A new approach to calculating the Berry phase

Wolfgang Bulla, P. Falkensteiner, Harald Grosse

D Moore

Xuele Liu, G. S. Agarwal

Mikhail Orionovich Katanaev

Yang Zhi-An

In this paper, we have investigated the off-diagonal Berry phase of nonlinear systems and presented its explicit expression. The results show that, for nonlinear systems, the off-diagonal berry phase contains a new term in addition to the dynamical phase, the geometric phase and the nonlinear phase. This new term can describe a cross effect between the Bogoliubov excitation around one eigenstate and another instantaneous eigenstate, while the Bogoliubov excitations are found to be accumulated during the adiabatic evolution and contribute a finite phase of geometric nature. As an application, the off-diagonal Berry phase of a two-well trapped Bose-Einstein condensate system is calculated.

Yian Lei, J. Y. Zeng

The nonadiabatic Berry phases in the magnetic resonance under various initial conditions are investigated and compared with the adiabatic Berry phase. The general formalism for calculating the nonadiabatic Berry phase of a two-state system in terms of the expansion of instantaneous energy eigenstates is presented. Some numerical calculations and discussions are made. The Berry phase of a two-statesystem under an impulsive interaction is addressed.