Mathematical Physics Seminar

 

 

 

Classical “kicked Hall systems”(KHSs), i.e., periodically kicked charges in the presence of uniform magnetic and electric fields that are perpendicular to each other and to the kicking direction, have been introduced and studied recently [M. Ben-Harush and I. Dana, Phys. Rev. E 93, 052207 (2016)]. It was shown that KHSs exhibit, under generic conditions, the phenomenon of “superweak chaos”(SWC), i.e., for small kick strength $\kappa$, a KHS behaves as if this strength were effectively $\kappa^2$ rather than $\kappa$.

 

Here we investigate several quantum manifestations of this generic SWC [I. Dana and K. Kubo, unpublished]. We first derive general expressions for quantum effective Hamiltonians for the KHSs. We then show that the phenomenon of quantum antiresonance (QAR), i.e., “frozen” quantum dynamics with flat quasienergy (QE) bands, takes place for integer values of a scaled Planck constant $\hbar_s$ and for a generic family of periodic kicking potentials. The vicinity of QAR is shown to correspond semiclassically to SWC.

 

In the case of standard (cosine) potentials, SWC is manifested by the fact that the QE spectrum as function of $\hbar_s$, at fixed small value of $\kappa/\hbar_s$, is approximately given by a “double” Hofstadter butterfly. The latter has topological properties basically different from those of the ordinary Hofstadter butterfly.

 

Also, for standard potentials and for small $\hbar_s$ (semiclassical regime), the evolution of the kinetic-energy expectation value exhibits a relatively slow quantum-diffusive behavior having universal features, as predicted by the effective Hamiltonian. All these quantum manifestations of SWC in KHSs occur under conditions much more generic than in other systems.