Anomalous Relaxation Processes in Two-state Systems

Authors Yu.S. Bystrik , L.A. Denisova

Sumy State University, 2, Rimsky Korsakov St., 40007 Sumy, Ukraine

Issue Volume 7, Year 2015, Number 3
Dates Received 05 August 2015; published online 20 October 2015
Citation Yu.S. Bystrik, L.A. Denisova, J. Nano- Electron. Phys. 7 No 3, 03049 (2015)
PACS Number(s) 05.40.Fb, 02.50.Ey, 76.20. + q
Keywords Anomalous relaxation, Dichotomous process, Heavy / superheavy probability densities.
Annotation In this paper the biased relaxation processes in the two-state systems whose structural elements evolve in accordance with the dichotomous random process are investigated. Using the continuous-time random walk approach we obtain the integral equation whose solution is the relaxation function and show that relaxation in these systems demonstrates the memory effects. Also our attention is paid to studying the long-time behavior of the relaxation laws in the case when probability densities of the waiting times in the up and down states of system have heavy and / or superheavy tails. From the asymptotic results it follows that the relaxation of these systems to the certain equilibrium state may occur in an anomalously slow way. Finally, we perform numerical calculations that confirm our theoretical predictions.

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