1996/01/04 by Cécile Monthus, Jean‐Philippe Bouchaud, Jean-Philippe Bouchaud · 11 citations
Materials Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Condensed matter physics #Diffusion #Ergodic theory #Exponential decay #Exponential function #Exponential growth #Fick's laws of diffusion #Lattice (music) #Material Dynamics and Properties #Mathematical analysis #Mathematics #Phase transition #Phenomenology (philosophy) #Physics #Quantum mechanics #Relaxation (psychology) #Statistical physics #Theoretical and Computational Physics #Thermodynamics #cond-mat
paper · pdf · doi:10.1088/0305-4470/29/14/012
published as J. Phys. A 29 (1996) 3847 · 35 pages, 2 figures (not included). The two figures are available upon request
arxiv created 1996/01/04 · openalex publication_date 1996/07/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study various models of independent particles hopping between energy `traps' with a density of energy barriers , on a d-dimensional lattice or on a fully connected lattice. If decays exponentially, a true dynamical phase transition between a high-temperature `liquid' phase and a low-temperature `aging' phase occurs. More generally, however, one expects that for a large class of , `interrupted' aging effects appear at low enough temperatures, with an ergodic time growing faster than exponentially. The relaxation functions exhibit a characteristic shoulder, which can be fitted as stretched exponentials. A simple way of introducing interactions between the particles leads to a modified model with an effective diffusion constant in energy space, which we discuss in detail.