diffusion #Fick's laws of diffusion #Langevin dynamics #Langevin equation #Material Dynamics and Properties #Mathematical physics #NMR spectroscopy and applications #Perturbation theory (quantum mechanics) #Physics #Quantum mechanics #Renormalization #Renormalization group #Statistical physics #Theoretical and Computational Physics #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.69.061111
published in Physical Review E 69(6), 061111 (American Physical Society) · 12 pages, 8 figures .eps
arxiv created 2004/01/22 · openalex publication_date 2004/06/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The behavior of the self-diffusion constant of Langevin particles interacting via a pairwise interaction is considered. The diffusion constant is calculated approximately within a perturbation theory in the potential strength about the bare diffusion constant. It is shown how this expansion leads to a systematic double expansion in the inverse temperature beta and the particle density rho. The one-loop diagrams in this expansion can be summed exactly and we show that this result is exact in the limit of small beta and rhobeta constants. The one-loop result can also be resummed using a semiphenomenological renormalization group method which has proved useful in the study of diffusion in random media. In certain cases the renormalization group calculation predicts the existence of a diverging relaxation time signaled by the vanishing of the diffusion constant, possible forms of divergence coming from this approximation are discussed. Finally, at a more quantitative level, the results are compared with numerical simulations, in two dimensions, of particles interacting via a soft potential recently used to model the interaction between coiled polymers.