Berry's phase, density matrices and incompatible observables

K. Datta

L. Dąbrowski

Zheng-Chuan Wang

This study presents the generalization of geometric phases in density matrices. We show that the extended sub-geometric phase has an unified expression during the adiabatic or nonadiabatic process and establish the relations between them and the usual Berry or Aharonov-Anandan phases. We also demonstrate the influence of sub-geometric phases on the physical observables. Finally, the above treatment is used to investigate the geometric phase in a mixed state.

Mitchel Weissbluth

Takafumi Kita

Jochen Dittmann, Gerd Rudolph

A class of connections governing parallel transport along nondegenerate density matrices is discussed. These connections are given by certain analytic functions. We develop a calculus for operator-valued differential forms, which enables us to calculate the curvature of these connections. The class under consideration contains a non-Abelian generalization of Berry’s phase recently proposed by Uhlmann.