Different types of spatial correlation functions for non-ergodic stochastic processes of macroscopic systems - Archive ouverte HAL
Article Dans Une Revue European Physical Journal E: Soft matter and biological physics Année : 2022

Different types of spatial correlation functions for non-ergodic stochastic processes of macroscopic systems

Joachim Wittmer
Alexander Semenov
Jörg Baschnagel

Résumé

Focusing on non-ergodic macroscopic systems we reconsider the variances δO 2 of time averages O[x] of time-series x. The total variance δO 2 tot = δO 2 int + δO 2 ext (direct average over all time-series) is known to be the sum of an internal variance δO 2 int (fluctuations within the meta-basins) and an external variance δO 2 ext (fluctuations between meta-basins). It is shown that whenever O[x] can be expressed as a volume average of a local field Or the three variances can be written as volume averages of correlation functions Ctot(r), Cint(r) and Cext(r) with Ctot(r) = Cint(r) + Cext(r). The dependences of the δO 2 on the sampling time ∆τ and the system volume V can thus be traced back to Cint(r) and Cext(r). Various relations are illustrated using lattice spring models with spatially correlated spring constants.
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Dates et versions

hal-03786941 , version 1 (23-09-2022)

Identifiants

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Joachim Wittmer, Alexander Semenov, Jörg Baschnagel. Different types of spatial correlation functions for non-ergodic stochastic processes of macroscopic systems. European Physical Journal E: Soft matter and biological physics, 2022, 45 (8), pp.65. ⟨10.1140/epje/s10189-022-00222-1⟩. ⟨hal-03786941⟩
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