Quasi-localization dynamics in a Fibonacci quantum rotor

Abstract

The dynamics of a quantum kicked rotor(QKR), unlike that of its classical counterpart, is known to be non-ergodic. This is due to the emergence of a dynamically localized wave-function in the angular momentum space, courtesy of interference affects. In this work, we analyze the dynamics of a quantum rotor kicked with a binary Fibonacci sequence of two distinct drive amplitudes. While the dynamics at low drive frequencies is found to be diffusive, a long-lived pre-ergodic regime emerges in the other limit. The dynamics in this pre-ergodic regime mimics that of a regular QKR and can be associated with the onset of a dynamical quasi-localization. We establish that this peculiar behavior arises due to the presence of localized eigenstates of an approximately conserved effective Hamiltonian, which drives the evolution at Fibonacci instants. However, the effective Hamiltonian picture does not persist indefinitely and the dynamics eventually becomes ergodic after asymptotically long times.