# Anomalous dynamical evolution and nonadiabatic level crossing in exactly solvable time-dependent quantum systems

## TL;DR

This paper investigates anomalous dynamical behavior and nonadiabatic level crossing in exactly solvable time-dependent quantum systems, revealing unique evolution patterns and proposing new quantum control protocols.

## Contribution

It introduces a reverse-engineering approach to analyze anomalous dynamics and designs driven models with novel state evolution behaviors.

## Key findings

- Opposite evolution of adiabatic and nonadiabatic states.
- Nonadiabatic level crossing occurs at perpendicular vectors in parameter space.
- New protocols for quantum state control based on anomalous dynamics.

## Abstract

The anomalous dynamical evolution and the crossing of nonadiabatic energy levels are investigated for exactly solvable time-dependent quantum systems through a reverse-engineering scheme. By exploiting a typical driven model, we elucidate the peculiarities of its dynamics with anomalous behavior: the evolution of the adiabatic states and of the nonadiabatic ones exhibits opposite behavior with their representative vectors evolving from a parallel state to an antiparallel state: the nonadiabatic level crossing is identified as a necessary consequence since the crossing point corresponds exactly to the perpendicular point of the two vectors in the parametric space. In the light of these results, we show that various driven models with anomalous dynamical evolution can be designed and they offer alternative protocols for the quantum state control.