Symmetry-breaking in local Lyapunov exponents

  • R. Ramaswamy


Integrable dynamical systems, namely those having as many independent conserved quantities as freedoms, have all Lyapunov exponents equal to zero. Locally, the instantaneous or finite time Lyapunov exponents are nonzero, but owing to a symmetry, their global averages vanish. When the system becomes nonintegrable, this symmetry is broken. A parallel to this phenomenon occurs in mappings which derive from quasiperiodic Schrödinger problems in 1-dimension. For values of the energy such that the eigenstate is extended, the Lyapunov exponent is zero, while if the eigenstate is localized, the Lyapunov exponent becomes negative. This occurs by a breaking of the quasiperiodic symmetry of local Lyapunov exponents, and corresponds to a breaking of a symmetry of the wavefunction in extended and critical states.

PACS. 05.45.-a Nonlinear dynamics and nonlinear dynamical systems – 05.45.Pq Numerical simulations of chaotic models – 71.30.+h Metal-insulator transitions and other electronic transitions 


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Copyright information

© EDP Sciences, Springer-Verlag 2002

Authors and Affiliations

  • R. Ramaswamy
    • 1
  1. 1.School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067, IndiaIN

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