Geometric Phases in Nonlinear Quantum Systems

Jie Liu, Sheng-Chang Li, Libin Fu +1 more

Biao Wu, Jie Liu, Qian Niu

The concept of a geometric phase (Berry's phase) is generalized to the case of noneigenstates, which is applicable to both linear and nonlinear quantum systems. This is particularly important to nonlinear quantum systems, where, due to the lack of the superposition principle, the adiabatic evolution of a general state cannot be described in terms of eigenstates. For linear quantum systems, our new geometric phase reduces to a statistical average of Berry's phases. Our results are demonstrated with a nonlinear two-level model.

Arno Böhm, Ali Mostafazadeh, Hiroyasu Koizumi +2 more

Wang Kaige, Jian Wang, Yang Guojian

We apply the geometric phase theory to the dissipative system of a set of nonlinear coupled oscillators. We found an area theorem for the geometric phase, which provides a direct and simple geometric method for observing the geometric phase of this system. The area theorem shows evidence that the geometric phase is related to certain dynamical features of the systems.

At Wien

Lou Ben-zhuo

The background and evolvement of phase problem in quantum mechanics is overviewed.Berry phase which was brought up originally by Berry M.V.for adiabatic evolution in linear systems is limited in practical applications.Berry phase is generalized to nonadiabatic evolution(AA phase),noncyclic quantum evolution(off-diagonal geometric phase)and nonlinear systems(geometric phase of general quantum states).It is pointed out that the off-diagonal geometric phase in nonlinear system is a new area for research.The prospect of this subject is viewed as well.