Statistics of Floquet quasienergy spectrum for one-dimensional periodic, Fibonacci quasiperiodic and random discrete-time quantum walks

Discrete-time quantum walks are Floquet systems if the quantum walk operator is independent of time. We consider such one-dimensional quantum walks with two quantum coin operators arranged in discrete space according to periodic, Fibonacci quasiperiodic and random sequences. We explore the correlation dimension of Floquet quasienergy spectrum, Floquet level spacing ratio and inverse participation ratio of Floquet states, respectively. We find they increase with spreading exponent and surviving exponent, so the statistics of Floquet quasienergy is an effective quantity to reflect dynamical properties in quantum transport of discrete-time quantum walks. We also contrast the differences among the three kinds of quantum walks.