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Beyond the first recurrence in scar phenomena

Wisniacki1, Borondo, Vergini

  • 1Departamento de Quimica, C-IX, Universidad Autonoma de Madrid, Cantoblanco-28049, Madrid, Spain and Departamento de Fisica "J. J. Giambiagi," FCEN, UBA, Pabellon 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|January 4, 2001
PubMed
Summary

Long-term dynamics in chaotic systems are governed by a few key periodic orbits. Understanding their interplay reveals the scarring effect beyond initial recurrence times.

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Area of Science:

  • Physics
  • Quantum mechanics
  • Chaos theory

Background:

  • The scarring effect of short unstable periodic orbits is understood up to the first recurrence time.
  • Long-term dynamics and their controlling mechanisms beyond this limit remain less understood.

Purpose of the Study:

  • To investigate the long-term dynamical behavior of systems past the initial recurrence time.
  • To identify the key factors controlling dynamics at extended timescales.

Main Methods:

  • Analysis of the evolution of a dynamically averaged wave packet.
  • Focus on the interplay of short periodic orbits.

Main Results:

  • Dynamics at longer times are primarily controlled by a small set of related short periodic orbits.

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  • The interplay between these orbits dictates the system's long-term scarring effects.

    • Conclusions:

    • A limited number of periodic orbits govern the scarring effect in the long-term dynamics.
    • This finding offers a new perspective on understanding complex system behavior beyond short-time approximations.