Berry's phase and Aharonov-Anandan's phase

Pierre-Louis Giscard

Jing‐Bo Xu, Tiezheng Qian, Gao Xiaochun

Some examples of a new kind of the Aharonov-Anandan phase which is of mechanical origin are studied. It is the non-adiabatic generalization of the mechanical Berry phase. We first study the periodic motion and then the interference effect. Finally we discuss the relation between Aharonov-Anandan phase and Berry phase.

许晶波, 高隽, 高孝纯

Ⅰ. INTRODUCTION Since Berry’s discovery of the geometric phase in quantum adiabatic evolution, there has been increased interest in this holonomy phenomenon referred to as Berry phase. Aharonov and Anandan removed the adiabatic condition and studied the geometric phase (AA phase) for any cyclic evolution. AA phase and Berry phase have been verified in experi

Xiao-Gang He, Bruce H. J. McKellar

R. H. Silsbee

Mai-Lin Liang, Shun-Lin Shu, Bing Yuan

Aharonov–Anandan (AA) phases for two coupled spins in a rotating magnetic field are obtained. The conditions for the adiabatic limit are also derived. It is found that if the rotating field is confined to a plane and the total spin is an integer, the adiabatic phase or the Berry phase will be zero, but the AA phase will not. Unlike adiabatic evolution, the AA phase is not the sum of geometric phases for the subsystems.