The Non-Adiabatic Sub-Geometric Phase and Its Application on Quantum Transition

TL;DR

This paper extends the concept of geometric phase to non-adiabatic quantum transitions, revealing that both real and imaginary parts influence resonance behavior and state stability, with applications demonstrated in two quantum systems.

Contribution

It introduces the non-adiabatic sub-geometric phase and explores its effects on quantum transition, providing new insights into phase influence beyond adiabatic conditions.

Findings

Imaginary part of sub-geometric phase affects resonance peaks.

Real part determines initial state stability.

Both parts influence quantum transition in example systems.

Abstract

Based on the adiabatic geometric phase concerning with density matrix[1] , we extend it to the sub-geometric phase in the non-adiabatic case. It is found that whatever the real part or imaginary part of the sub-geometric phase can play an important role in quantum transition. The imaginary part of sub-geometric phase can deviate the resonance peak in the quantum transition, which may bring modification on the level crossing, while the real part of sub-geometric phase will determine the stability of initial state according to the linear stability analysis theory, which can be regarded as somewhat complement on the selection rule of quantum transition. Finally, we illustrate them by two examples: one is the system with time-dependent perturbation, the other is a two-level system. It indicates that both the real and imaginary parts of sub-geometric phase have influence on quantum transition.