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Mixing, ergodicity and slow relaxation phenomena

Author

Listed:
  • Costa, I.V.L.
  • Vainstein, M.H.
  • Lapas, L.C.
  • Batista, A.A.
  • Oliveira, F.A.

Abstract

Investigations on diffusion in systems with memory [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] have established a hierarchical connection between mixing, ergodicity, and the fluctuation–dissipation theorem (FDT). This hierarchy means that ergodicity is a necessary condition for the validity of the FDT, and mixing is a necessary condition for ergodicity. In this work, we compare those results with recent investigations using the Lee recurrence relations method [M.H. Lee, Phys. Rev. B 26 (1982) 2547; M.H. Lee, Phys. Rev. Lett. 87 (2001) 250601; M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. Lee shows that ergodicity is violated in the dynamics of the electron gas [M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. This reinforces both works and implies that the results of [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] are more general than the framework in which they were obtained. Some applications to slow relaxation phenomena are discussed.

Suggested Citation

  • Costa, I.V.L. & Vainstein, M.H. & Lapas, L.C. & Batista, A.A. & Oliveira, F.A., 2006. "Mixing, ergodicity and slow relaxation phenomena," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(1), pages 130-134.
    • Handle: RePEc:eee:phsmap:v:371:y:2006:i:1:p:130-134
    DOI: 10.1016/j.physa.2006.04.096
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    Cited by:

    1. Petrus H. R. Anjos & Fernando A. Oliveira & David L. Azevedo, 2024. "Fractality in resistive circuits: the Fibonacci resistor networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(8), pages 1-10, August.

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