Spectral characterization of aging: The REM-like trap model

• 成果类型: Article
• 署名作者: Bovier, A; Faggionato, A
• 署名单位: Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technical University of Berlin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000359
• 发表日期: 2005
• 页码: 1997-2037
• 关键词: random energy-model; glauber dynamics

摘要

We review the aging phenomenon in the context of the simplest trap model, Bouchaud's REM-like trap model, from a spectral theoretic point of view. We show that the generator of the dynamics of this model can be diagonalized exactly. Using this result, we derive closed expressions for correlation functions in terms of complex contour integrals that permit an easy investigation into their large time asymptotics in the thermodynamic limit. We also give a grand canonical representation of the model in terms of the Markov process on a Poisson point process. In this context we analyze the dynamics on various time scales.