Berry phase for a nondegenerate three-level quantum system

I. V. Bukanov, E. A. Tolkachev, A. Ya. Tregubovich

Mai-Lin Liang, Zongcheng Xu, Bing Yuan

Diana Monteoliva, H. J. Korsch, J A Nunez

A formalism is developed for calculating Berry phases for nonadiabatic time-periodic quantum systems when a dynamical invariant is known. It is found that, when the invariant is periodic and has a nondegenerate spectrum, this method allows a convenient way to obtain generalized Berry phases and the proper cyclic initial states. The method is applied to the generalized harmonic oscillator and the two-level system, where the invariant operators are explicitly constructed. Formulae for the conventional Berry's phases are readily obtained by taking the adiabatic limit of the exact results.

R. R. Aldinger, A. B�hm, Mark E. Loewe

M. A. Alves, M. T. Thomaz

We study the evolution of a quantum system under adiabatic conditions using the path integral formulation. We obtain the Berry phase for systems with nondegenerate and degenerate energy spectra and recover well-known results. We also present a simple derivation of the adiabatic theorem.

Holger Lyre