Dresden 2009 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 22: Brownian motion and transport II
DY 22.9: Vortrag
Donnerstag, 26. März 2009, 12:30–12:45, ZEU 118
1/fβ Noise in Systems showing Weak Ergodicity Breaking — •Markus Niemann, Ivan Szendro, and Holger Kantz — Max-Planck-Institut für Physik komplexer Systeme, Dresden, Germany
Systems with weakly broken ergodicity are characterized by the property that the temporal average of an observable does not converge towards its mean value (the ensemble average) in the long time limit, although the phase space does not decompose into mutually inaccessible regions. This behavior is commonly found in systems with power law relaxation such that the relaxation time diverges to infinity. Here the weak ergodicity breaking expresses itself in the fact that the limit of the time average is described by a nontrivial probability distribution. Rebenshtok and Barkai introduced a stochastic model describing these features [PRL 99, 210601 (2007); J Stat Phys 133, 565 (2008)] using which they calculated the limit probability distributions of the time average.
By using a recently published method [PRE 78, 051104 (2008)] we determine the spectral properties of this model. We find analytically that the model shows 1/fβ noise, but similarly to the time average the spectrum does not converge to a fixed value but remains a probability distribution in the limit of the observation time going to infinity. Furthermore, the spectral values for different frequencies are only weakly correlated resulting in pronounced fluctuation around the 1/fβ behavior. We illustrate these analytical results by numerical simulations.