论文标题
关于非线性系统中AB相的量化
On the quantization of AB phase in nonlinear systems
论文作者
论文摘要
在平均场水平上的非线性可以诱导动量空间中的自我交接能带结构，而所谓的非线性狄拉克锥是一个有趣的结果。使用Qi-wu-zhang模型加功率定律的非线性，我们在本文中系统地研究了与动量空间中与绝热过程相关的Aharonov-Bohm（AB）阶段，两个绝热路径围绕一个非线性dirac锥圆圈圆圈。有趣的是，对于仅对于Kerr非线性而言，AB阶段在关键的非线性下会出现$π$的跳跃，在该非线性中，狄拉克锥出现或消失了，而对于所有其他非线性的其他力量，AB阶段总是会随着非线性强度而持续变化。我们的结果可能对于幂律非线性的实验测量可能很有用，并应激发在非线性系统中几何阶段和绝热方面的进一步基本兴趣。
Self-intersecting energy band structures in momentum space can be induced by nonlinearity at the mean-field level, with the so-called nonlinear Dirac cones as one intriguing consequence. Using the Qi-Wu-Zhang model plus power law nonlinearity, we systematically study in this paper the Aharonov-Bohm (AB) phase associated with an adiabatic process in the momentum space, with two adiabatic paths circling around one nonlinear Dirac cone. Interestingly, for and only for Kerr nonlinearity, the AB phase experiences a jump of $π$ at the critical nonlinearity at which the Dirac cone appears or disappears, whereas for all other powers of nonlinearity the AB phase always changes continuously with the nonlinear strength. Our results may be useful for experimental measurement of power-law nonlinearity and shall motivate further fundamental interest in aspects of geometric phase and adiabatic following in nonlinear systems.
