双孤子非线性干涉中的狄拉克磁单极势

Dirac magnetic monopoles potential in the nonlinear double-soliton interference

本文深入研究了孤子干涉过程中的相位演化特性及其背后的拓扑矢势.基于一维非线性薛定谔方程的双孤子解,发现波函数密度零点广泛存在于拓展的复平面内,并且每一个密度零点对应狄拉克磁单极的矢势场.矢势场是由周期排布的具有相反磁荷的狄拉克磁单极对组成.通过观察磁单极子的运动,可以方便地理解干涉过程中的相位演化特征.特别发现,一对正负磁单极对在实轴上的碰撞恰好对应波函数相位在节点处的π跃变.此外,还对比讨论了线性波包干涉动力学中的狄拉克磁单极.结果表明狄拉克磁单极势广泛存在于波场的干涉现象之中,并且磁单极在拓展的复平面内分布特征可用于区分线性干涉和非线性干涉过程背后的拓扑性质.

In this paper,we deeply investigate the phase evolution and the underlying topological vector potential in the nonlinear interference of solitons.Based on the double-soliton solution of 1D nonlinear Schrödinger equation,we find that the density zeros of wave function generally exist in the extended complex space,each density zero corresponds to the vector potential produced by Dirac magnetic monopole.The vector potential field is composed of periodically distributed Dirac magnetic monopole pairs with opposite magnetic charges.By observing the motion of magnetic monopoles,we can conveniently understand the phase evolution characteristics during the interference process.In particular,we find that the collision of a pair of magnetic monopoles with opposite charge on the real axis corresponds exactly to the ±π jump of the wave function phase at nodes.For comparison,we also discuss Dirac magnetic monopoles and vector potential field in linear wave packet interference case.The results show that the Dirac magnetic monopole potential widely exists in the interference phenomena of wave fields,and the distribution of magnetic monopoles in the extended complex space can be used to distinguish the topological properties behind the linear and nonlinear interference process.