https://doi.org/10.1140/epjb/s10051-022-00339-4
Regular Article - Mesoscopic and Nanoscale Systems
Statistics of Floquet quasienergy spectrum for one-dimensional periodic, Fibonacci quasiperiodic and random discrete-time quantum walks
1
College of science and New energy technology Engineering of Jiangsu province, Nanjing University of Posts and Telecommunications, 210003, Nanjing, China
2
Institute of Signal Processing and Transmission, Nanjing University of Posts and Telecommunications, 210003, Nanjing, China
Received:
6
February
2022
Accepted:
22
April
2022
Published online:
6
May
2022
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.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2022
