Resolving time-dependent quantum systems via the concatenated cranking procedure: Methods and applications

The concatenated cranking procedure (CCP) is exploited to resolve time-dependent quantum systems with different driving fields. We show that the scheme of CCP is able to achieve dynamical invariants for a couple of extended spin-12 models, by which the inconsistency of quantitative condition in the adiabatic theorem can be manifested conveniently. Furthermore, we propose a sectioned CCP scheme and apply it to resolve the time evolution for a modulated Landau–Zener model which cannot guarantee the convergency of the CCP in an overall evolution.

► We study time-dependent quantum systems by the concatenated cranking approach.
► Dynamical invariants of a couple of extended spin-half models are derived.
► Inconsistency of the quantitative condition in the adiabatic theorem is manifested.
► We propose also a sectioned scheme to solve a modulated Landau–Zener model.