Diffusion for ensembles of standard maps

Or Alus and Shmuel Fishman
Phys. Rev. E 92, 042904 – Published 2 October 2015

Abstract

Two types of random evolution processes are studied for ensembles of the standard map with driving parameter K that determines its degree of stochasticity. For one type of process the parameter K is chosen at random from a Gaussian distribution and is then kept fixed, while for the other type it varies from step to step. In addition, noise that can be arbitrarily weak is added. The ensemble average and the average over noise of the diffusion coefficient are calculated for both types of processes. These two types of processes are relevant for two types of experimental situations as explained in the paper. Both types of processes destroy fine details of the dynamics, and the second process is found to be more effective in destroying the fine details. We hope that this work is a step in the efforts for developing a statistical theory for systems with mixed phase space (regular in some parts and chaotic in other parts).

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  • Received 6 June 2015

DOI:https://doi.org/10.1103/PhysRevE.92.042904

©2015 American Physical Society

Authors & Affiliations

Or Alus* and Shmuel Fishman

  • Physics Department, Technion–Israel Institute of Technology, Haifa 32000, Israel

  • *oralus@tx.technion.ac.il
  • fishman@physics.technion.ac.il

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Issue

Vol. 92, Iss. 4 — October 2015

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