https://doi.org/10.1140/epjb/e2002-00313-8
Symmetry–breaking in local exponents
School of Physical Sciences, Jawaharlal Nehru
University, New Delhi 110 067, India
Corresponding author: a r.ramaswamy@mail.jnu.ac.in
Received:
25
October
2001
Revised:
8
December
2001
Published online:
2
October
2002
Integrable dynamical systems, namely those having as many independent conserved quantities as freedoms, have all exponents equal to zero. Locally, the instantaneous or finite time 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 exponent is zero, while if the eigenstate is localized, the exponent becomes negative. This occurs by a breaking of the quasiperiodic symmetry of local 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
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002
