We present results concerning quantum dynamical and topological manifestations of "superweak chaos" (SWC) occurring under generic conditions in the Floquet "kicked Hall systems" (KHSs) [1]; these are periodically kicked charges in the presence of uniform magnetic (B) and electric (E) fields that are perpendicular to each other and to the kicking direction. For "resonance" values of B and E, with small kick strength κ, the classical KHS behaves as if this strength is effectively κ² rather than κ [2]; this is SWC. SWC in the KHSs emerges under much more generic conditions than in the E = 0 case [3,4]. The quantum manifestations above of SWC occur under the same generic conditions. First, for integer values of an effective Planck constant ρ, one has "quantum antiresonance" ("frozen" quantum dynamics) and flat quasienergy (QE) bands. Second, for small ρ (semiclassical regime), the quantum evolution of the kinetic-energy expectation value is relatively slow and exhibits a universal behavior. Third, for rational values of ρ, the QE spectrum consists of bands characterized by topological Chern integers satisfying a Diophantine equation analogous to the one for the quantum Hall effect [5] and for kicked Harper systems [6]. Then, under the classical SWC conditions, the quantum KHS is described by an effective Harper Hamiltonian with ρ replaced by ρ' = 2ρ. This explains the fact that the QE spectrum vs. ρ is approximately given by a "double" Hofstadter butterfly. Thus, the Chern integers are determined by the Diophantine equation with ρ' replacing ρ.

References:

[1] I.Dana and K. Kubo, to be published.

[2] M. Ben-Harush and I. Dana, Phys. Rev. E  93, 052207 (2016).

[3] I. Dana, Phys. Rev. Lett. 73, 1609 (1994).

[4] I. Dana and D.L. Dorofeev, Phys. Rev. E 72, 046205 (2005).

[5] D.J. Thouless, M. Kohmoto, M.P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982); I. Dana, Y. Avron, and J. Zak, J. Phys. 18, L679 (1985); I. Dana and J. Zak, Phys. Rev. B 32, 3612 (1985), and references therein.

[6] I. Dana, Phys. Rev. E 52, 466 (1995).