Diffusion coefficient of piecewise linear maps

Chia Chu Chen

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

By using the cycle expansion, we obtain general expressions for the determination of the diffusion coefficient D of a piecewise linear map which is parametrized by k and h (where the map contains 2k+5 branches of line segment, and h is the height of the shortest line). By restricting h=β/m [β=1,...,(k+1)/2; m is the slope of the map], a closed form expression of D can be obtained and some of its consequences are discussed. The limiting form of D (k→) is then shown to be k2. For the simplest case with k=1, we also show that more exact results can be found. A limiting case with h→0 is discussed where agreement with the result obtained from the invariant measure approach is established.

Original languageEnglish
Pages (from-to)2815-2822
Number of pages8
JournalPhysical Review E
Volume51
Issue number4
DOIs
Publication statusPublished - 1995 Jan 1

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Physics and Astronomy(all)

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