Symmetry-breaking in local Lyapunov exponents |
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Authors: | R Ramaswamy |
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Institution: | (1) School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067, India, IN |
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Abstract: | 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 Schr?dinger 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.
Received 25 October 2001 / Received in final form 8 December 2001 Published online 2 October 2002
RID="a"
ID="a"e-mail: r.ramaswamy@mail.jnu.ac.in |
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Keywords: | 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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