TY - JOUR
T1 - From stretched exponential to inverse power-law
T2 - Fractional dynamics, Cole-Cole relaxation processes, and beyond
AU - Metzler, Ralf
AU - Klafter, Joseph
N1 - Funding Information:
We acknowledge financial assistance from the TMR programme of the European Commission. RM was supported through a fellowship from the Deutsche Forschungsgemeinschaft (DFG) within the Emmy Noether programme.
PY - 2002/7
Y1 - 2002/7
N2 - We present a generalisation of the classical exponential relaxation based on the fractional Fokker-Planck equation framework. We show how fractional dynamics modifies the Brownian dynamics underlying standard relaxation processes, and gives rise to the Mittag-Leffler relaxation of modes and moments. The latter is characterised through a turnover from an initial stretched exponential to a final inverse power-law pattern and the associated complex susceptibility corresponds to the Cole-Cole pattern.
AB - We present a generalisation of the classical exponential relaxation based on the fractional Fokker-Planck equation framework. We show how fractional dynamics modifies the Brownian dynamics underlying standard relaxation processes, and gives rise to the Mittag-Leffler relaxation of modes and moments. The latter is characterised through a turnover from an initial stretched exponential to a final inverse power-law pattern and the associated complex susceptibility corresponds to the Cole-Cole pattern.
UR - http://www.scopus.com/inward/record.url?scp=0036642719&partnerID=8YFLogxK
U2 - 10.1016/S0022-3093(02)01124-9
DO - 10.1016/S0022-3093(02)01124-9
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AN - SCOPUS:0036642719
VL - 305
SP - 81
EP - 87
JO - Journal of Non-Crystalline Solids
JF - Journal of Non-Crystalline Solids
SN - 0022-3093
IS - 1-3
ER -