The Sub-Geometric Phases in Density Matrix

TL;DR

This paper generalizes the concept of geometric phase in density matrices, unifying adiabatic and nonadiabatic cases, and explores their influence on physical observables, especially in mixed states.

Contribution

It introduces a unified expression for sub-geometric phases applicable to both adiabatic and nonadiabatic processes, linking them to Berry and Aharonov-Anandan phases.

Findings

Unified expression for sub-geometric phases derived.

Demonstrated influence of phases on physical observables.

Applied framework to geometric phase in mixed states.

Abstract

In this letter, the generalization of geometric phase in density matrix is presented, we show that the extended sub-geometric phase have unified expression whatever in adiabatic or nonadiabatic procedure, the relations between them and the usual Berry phase or Aharonov-Anandan phase are established. We also demonstrated the influence of sub-geometric phases on the physical observables. Finally, our treatment is naturally used to investigate the geometric phase in mixed state.