Topological Properties of Adiabatically Varied Nonintegrable Systems

  Guy Amit  ,  Itzhack Dana  
Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel

The topological characterization of band spectra by Chern integers was introduced by Thouless, Kohmoto, Nightingale, and den Nijs (TKNN) [1] to explain the quantum Hall effect in a 2D periodic potential. The TKNN integers, giving the Hall conductances, satisfy a Diophantine equation (DE) which was later shown [2] to be a general consequence of magnetic (phase-space) translational invariance and to have several implications [3]. The topological characterization was subsequently extended to quasienergy (QE) band spectra of classically nonintegrable Floquet (time-periodic) systems with phase-space translational invariance [4-6] and a DE was derived also for these systems [5]. More recently, topological properties of Floquet systems have attracted much attention (see, e.g., Refs. [7-11]). Chern integers were associated with the QE bands of nonintegrable double kicked rotors depending periodically on an external parameter [9,10]; an exact quantitative meaning of these integers was given in terms of adiabatic transport in momentum space when the external parameter is slowly varied [9]. In this work, we show that the adiabatically varied double kicked rotors exhibit phase-space translational invariance which allows to derive a DE for the Chern integers, involving both classical and quantum parameters [12].

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[12] I. Dana, to be published.