摘要:
研究了非线性系统中非对角情况的Berry相位,给出了非线性非对角Berry相位的计算公式.结果表明,在非线性非对角情况下,总相位包含有动力学相位,通常意义的Berry相位,以及非线性引起的附加相位.此外,还包含有非对角情况时所特有的新的附加项.这新的一项表示,当系统哈密顿慢变时产生的Bogoliubov涨落,与另一个瞬时本征态之间的交叉效应,进而对总的Berry相位产生影响.作为应用,对二能级玻色爱因斯坦凝聚体系,具体计算了非线性非对角的Berry相位.
Abstract:
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.
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